TSTP Solution File: GRP068-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:34:14 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 86
% Syntax : Number of clauses : 313 ( 163 unt; 0 nHn; 155 RR)
% Number of literals : 530 ( 529 equ; 223 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 565 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = Y ).
cnf(multiply,axiom,
multiply(X,Y) = divide(X,divide(identity,Y)) ).
cnf(inverse,axiom,
inverse(X) = divide(identity,X) ).
cnf(identity,axiom,
identity = divide(X,X) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ).
cnf(refute_0_0,plain,
identity = divide(inverse(X_3),inverse(X_3)),
inference(subst,[],[identity:[bind(X,$fot(inverse(X_3)))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( inverse(X) != divide(identity,X)
| divide(identity,X) = inverse(X) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(divide(identity,X)))]]) ).
cnf(refute_0_5,plain,
divide(identity,X) = inverse(X),
inference(resolve,[$cnf( $equal(inverse(X),divide(identity,X)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(identity,Y) = inverse(Y),
inference(subst,[],[refute_0_5:[bind(X,$fot(Y))]]) ).
cnf(refute_0_7,plain,
divide(X,divide(identity,Y)) = divide(X,divide(identity,Y)),
introduced(tautology,[refl,[$fot(divide(X,divide(identity,Y)))]]) ).
cnf(refute_0_8,plain,
( divide(X,divide(identity,Y)) != divide(X,divide(identity,Y))
| divide(identity,Y) != inverse(Y)
| divide(X,divide(identity,Y)) = divide(X,inverse(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X,divide(identity,Y)),divide(X,divide(identity,Y))) ),[1,1],$fot(inverse(Y))]]) ).
cnf(refute_0_9,plain,
( divide(identity,Y) != inverse(Y)
| divide(X,divide(identity,Y)) = divide(X,inverse(Y)) ),
inference(resolve,[$cnf( $equal(divide(X,divide(identity,Y)),divide(X,divide(identity,Y))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(X,divide(identity,Y)) = divide(X,inverse(Y)),
inference(resolve,[$cnf( $equal(divide(identity,Y),inverse(Y)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiply(X,Y) != divide(X,divide(identity,Y))
| divide(X,divide(identity,Y)) != divide(X,inverse(Y))
| multiply(X,Y) = divide(X,inverse(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,Y),divide(X,inverse(Y))) ),[0],$fot(divide(X,divide(identity,Y)))]]) ).
cnf(refute_0_12,plain,
( multiply(X,Y) != divide(X,divide(identity,Y))
| multiply(X,Y) = divide(X,inverse(Y)) ),
inference(resolve,[$cnf( $equal(divide(X,divide(identity,Y)),divide(X,inverse(Y))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(X,Y) = divide(X,inverse(Y)),
inference(resolve,[$cnf( $equal(multiply(X,Y),divide(X,divide(identity,Y))) )],[multiply,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(inverse(X_3),X_3) = divide(inverse(X_3),inverse(X_3)),
inference(subst,[],[refute_0_13:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_15,plain,
( multiply(inverse(X_3),X_3) != divide(inverse(X_3),inverse(X_3))
| divide(inverse(X_3),inverse(X_3)) = multiply(inverse(X_3),X_3) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(inverse(X_3),X_3))),bind(Y0,$fot(divide(inverse(X_3),inverse(X_3))))]]) ).
cnf(refute_0_16,plain,
divide(inverse(X_3),inverse(X_3)) = multiply(inverse(X_3),X_3),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),divide(inverse(X_3),inverse(X_3))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( divide(inverse(X_3),inverse(X_3)) != multiply(inverse(X_3),X_3)
| identity != divide(inverse(X_3),inverse(X_3))
| identity = multiply(inverse(X_3),X_3) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(inverse(X_3),inverse(X_3))) ),[1],$fot(multiply(inverse(X_3),X_3))]]) ).
cnf(refute_0_18,plain,
( identity != divide(inverse(X_3),inverse(X_3))
| identity = multiply(inverse(X_3),X_3) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_3),inverse(X_3)),multiply(inverse(X_3),X_3)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
identity = multiply(inverse(X_3),X_3),
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_3),inverse(X_3))) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( identity != multiply(inverse(X_3),X_3)
| multiply(inverse(X_3),X_3) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(inverse(X_3),X_3)))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_3),X_3) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(X_3),X_3)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(inverse(a1),a1) = identity,
inference(subst,[],[refute_0_21:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_23,plain,
( multiply(inverse(a1),a1) != identity
| identity != identity
| multiply(inverse(a1),a1) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_24,plain,
( identity != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_24,prove_these_axioms]) ).
cnf(refute_0_26,plain,
inverse(inverse(X_3)) = divide(identity,inverse(X_3)),
inference(subst,[],[inverse:[bind(X,$fot(inverse(X_3)))]]) ).
cnf(refute_0_27,plain,
multiply(identity,X_3) = divide(identity,inverse(X_3)),
inference(subst,[],[refute_0_13:[bind(X,$fot(identity)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_28,plain,
( multiply(identity,X_3) != divide(identity,inverse(X_3))
| divide(identity,inverse(X_3)) = multiply(identity,X_3) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(identity,X_3))),bind(Y0,$fot(divide(identity,inverse(X_3))))]]) ).
cnf(refute_0_29,plain,
divide(identity,inverse(X_3)) = multiply(identity,X_3),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),divide(identity,inverse(X_3))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( divide(identity,inverse(X_3)) != multiply(identity,X_3)
| inverse(inverse(X_3)) != divide(identity,inverse(X_3))
| inverse(inverse(X_3)) = multiply(identity,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_3)),divide(identity,inverse(X_3))) ),[1],$fot(multiply(identity,X_3))]]) ).
cnf(refute_0_31,plain,
( inverse(inverse(X_3)) != divide(identity,inverse(X_3))
| inverse(inverse(X_3)) = multiply(identity,X_3) ),
inference(resolve,[$cnf( $equal(divide(identity,inverse(X_3)),multiply(identity,X_3)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(inverse(X_3)) = multiply(identity,X_3),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),divide(identity,inverse(X_3))) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
( identity != divide(X,X)
| divide(X,X) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(divide(X,X)))]]) ).
cnf(refute_0_34,plain,
divide(X,X) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X,X)) )],[identity,refute_0_33]) ).
cnf(refute_0_35,plain,
divide(divide(X,X),X) = divide(divide(X,X),X),
introduced(tautology,[refl,[$fot(divide(divide(X,X),X))]]) ).
cnf(refute_0_36,plain,
( divide(X,X) != identity
| divide(divide(X,X),X) != divide(divide(X,X),X)
| divide(divide(X,X),X) = divide(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X,X),X),divide(divide(X,X),X)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_37,plain,
( divide(X,X) != identity
| divide(divide(X,X),X) = divide(identity,X) ),
inference(resolve,[$cnf( $equal(divide(divide(X,X),X),divide(divide(X,X),X)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
divide(divide(X,X),X) = divide(identity,X),
inference(resolve,[$cnf( $equal(divide(X,X),identity) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_40,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_3,refute_0_39]) ).
cnf(refute_0_41,plain,
( divide(divide(X,X),X) != divide(identity,X)
| divide(identity,X) != inverse(X)
| divide(divide(X,X),X) = inverse(X) ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(divide(divide(X,X),X))),bind(Y0,$fot(divide(identity,X))),bind(Z0,$fot(inverse(X)))]]) ).
cnf(refute_0_42,plain,
( divide(identity,X) != inverse(X)
| divide(divide(X,X),X) = inverse(X) ),
inference(resolve,[$cnf( $equal(divide(divide(X,X),X),divide(identity,X)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
divide(divide(X,X),X) = inverse(X),
inference(resolve,[$cnf( $equal(divide(identity,X),inverse(X)) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
divide(divide(divide(X,X),X),Z) = divide(divide(divide(X,X),X),Z),
introduced(tautology,[refl,[$fot(divide(divide(divide(X,X),X),Z))]]) ).
cnf(refute_0_45,plain,
( divide(divide(X,X),X) != inverse(X)
| divide(divide(divide(X,X),X),Z) != divide(divide(divide(X,X),X),Z)
| divide(divide(divide(X,X),X),Z) = divide(inverse(X),Z) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X,X),X),Z),divide(divide(divide(X,X),X),Z)) ),[1,0],$fot(inverse(X))]]) ).
cnf(refute_0_46,plain,
( divide(divide(X,X),X) != inverse(X)
| divide(divide(divide(X,X),X),Z) = divide(inverse(X),Z) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X,X),X),Z),divide(divide(divide(X,X),X),Z)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
divide(divide(divide(X,X),X),Z) = divide(inverse(X),Z),
inference(resolve,[$cnf( $equal(divide(divide(X,X),X),inverse(X)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)),
introduced(tautology,[refl,[$fot(divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)))]]) ).
cnf(refute_0_49,plain,
( divide(divide(divide(X,X),X),Z) != divide(inverse(X),Z)
| divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z))
| divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z))) ),[1,1],$fot(divide(inverse(X),Z))]]) ).
cnf(refute_0_50,plain,
( divide(divide(divide(X,X),X),Z) != divide(inverse(X),Z)
| divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)) ),
inference(resolve,[$cnf( $equal(divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)),
inference(resolve,[$cnf( $equal(divide(divide(divide(X,X),X),Z),divide(inverse(X),Z)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
divide(divide(identity,Y),Z) = divide(divide(identity,Y),Z),
introduced(tautology,[refl,[$fot(divide(divide(identity,Y),Z))]]) ).
cnf(refute_0_53,plain,
( divide(divide(identity,Y),Z) != divide(divide(identity,Y),Z)
| divide(identity,Y) != inverse(Y)
| divide(divide(identity,Y),Z) = divide(inverse(Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,Y),Z),divide(divide(identity,Y),Z)) ),[1,0],$fot(inverse(Y))]]) ).
cnf(refute_0_54,plain,
( divide(identity,Y) != inverse(Y)
| divide(divide(identity,Y),Z) = divide(inverse(Y),Z) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,Y),Z),divide(divide(identity,Y),Z)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
divide(divide(identity,Y),Z) = divide(inverse(Y),Z),
inference(resolve,[$cnf( $equal(divide(identity,Y),inverse(Y)) )],[refute_0_6,refute_0_54]) ).
cnf(refute_0_56,plain,
divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)),
introduced(tautology,[refl,[$fot(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)))]]) ).
cnf(refute_0_57,plain,
( divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))
| divide(divide(identity,Y),Z) != divide(inverse(Y),Z)
| divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) ),[1,0],$fot(divide(inverse(Y),Z))]]) ).
cnf(refute_0_58,plain,
( divide(divide(identity,Y),Z) != divide(inverse(Y),Z)
| divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)),
inference(resolve,[$cnf( $equal(divide(divide(identity,Y),Z),divide(inverse(Y),Z)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z))
| divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(inverse(X),Z))
| divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)) ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)))),bind(Y0,$fot(divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)))),bind(Z0,$fot(divide(divide(inverse(Y),Z),divide(inverse(X),Z))))]]) ).
cnf(refute_0_61,plain,
( divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(inverse(X),Z))
| divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) = divide(divide(inverse(Y),Z),divide(inverse(X),Z)),
inference(resolve,[$cnf( $equal(divide(divide(inverse(Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(inverse(Y),Z),divide(inverse(X),Z))) )],[refute_0_51,refute_0_61]) ).
cnf(refute_0_63,plain,
divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),
introduced(tautology,[refl,[$fot(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))))]]) ).
cnf(refute_0_64,plain,
( divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) != divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)))
| divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(inverse(X),Z))
| divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)))) ),[1,1],$fot(divide(divide(inverse(Y),Z),divide(inverse(X),Z)))]]) ).
cnf(refute_0_65,plain,
( divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)) != divide(divide(inverse(Y),Z),divide(inverse(X),Z))
| divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))),
inference(resolve,[$cnf( $equal(divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z)),divide(divide(inverse(Y),Z),divide(inverse(X),Z))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) != Y
| divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) != divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z)))
| divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),Y) ),[0],$fot(divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))))]]) ).
cnf(refute_0_68,plain,
( divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) != Y
| divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) = Y ),
inference(resolve,[$cnf( $equal(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) = Y,
inference(resolve,[$cnf( $equal(divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))),Y) )],[single_axiom,refute_0_68]) ).
cnf(refute_0_70,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(X_8)),divide(inverse(X_7),inverse(X_8)))) = X_8,
inference(subst,[],[refute_0_69:[bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(inverse(X_8)))]]) ).
cnf(refute_0_71,plain,
identity = divide(inverse(X_8),inverse(X_8)),
inference(subst,[],[identity:[bind(X,$fot(inverse(X_8)))]]) ).
cnf(refute_0_72,plain,
( identity != divide(inverse(X_8),inverse(X_8))
| divide(inverse(X_8),inverse(X_8)) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(divide(inverse(X_8),inverse(X_8))))]]) ).
cnf(refute_0_73,plain,
divide(inverse(X_8),inverse(X_8)) = identity,
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_8),inverse(X_8))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_8)),divide(inverse(X_7),inverse(X_8)))) != X_8
| divide(inverse(X_8),inverse(X_8)) != identity
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_8)),divide(inverse(X_7),inverse(X_8)))),X_8) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_75,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_8)),divide(inverse(X_7),inverse(X_8)))) != X_8
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(X_8),inverse(X_8)),identity) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_8)),divide(inverse(X_7),inverse(X_8)))),X_8) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiply(X,Y) != divide(X,inverse(Y))
| divide(X,inverse(Y)) = multiply(X,Y) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(divide(X,inverse(Y))))]]) ).
cnf(refute_0_78,plain,
divide(X,inverse(Y)) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),divide(X,inverse(Y))) )],[refute_0_13,refute_0_77]) ).
cnf(refute_0_79,plain,
divide(X_7,inverse(multiply(inverse(X_7),X_8))) = multiply(X_7,multiply(inverse(X_7),X_8)),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_7)),bind(Y,$fot(multiply(inverse(X_7),X_8)))]]) ).
cnf(refute_0_80,plain,
divide(inverse(X_7),inverse(X_8)) = multiply(inverse(X_7),X_8),
inference(subst,[],[refute_0_78:[bind(X,$fot(inverse(X_7))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_81,plain,
inverse(divide(inverse(X_7),inverse(X_8))) = inverse(divide(inverse(X_7),inverse(X_8))),
introduced(tautology,[refl,[$fot(inverse(divide(inverse(X_7),inverse(X_8))))]]) ).
cnf(refute_0_82,plain,
( divide(inverse(X_7),inverse(X_8)) != multiply(inverse(X_7),X_8)
| inverse(divide(inverse(X_7),inverse(X_8))) != inverse(divide(inverse(X_7),inverse(X_8)))
| inverse(divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_7),inverse(X_8))),inverse(divide(inverse(X_7),inverse(X_8)))) ),[1,0],$fot(multiply(inverse(X_7),X_8))]]) ).
cnf(refute_0_83,plain,
( divide(inverse(X_7),inverse(X_8)) != multiply(inverse(X_7),X_8)
| inverse(divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)) ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),inverse(X_8))),inverse(divide(inverse(X_7),inverse(X_8)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)),
inference(resolve,[$cnf( $equal(divide(inverse(X_7),inverse(X_8)),multiply(inverse(X_7),X_8)) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
divide(identity,divide(inverse(X_7),inverse(X_8))) = inverse(divide(inverse(X_7),inverse(X_8))),
inference(subst,[],[refute_0_5:[bind(X,$fot(divide(inverse(X_7),inverse(X_8))))]]) ).
cnf(refute_0_86,plain,
( divide(identity,divide(inverse(X_7),inverse(X_8))) != inverse(divide(inverse(X_7),inverse(X_8)))
| inverse(divide(inverse(X_7),inverse(X_8))) != inverse(multiply(inverse(X_7),X_8))
| divide(identity,divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)) ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(divide(identity,divide(inverse(X_7),inverse(X_8))))),bind(Y0,$fot(inverse(divide(inverse(X_7),inverse(X_8))))),bind(Z0,$fot(inverse(multiply(inverse(X_7),X_8))))]]) ).
cnf(refute_0_87,plain,
( inverse(divide(inverse(X_7),inverse(X_8))) != inverse(multiply(inverse(X_7),X_8))
| divide(identity,divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)) ),
inference(resolve,[$cnf( $equal(divide(identity,divide(inverse(X_7),inverse(X_8))),inverse(divide(inverse(X_7),inverse(X_8)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
divide(identity,divide(inverse(X_7),inverse(X_8))) = inverse(multiply(inverse(X_7),X_8)),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),inverse(X_8))),inverse(multiply(inverse(X_7),X_8))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),
introduced(tautology,[refl,[$fot(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))))]]) ).
cnf(refute_0_90,plain,
( divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) != divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8))))
| divide(identity,divide(inverse(X_7),inverse(X_8))) != inverse(multiply(inverse(X_7),X_8))
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = divide(X_7,inverse(multiply(inverse(X_7),X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8))))) ),[1,1],$fot(inverse(multiply(inverse(X_7),X_8)))]]) ).
cnf(refute_0_91,plain,
( divide(identity,divide(inverse(X_7),inverse(X_8))) != inverse(multiply(inverse(X_7),X_8))
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = divide(X_7,inverse(multiply(inverse(X_7),X_8))) ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8))))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = divide(X_7,inverse(multiply(inverse(X_7),X_8))),
inference(resolve,[$cnf( $equal(divide(identity,divide(inverse(X_7),inverse(X_8))),inverse(multiply(inverse(X_7),X_8))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) != divide(X_7,inverse(multiply(inverse(X_7),X_8)))
| divide(X_7,inverse(multiply(inverse(X_7),X_8))) != multiply(X_7,multiply(inverse(X_7),X_8))
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = multiply(X_7,multiply(inverse(X_7),X_8)) ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))))),bind(Y0,$fot(divide(X_7,inverse(multiply(inverse(X_7),X_8))))),bind(Z0,$fot(multiply(X_7,multiply(inverse(X_7),X_8))))]]) ).
cnf(refute_0_94,plain,
( divide(X_7,inverse(multiply(inverse(X_7),X_8))) != multiply(X_7,multiply(inverse(X_7),X_8))
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = multiply(X_7,multiply(inverse(X_7),X_8)) ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),divide(X_7,inverse(multiply(inverse(X_7),X_8)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) = multiply(X_7,multiply(inverse(X_7),X_8)),
inference(resolve,[$cnf( $equal(divide(X_7,inverse(multiply(inverse(X_7),X_8))),multiply(X_7,multiply(inverse(X_7),X_8))) )],[refute_0_79,refute_0_94]) ).
cnf(refute_0_96,plain,
( divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) != X_8
| divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) != multiply(X_7,multiply(inverse(X_7),X_8))
| multiply(X_7,multiply(inverse(X_7),X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),X_8) ),[0],$fot(multiply(X_7,multiply(inverse(X_7),X_8)))]]) ).
cnf(refute_0_97,plain,
( divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))) != X_8
| multiply(X_7,multiply(inverse(X_7),X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),multiply(X_7,multiply(inverse(X_7),X_8))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(X_7,multiply(inverse(X_7),X_8)) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(identity,divide(inverse(X_7),inverse(X_8)))),X_8) )],[refute_0_76,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))) = inverse(inverse(X_7)),
inference(subst,[],[refute_0_98:[bind(X_8,$fot(inverse(inverse(X_7))))]]) ).
cnf(refute_0_100,plain,
multiply(X_12,multiply(inverse(X_12),identity)) = identity,
inference(subst,[],[refute_0_98:[bind(X_7,$fot(X_12)),bind(X_8,$fot(identity))]]) ).
cnf(refute_0_101,plain,
divide(X_7,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))) = X_7,
inference(subst,[],[refute_0_69:[bind(X,$fot(X_7)),bind(Y,$fot(X_7)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_102,plain,
identity = divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9)),
inference(subst,[],[identity:[bind(X,$fot(divide(inverse(X_7),X_9)))]]) ).
cnf(refute_0_103,plain,
( identity != divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))
| divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9)) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))))]]) ).
cnf(refute_0_104,plain,
divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9)) = identity,
inference(resolve,[$cnf( $equal(identity,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( divide(X_7,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))) != X_7
| divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9)) != identity
| divide(X_7,identity) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))),X_7) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_106,plain,
( divide(X_7,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))) != X_7
| divide(X_7,identity) = X_7 ),
inference(resolve,[$cnf( $equal(divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9)),identity) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
divide(X_7,identity) = X_7,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_7),X_9),divide(inverse(X_7),X_9))),X_7) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(X_2,identity) = divide(X_2,inverse(identity)),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_2)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_109,plain,
identity = divide(identity,identity),
inference(subst,[],[identity:[bind(X,$fot(identity))]]) ).
cnf(refute_0_110,plain,
inverse(identity) = divide(identity,identity),
inference(subst,[],[inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_111,plain,
( inverse(identity) != divide(identity,identity)
| divide(identity,identity) = inverse(identity) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(divide(identity,identity)))]]) ).
cnf(refute_0_112,plain,
divide(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),divide(identity,identity)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( divide(identity,identity) != inverse(identity)
| identity != divide(identity,identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(identity,identity)) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_114,plain,
( identity != divide(identity,identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(divide(identity,identity),inverse(identity)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,divide(identity,identity)) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(identity)))]]) ).
cnf(refute_0_117,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( multiply(X_2,identity) != divide(X_2,inverse(identity))
| inverse(identity) != identity
| multiply(X_2,identity) = divide(X_2,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,identity),divide(X_2,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_119,plain,
( multiply(X_2,identity) != divide(X_2,inverse(identity))
| multiply(X_2,identity) = divide(X_2,identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(X_2,identity) = divide(X_2,identity),
inference(resolve,[$cnf( $equal(multiply(X_2,identity),divide(X_2,inverse(identity))) )],[refute_0_108,refute_0_119]) ).
cnf(refute_0_121,plain,
( multiply(X_2,identity) != divide(X_2,identity)
| divide(X_2,identity) = multiply(X_2,identity) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_2,identity))),bind(Y0,$fot(divide(X_2,identity)))]]) ).
cnf(refute_0_122,plain,
divide(X_2,identity) = multiply(X_2,identity),
inference(resolve,[$cnf( $equal(multiply(X_2,identity),divide(X_2,identity)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
divide(X_7,identity) = multiply(X_7,identity),
inference(subst,[],[refute_0_122:[bind(X_2,$fot(X_7))]]) ).
cnf(refute_0_124,plain,
( divide(X_7,identity) != X_7
| divide(X_7,identity) != multiply(X_7,identity)
| multiply(X_7,identity) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,identity),X_7) ),[0],$fot(multiply(X_7,identity))]]) ).
cnf(refute_0_125,plain,
( divide(X_7,identity) != X_7
| multiply(X_7,identity) = X_7 ),
inference(resolve,[$cnf( $equal(divide(X_7,identity),multiply(X_7,identity)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(X_7,identity) = X_7,
inference(resolve,[$cnf( $equal(divide(X_7,identity),X_7) )],[refute_0_107,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(inverse(X_12),identity) = inverse(X_12),
inference(subst,[],[refute_0_126:[bind(X_7,$fot(inverse(X_12)))]]) ).
cnf(refute_0_128,plain,
( multiply(X_12,multiply(inverse(X_12),identity)) != identity
| multiply(inverse(X_12),identity) != inverse(X_12)
| multiply(X_12,inverse(X_12)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_12,multiply(inverse(X_12),identity)),identity) ),[0,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_129,plain,
( multiply(X_12,multiply(inverse(X_12),identity)) != identity
| multiply(X_12,inverse(X_12)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),identity),inverse(X_12)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(X_12,inverse(X_12)) = identity,
inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X_12),identity)),identity) )],[refute_0_100,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(inverse(X_7),inverse(inverse(X_7))) = identity,
inference(subst,[],[refute_0_130:[bind(X_12,$fot(inverse(X_7)))]]) ).
cnf(refute_0_132,plain,
( multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))) != inverse(inverse(X_7))
| multiply(inverse(X_7),inverse(inverse(X_7))) != identity
| multiply(X_7,identity) = inverse(inverse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))),inverse(inverse(X_7))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_133,plain,
( multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))) != inverse(inverse(X_7))
| multiply(X_7,identity) = inverse(inverse(X_7)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_7),inverse(inverse(X_7))),identity) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(X_7,identity) = inverse(inverse(X_7)),
inference(resolve,[$cnf( $equal(multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))),inverse(inverse(X_7))) )],[refute_0_99,refute_0_133]) ).
cnf(refute_0_135,plain,
( multiply(X_7,identity) != X_7
| multiply(X_7,identity) != inverse(inverse(X_7))
| X_7 = inverse(inverse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_7,identity),inverse(inverse(X_7))) ),[0],$fot(X_7)]]) ).
cnf(refute_0_136,plain,
( multiply(X_7,identity) != inverse(inverse(X_7))
| X_7 = inverse(inverse(X_7)) ),
inference(resolve,[$cnf( $equal(multiply(X_7,identity),X_7) )],[refute_0_126,refute_0_135]) ).
cnf(refute_0_137,plain,
X_7 = inverse(inverse(X_7)),
inference(resolve,[$cnf( $equal(multiply(X_7,identity),inverse(inverse(X_7))) )],[refute_0_134,refute_0_136]) ).
cnf(refute_0_138,plain,
( X_7 != inverse(inverse(X_7))
| inverse(inverse(X_7)) = X_7 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(X_7)),bind(Y0,$fot(inverse(inverse(X_7))))]]) ).
cnf(refute_0_139,plain,
inverse(inverse(X_7)) = X_7,
inference(resolve,[$cnf( $equal(X_7,inverse(inverse(X_7))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
inverse(inverse(X_3)) = X_3,
inference(subst,[],[refute_0_139:[bind(X_7,$fot(X_3))]]) ).
cnf(refute_0_141,plain,
( inverse(inverse(X_3)) != X_3
| inverse(inverse(X_3)) != multiply(identity,X_3)
| X_3 = multiply(identity,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_3)),multiply(identity,X_3)) ),[0],$fot(X_3)]]) ).
cnf(refute_0_142,plain,
( inverse(inverse(X_3)) != multiply(identity,X_3)
| X_3 = multiply(identity,X_3) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),X_3) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
X_3 = multiply(identity,X_3),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),multiply(identity,X_3)) )],[refute_0_32,refute_0_142]) ).
cnf(refute_0_144,plain,
( X_3 != multiply(identity,X_3)
| multiply(identity,X_3) = X_3 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(X_3)),bind(Y0,$fot(multiply(identity,X_3)))]]) ).
cnf(refute_0_145,plain,
multiply(identity,X_3) = X_3,
inference(resolve,[$cnf( $equal(X_3,multiply(identity,X_3)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(identity,a2) = a2,
inference(subst,[],[refute_0_145:[bind(X_3,$fot(a2))]]) ).
cnf(refute_0_147,plain,
( multiply(identity,a2) != a2
| a2 != a2
| multiply(identity,a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_148,plain,
( a2 != a2
| multiply(identity,a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_148,refute_0_25]) ).
cnf(refute_0_150,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_151,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| identity != identity ),
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_150,refute_0_149]) ).
cnf(refute_0_152,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_153,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_152,refute_0_151]) ).
cnf(refute_0_154,plain,
multiply(X_7,multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))) = divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),
inference(subst,[],[refute_0_98:[bind(X_8,$fot(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))))]]) ).
cnf(refute_0_155,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(Y)),divide(inverse(X_7),inverse(Y)))) = X_8,
inference(subst,[],[refute_0_69:[bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(inverse(Y)))]]) ).
cnf(refute_0_156,plain,
multiply(inverse(X_7),Y) = divide(inverse(X_7),inverse(Y)),
inference(subst,[],[refute_0_13:[bind(X,$fot(inverse(X_7)))]]) ).
cnf(refute_0_157,plain,
( multiply(inverse(X_7),Y) != divide(inverse(X_7),inverse(Y))
| divide(inverse(X_7),inverse(Y)) = multiply(inverse(X_7),Y) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(inverse(X_7),Y))),bind(Y0,$fot(divide(inverse(X_7),inverse(Y))))]]) ).
cnf(refute_0_158,plain,
divide(inverse(X_7),inverse(Y)) = multiply(inverse(X_7),Y),
inference(resolve,[$cnf( $equal(multiply(inverse(X_7),Y),divide(inverse(X_7),inverse(Y))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(Y)),divide(inverse(X_7),inverse(Y)))) != X_8
| divide(inverse(X_7),inverse(Y)) != multiply(inverse(X_7),Y)
| divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),divide(inverse(X_7),inverse(Y)))),X_8) ),[0,1,1],$fot(multiply(inverse(X_7),Y))]]) ).
cnf(refute_0_160,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(Y)),divide(inverse(X_7),inverse(Y)))) != X_8
| divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(X_7),inverse(Y)),multiply(inverse(X_7),Y)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),divide(inverse(X_7),inverse(Y)))),X_8) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
divide(inverse(X_8),inverse(Y)) = multiply(inverse(X_8),Y),
inference(subst,[],[refute_0_78:[bind(X,$fot(inverse(X_8)))]]) ).
cnf(refute_0_163,plain,
divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) = divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)),
introduced(tautology,[refl,[$fot(divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)))]]) ).
cnf(refute_0_164,plain,
( divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) != divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))
| divide(inverse(X_8),inverse(Y)) != multiply(inverse(X_8),Y)
| divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) = divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)),divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) ),[1,0],$fot(multiply(inverse(X_8),Y))]]) ).
cnf(refute_0_165,plain,
( divide(inverse(X_8),inverse(Y)) != multiply(inverse(X_8),Y)
| divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) = divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)) ),
inference(resolve,[$cnf( $equal(divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)),divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) = divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)),
inference(resolve,[$cnf( $equal(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_8),Y)) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),
introduced(tautology,[refl,[$fot(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))))]]) ).
cnf(refute_0_168,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) != divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)))
| divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) != divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))
| divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)))) ),[1,1],$fot(divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)))]]) ).
cnf(refute_0_169,plain,
( divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)) != divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))
| divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) = divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))),
inference(resolve,[$cnf( $equal(divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y)),divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) != X_8
| divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) != divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)))
| divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),X_8) ),[0],$fot(divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))))]]) ).
cnf(refute_0_172,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))) != X_8
| divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y)))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(Y)),multiply(inverse(X_7),Y))),X_8) )],[refute_0_161,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(X,divide(X_33,X_34)) = divide(X,inverse(divide(X_33,X_34))),
inference(subst,[],[refute_0_13:[bind(Y,$fot(divide(X_33,X_34)))]]) ).
cnf(refute_0_175,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),divide(inverse(X_7),inverse(X_7)))) = X_8,
inference(subst,[],[refute_0_69:[bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(inverse(X_7)))]]) ).
cnf(refute_0_176,plain,
identity = divide(inverse(X_7),inverse(X_7)),
inference(subst,[],[identity:[bind(X,$fot(inverse(X_7)))]]) ).
cnf(refute_0_177,plain,
( identity != divide(inverse(X_7),inverse(X_7))
| divide(inverse(X_7),inverse(X_7)) = identity ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(identity)),bind(Y0,$fot(divide(inverse(X_7),inverse(X_7))))]]) ).
cnf(refute_0_178,plain,
divide(inverse(X_7),inverse(X_7)) = identity,
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_7),inverse(X_7))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),divide(inverse(X_7),inverse(X_7)))) != X_8
| divide(inverse(X_7),inverse(X_7)) != identity
| divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),divide(inverse(X_7),inverse(X_7)))),X_8) ),[0,1,1],$fot(identity)]]) ).
cnf(refute_0_180,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),divide(inverse(X_7),inverse(X_7)))) != X_8
| divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(X_7),inverse(X_7)),identity) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),divide(inverse(X_7),inverse(X_7)))),X_8) )],[refute_0_175,refute_0_180]) ).
cnf(refute_0_182,plain,
divide(inverse(X_8),inverse(X_7)) = multiply(inverse(X_8),X_7),
inference(subst,[],[refute_0_78:[bind(X,$fot(inverse(X_8))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_183,plain,
multiply(divide(inverse(X_8),inverse(X_7)),identity) = multiply(divide(inverse(X_8),inverse(X_7)),identity),
introduced(tautology,[refl,[$fot(multiply(divide(inverse(X_8),inverse(X_7)),identity))]]) ).
cnf(refute_0_184,plain,
( multiply(divide(inverse(X_8),inverse(X_7)),identity) != multiply(divide(inverse(X_8),inverse(X_7)),identity)
| divide(inverse(X_8),inverse(X_7)) != multiply(inverse(X_8),X_7)
| multiply(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(inverse(X_8),inverse(X_7)),identity),multiply(divide(inverse(X_8),inverse(X_7)),identity)) ),[1,0],$fot(multiply(inverse(X_8),X_7))]]) ).
cnf(refute_0_185,plain,
( divide(inverse(X_8),inverse(X_7)) != multiply(inverse(X_8),X_7)
| multiply(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity) ),
inference(resolve,[$cnf( $equal(multiply(divide(inverse(X_8),inverse(X_7)),identity),multiply(divide(inverse(X_8),inverse(X_7)),identity)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity),
inference(resolve,[$cnf( $equal(divide(inverse(X_8),inverse(X_7)),multiply(inverse(X_8),X_7)) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
divide(divide(inverse(X_8),inverse(X_7)),identity) = multiply(divide(inverse(X_8),inverse(X_7)),identity),
inference(subst,[],[refute_0_122:[bind(X_2,$fot(divide(inverse(X_8),inverse(X_7))))]]) ).
cnf(refute_0_188,plain,
( multiply(divide(inverse(X_8),inverse(X_7)),identity) != multiply(multiply(inverse(X_8),X_7),identity)
| divide(divide(inverse(X_8),inverse(X_7)),identity) != multiply(divide(inverse(X_8),inverse(X_7)),identity)
| divide(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity) ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(divide(divide(inverse(X_8),inverse(X_7)),identity))),bind(Y0,$fot(multiply(divide(inverse(X_8),inverse(X_7)),identity))),bind(Z0,$fot(multiply(multiply(inverse(X_8),X_7),identity)))]]) ).
cnf(refute_0_189,plain,
( multiply(divide(inverse(X_8),inverse(X_7)),identity) != multiply(multiply(inverse(X_8),X_7),identity)
| divide(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity) ),
inference(resolve,[$cnf( $equal(divide(divide(inverse(X_8),inverse(X_7)),identity),multiply(divide(inverse(X_8),inverse(X_7)),identity)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
divide(divide(inverse(X_8),inverse(X_7)),identity) = multiply(multiply(inverse(X_8),X_7),identity),
inference(resolve,[$cnf( $equal(multiply(divide(inverse(X_8),inverse(X_7)),identity),multiply(multiply(inverse(X_8),X_7),identity)) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),
introduced(tautology,[refl,[$fot(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)))]]) ).
cnf(refute_0_192,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) != divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity))
| divide(divide(inverse(X_8),inverse(X_7)),identity) != multiply(multiply(inverse(X_8),X_7),identity)
| divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity))) ),[1,1],$fot(multiply(multiply(inverse(X_8),X_7),identity))]]) ).
cnf(refute_0_193,plain,
( divide(divide(inverse(X_8),inverse(X_7)),identity) != multiply(multiply(inverse(X_8),X_7),identity)
| divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) = divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),
inference(resolve,[$cnf( $equal(divide(divide(inverse(X_8),inverse(X_7)),identity),multiply(multiply(inverse(X_8),X_7),identity)) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) != X_8
| divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) != divide(X_7,multiply(multiply(inverse(X_8),X_7),identity))
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),X_8) ),[0],$fot(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)))]]) ).
cnf(refute_0_196,plain,
( divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)) != X_8
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),divide(X_7,multiply(multiply(inverse(X_8),X_7),identity))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(inverse(X_8),inverse(X_7)),identity)),X_8) )],[refute_0_181,refute_0_196]) ).
cnf(refute_0_198,plain,
multiply(multiply(inverse(X_8),X_7),identity) = multiply(inverse(X_8),X_7),
inference(subst,[],[refute_0_126:[bind(X_7,$fot(multiply(inverse(X_8),X_7)))]]) ).
cnf(refute_0_199,plain,
divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),
introduced(tautology,[refl,[$fot(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)))]]) ).
cnf(refute_0_200,plain,
( multiply(multiply(inverse(X_8),X_7),identity) != multiply(inverse(X_8),X_7)
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) != divide(X_7,multiply(multiply(inverse(X_8),X_7),identity))
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = divide(X_7,multiply(inverse(X_8),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),divide(X_7,multiply(multiply(inverse(X_8),X_7),identity))) ),[1,1],$fot(multiply(inverse(X_8),X_7))]]) ).
cnf(refute_0_201,plain,
( multiply(multiply(inverse(X_8),X_7),identity) != multiply(inverse(X_8),X_7)
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = divide(X_7,multiply(inverse(X_8),X_7)) ),
inference(resolve,[$cnf( $equal(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),divide(X_7,multiply(multiply(inverse(X_8),X_7),identity))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) = divide(X_7,multiply(inverse(X_8),X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_8),X_7),identity),multiply(inverse(X_8),X_7)) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) != X_8
| divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) != divide(X_7,multiply(inverse(X_8),X_7))
| divide(X_7,multiply(inverse(X_8),X_7)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),X_8) ),[0],$fot(divide(X_7,multiply(inverse(X_8),X_7)))]]) ).
cnf(refute_0_204,plain,
( divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)) != X_8
| divide(X_7,multiply(inverse(X_8),X_7)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),divide(X_7,multiply(inverse(X_8),X_7))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
divide(X_7,multiply(inverse(X_8),X_7)) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,multiply(multiply(inverse(X_8),X_7),identity)),X_8) )],[refute_0_197,refute_0_204]) ).
cnf(refute_0_206,plain,
divide(X_19,multiply(inverse(inverse(X_7)),X_19)) = inverse(X_7),
inference(subst,[],[refute_0_205:[bind(X_7,$fot(X_19)),bind(X_8,$fot(inverse(X_7)))]]) ).
cnf(refute_0_207,plain,
( divide(X_19,multiply(inverse(inverse(X_7)),X_19)) != inverse(X_7)
| inverse(inverse(X_7)) != X_7
| divide(X_19,multiply(X_7,X_19)) = inverse(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_19,multiply(inverse(inverse(X_7)),X_19)),inverse(X_7)) ),[0,1,0],$fot(X_7)]]) ).
cnf(refute_0_208,plain,
( divide(X_19,multiply(inverse(inverse(X_7)),X_19)) != inverse(X_7)
| divide(X_19,multiply(X_7,X_19)) = inverse(X_7) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_7)),X_7) )],[refute_0_139,refute_0_207]) ).
cnf(refute_0_209,plain,
divide(X_19,multiply(X_7,X_19)) = inverse(X_7),
inference(resolve,[$cnf( $equal(divide(X_19,multiply(inverse(inverse(X_7)),X_19)),inverse(X_7)) )],[refute_0_206,refute_0_208]) ).
cnf(refute_0_210,plain,
divide(X_31,multiply(divide(X_21,X_31),X_31)) = inverse(divide(X_21,X_31)),
inference(subst,[],[refute_0_209:[bind(X_19,$fot(X_31)),bind(X_7,$fot(divide(X_21,X_31)))]]) ).
cnf(refute_0_211,plain,
multiply(multiply(X_21,inverse(Y)),Y) = divide(multiply(X_21,inverse(Y)),inverse(Y)),
inference(subst,[],[refute_0_13:[bind(X,$fot(multiply(X_21,inverse(Y))))]]) ).
cnf(refute_0_212,plain,
divide(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8))) = X_20,
inference(subst,[],[refute_0_205:[bind(X_7,$fot(multiply(inverse(inverse(X_20)),X_8))),bind(X_8,$fot(X_20))]]) ).
cnf(refute_0_213,plain,
multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8)) = X_8,
inference(subst,[],[refute_0_98:[bind(X_7,$fot(inverse(X_20)))]]) ).
cnf(refute_0_214,plain,
( multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8)) != X_8
| divide(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8))) != X_20
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8))),X_20) ),[0,1],$fot(X_8)]]) ).
cnf(refute_0_215,plain,
( divide(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8))) != X_20
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) = X_20 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8)),X_8) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
divide(multiply(inverse(inverse(X_20)),X_8),X_8) = X_20,
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(X_20),multiply(inverse(inverse(X_20)),X_8))),X_20) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
inverse(inverse(X_20)) = X_20,
inference(subst,[],[refute_0_139:[bind(X_7,$fot(X_20))]]) ).
cnf(refute_0_218,plain,
multiply(inverse(inverse(X_20)),X_8) = multiply(inverse(inverse(X_20)),X_8),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_20)),X_8))]]) ).
cnf(refute_0_219,plain,
( multiply(inverse(inverse(X_20)),X_8) != multiply(inverse(inverse(X_20)),X_8)
| inverse(inverse(X_20)) != X_20
| multiply(inverse(inverse(X_20)),X_8) = multiply(X_20,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(inverse(X_20)),X_8)) ),[1,0],$fot(X_20)]]) ).
cnf(refute_0_220,plain,
( inverse(inverse(X_20)) != X_20
| multiply(inverse(inverse(X_20)),X_8) = multiply(X_20,X_8) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_20)),X_8),multiply(inverse(inverse(X_20)),X_8)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(inverse(inverse(X_20)),X_8) = multiply(X_20,X_8),
inference(resolve,[$cnf( $equal(inverse(inverse(X_20)),X_20) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
divide(multiply(inverse(inverse(X_20)),X_8),X_8) = divide(multiply(inverse(inverse(X_20)),X_8),X_8),
introduced(tautology,[refl,[$fot(divide(multiply(inverse(inverse(X_20)),X_8),X_8))]]) ).
cnf(refute_0_223,plain,
( multiply(inverse(inverse(X_20)),X_8) != multiply(X_20,X_8)
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) != divide(multiply(inverse(inverse(X_20)),X_8),X_8)
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) = divide(multiply(X_20,X_8),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),X_8),divide(multiply(inverse(inverse(X_20)),X_8),X_8)) ),[1,0],$fot(multiply(X_20,X_8))]]) ).
cnf(refute_0_224,plain,
( multiply(inverse(inverse(X_20)),X_8) != multiply(X_20,X_8)
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) = divide(multiply(X_20,X_8),X_8) ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),X_8),divide(multiply(inverse(inverse(X_20)),X_8),X_8)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
divide(multiply(inverse(inverse(X_20)),X_8),X_8) = divide(multiply(X_20,X_8),X_8),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_20)),X_8),multiply(X_20,X_8)) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( divide(multiply(inverse(inverse(X_20)),X_8),X_8) != X_20
| divide(multiply(inverse(inverse(X_20)),X_8),X_8) != divide(multiply(X_20,X_8),X_8)
| divide(multiply(X_20,X_8),X_8) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),X_8),X_20) ),[0],$fot(divide(multiply(X_20,X_8),X_8))]]) ).
cnf(refute_0_227,plain,
( divide(multiply(inverse(inverse(X_20)),X_8),X_8) != X_20
| divide(multiply(X_20,X_8),X_8) = X_20 ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),X_8),divide(multiply(X_20,X_8),X_8)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
divide(multiply(X_20,X_8),X_8) = X_20,
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_20)),X_8),X_8),X_20) )],[refute_0_216,refute_0_227]) ).
cnf(refute_0_229,plain,
divide(multiply(X_21,inverse(Y)),inverse(Y)) = X_21,
inference(subst,[],[refute_0_228:[bind(X_20,$fot(X_21)),bind(X_8,$fot(inverse(Y)))]]) ).
cnf(refute_0_230,plain,
( multiply(multiply(X_21,inverse(Y)),Y) != divide(multiply(X_21,inverse(Y)),inverse(Y))
| divide(multiply(X_21,inverse(Y)),inverse(Y)) != X_21
| multiply(multiply(X_21,inverse(Y)),Y) = X_21 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_21,inverse(Y)),Y),X_21) ),[0],$fot(divide(multiply(X_21,inverse(Y)),inverse(Y)))]]) ).
cnf(refute_0_231,plain,
( multiply(multiply(X_21,inverse(Y)),Y) != divide(multiply(X_21,inverse(Y)),inverse(Y))
| multiply(multiply(X_21,inverse(Y)),Y) = X_21 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_21,inverse(Y)),inverse(Y)),X_21) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(multiply(X_21,inverse(Y)),Y) = X_21,
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),divide(multiply(X_21,inverse(Y)),inverse(Y))) )],[refute_0_211,refute_0_231]) ).
cnf(refute_0_233,plain,
multiply(X,inverse(X_15)) = divide(X,inverse(inverse(X_15))),
inference(subst,[],[refute_0_13:[bind(Y,$fot(inverse(X_15)))]]) ).
cnf(refute_0_234,plain,
X_15 = inverse(inverse(X_15)),
inference(subst,[],[refute_0_137:[bind(X_7,$fot(X_15))]]) ).
cnf(refute_0_235,plain,
( X_15 != inverse(inverse(X_15))
| inverse(inverse(X_15)) = X_15 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(X_15)),bind(Y0,$fot(inverse(inverse(X_15))))]]) ).
cnf(refute_0_236,plain,
inverse(inverse(X_15)) = X_15,
inference(resolve,[$cnf( $equal(X_15,inverse(inverse(X_15))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
( multiply(X,inverse(X_15)) != divide(X,inverse(inverse(X_15)))
| inverse(inverse(X_15)) != X_15
| multiply(X,inverse(X_15)) = divide(X,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(X_15)),divide(X,inverse(inverse(X_15)))) ),[1,1],$fot(X_15)]]) ).
cnf(refute_0_238,plain,
( multiply(X,inverse(X_15)) != divide(X,inverse(inverse(X_15)))
| multiply(X,inverse(X_15)) = divide(X,X_15) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_15)),X_15) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
multiply(X,inverse(X_15)) = divide(X,X_15),
inference(resolve,[$cnf( $equal(multiply(X,inverse(X_15)),divide(X,inverse(inverse(X_15)))) )],[refute_0_233,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(X_21,inverse(Y)) = divide(X_21,Y),
inference(subst,[],[refute_0_239:[bind(X,$fot(X_21)),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_241,plain,
multiply(multiply(X_21,inverse(Y)),Y) = multiply(multiply(X_21,inverse(Y)),Y),
introduced(tautology,[refl,[$fot(multiply(multiply(X_21,inverse(Y)),Y))]]) ).
cnf(refute_0_242,plain,
( multiply(X_21,inverse(Y)) != divide(X_21,Y)
| multiply(multiply(X_21,inverse(Y)),Y) != multiply(multiply(X_21,inverse(Y)),Y)
| multiply(multiply(X_21,inverse(Y)),Y) = multiply(divide(X_21,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),multiply(multiply(X_21,inverse(Y)),Y)) ),[1,0],$fot(divide(X_21,Y))]]) ).
cnf(refute_0_243,plain,
( multiply(X_21,inverse(Y)) != divide(X_21,Y)
| multiply(multiply(X_21,inverse(Y)),Y) = multiply(divide(X_21,Y),Y) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),multiply(multiply(X_21,inverse(Y)),Y)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
multiply(multiply(X_21,inverse(Y)),Y) = multiply(divide(X_21,Y),Y),
inference(resolve,[$cnf( $equal(multiply(X_21,inverse(Y)),divide(X_21,Y)) )],[refute_0_240,refute_0_243]) ).
cnf(refute_0_245,plain,
( multiply(multiply(X_21,inverse(Y)),Y) != X_21
| multiply(multiply(X_21,inverse(Y)),Y) != multiply(divide(X_21,Y),Y)
| multiply(divide(X_21,Y),Y) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),X_21) ),[0],$fot(multiply(divide(X_21,Y),Y))]]) ).
cnf(refute_0_246,plain,
( multiply(multiply(X_21,inverse(Y)),Y) != X_21
| multiply(divide(X_21,Y),Y) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),multiply(divide(X_21,Y),Y)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(divide(X_21,Y),Y) = X_21,
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,inverse(Y)),Y),X_21) )],[refute_0_232,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(divide(X_21,X_31),X_31) = X_21,
inference(subst,[],[refute_0_247:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_249,plain,
( multiply(divide(X_21,X_31),X_31) != X_21
| divide(X_31,multiply(divide(X_21,X_31),X_31)) != inverse(divide(X_21,X_31))
| divide(X_31,X_21) = inverse(divide(X_21,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_31,multiply(divide(X_21,X_31),X_31)),inverse(divide(X_21,X_31))) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_250,plain,
( divide(X_31,multiply(divide(X_21,X_31),X_31)) != inverse(divide(X_21,X_31))
| divide(X_31,X_21) = inverse(divide(X_21,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(divide(X_21,X_31),X_31),X_21) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
divide(X_31,X_21) = inverse(divide(X_21,X_31)),
inference(resolve,[$cnf( $equal(divide(X_31,multiply(divide(X_21,X_31),X_31)),inverse(divide(X_21,X_31))) )],[refute_0_210,refute_0_250]) ).
cnf(refute_0_252,plain,
divide(X_34,X_33) = inverse(divide(X_33,X_34)),
inference(subst,[],[refute_0_251:[bind(X_21,$fot(X_33)),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_253,plain,
( divide(X_34,X_33) != inverse(divide(X_33,X_34))
| inverse(divide(X_33,X_34)) = divide(X_34,X_33) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(divide(X_34,X_33))),bind(Y0,$fot(inverse(divide(X_33,X_34))))]]) ).
cnf(refute_0_254,plain,
inverse(divide(X_33,X_34)) = divide(X_34,X_33),
inference(resolve,[$cnf( $equal(divide(X_34,X_33),inverse(divide(X_33,X_34))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
( multiply(X,divide(X_33,X_34)) != divide(X,inverse(divide(X_33,X_34)))
| inverse(divide(X_33,X_34)) != divide(X_34,X_33)
| multiply(X,divide(X_33,X_34)) = divide(X,divide(X_34,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,divide(X_33,X_34)),divide(X,inverse(divide(X_33,X_34)))) ),[1,1],$fot(divide(X_34,X_33))]]) ).
cnf(refute_0_256,plain,
( multiply(X,divide(X_33,X_34)) != divide(X,inverse(divide(X_33,X_34)))
| multiply(X,divide(X_33,X_34)) = divide(X,divide(X_34,X_33)) ),
inference(resolve,[$cnf( $equal(inverse(divide(X_33,X_34)),divide(X_34,X_33)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(X,divide(X_33,X_34)) = divide(X,divide(X_34,X_33)),
inference(resolve,[$cnf( $equal(multiply(X,divide(X_33,X_34)),divide(X,inverse(divide(X_33,X_34)))) )],[refute_0_174,refute_0_256]) ).
cnf(refute_0_258,plain,
( multiply(X,divide(X_33,X_34)) != divide(X,divide(X_34,X_33))
| divide(X,divide(X_34,X_33)) = multiply(X,divide(X_33,X_34)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X,divide(X_33,X_34)))),bind(Y0,$fot(divide(X,divide(X_34,X_33))))]]) ).
cnf(refute_0_259,plain,
divide(X,divide(X_34,X_33)) = multiply(X,divide(X_33,X_34)),
inference(resolve,[$cnf( $equal(multiply(X,divide(X_33,X_34)),divide(X,divide(X_34,X_33))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) = multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y))),
inference(subst,[],[refute_0_259:[bind(X,$fot(X_7)),bind(X_33,$fot(multiply(inverse(X_7),Y))),bind(X_34,$fot(multiply(inverse(X_8),Y)))]]) ).
cnf(refute_0_261,plain,
( divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) != X_8
| divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) != multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y)))
| multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))),X_8) ),[0],$fot(multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y))))]]) ).
cnf(refute_0_262,plain,
( divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))) != X_8
| multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))),multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
multiply(X_7,divide(multiply(inverse(X_7),Y),multiply(inverse(X_8),Y))) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(multiply(inverse(X_8),Y),multiply(inverse(X_7),Y))),X_8) )],[refute_0_173,refute_0_262]) ).
cnf(refute_0_264,plain,
multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) = X_45,
inference(subst,[],[refute_0_263:[bind(Y,$fot(X_43)),bind(X_7,$fot(inverse(X_7))),bind(X_8,$fot(X_45))]]) ).
cnf(refute_0_265,plain,
( multiply(X_7,multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))) != divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))
| multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) != X_45
| multiply(X_7,X_45) = divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_7,multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) ),[0,1],$fot(X_45)]]) ).
cnf(refute_0_266,plain,
( multiply(X_7,multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))) != divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))
| multiply(X_7,X_45) = divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))),X_45) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
multiply(X_7,X_45) = divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),
inference(resolve,[$cnf( $equal(multiply(X_7,multiply(inverse(X_7),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) )],[refute_0_154,refute_0_266]) ).
cnf(refute_0_268,plain,
multiply(inverse(inverse(X_7)),X_43) = multiply(inverse(inverse(X_7)),X_43),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_7)),X_43))]]) ).
cnf(refute_0_269,plain,
( multiply(inverse(inverse(X_7)),X_43) != multiply(inverse(inverse(X_7)),X_43)
| inverse(inverse(X_7)) != X_7
| multiply(inverse(inverse(X_7)),X_43) = multiply(X_7,X_43) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(inverse(X_7)),X_43)) ),[1,0],$fot(X_7)]]) ).
cnf(refute_0_270,plain,
( inverse(inverse(X_7)) != X_7
| multiply(inverse(inverse(X_7)),X_43) = multiply(X_7,X_43) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(inverse(X_7)),X_43)) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
multiply(inverse(inverse(X_7)),X_43) = multiply(X_7,X_43),
inference(resolve,[$cnf( $equal(inverse(inverse(X_7)),X_7) )],[refute_0_139,refute_0_270]) ).
cnf(refute_0_272,plain,
divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) = divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),
introduced(tautology,[refl,[$fot(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))]]) ).
cnf(refute_0_273,plain,
( multiply(inverse(inverse(X_7)),X_43) != multiply(X_7,X_43)
| divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) != divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))
| divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) ),[1,0],$fot(multiply(X_7,X_43))]]) ).
cnf(refute_0_274,plain,
( multiply(inverse(inverse(X_7)),X_43) != multiply(X_7,X_43)
| divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)) ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_7)),X_43),multiply(X_7,X_43)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( multiply(X_7,X_45) != divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))
| divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)) != divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43))
| multiply(X_7,X_45) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_7,X_45),divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43))) ),[0],$fot(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)))]]) ).
cnf(refute_0_277,plain,
( multiply(X_7,X_45) != divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))
| multiply(X_7,X_45) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)) ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43)),divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
multiply(X_7,X_45) = divide(multiply(X_7,X_43),multiply(inverse(X_45),X_43)),
inference(resolve,[$cnf( $equal(multiply(X_7,X_45),divide(multiply(inverse(inverse(X_7)),X_43),multiply(inverse(X_45),X_43))) )],[refute_0_267,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(X_50,multiply(X_48,X_37)) = divide(multiply(X_50,X_48),multiply(inverse(multiply(X_48,X_37)),X_48)),
inference(subst,[],[refute_0_278:[bind(X_43,$fot(X_48)),bind(X_45,$fot(multiply(X_48,X_37))),bind(X_7,$fot(X_50))]]) ).
cnf(refute_0_280,plain,
multiply(divide(inverse(X_37),Y),Y) = inverse(X_37),
inference(subst,[],[refute_0_247:[bind(X_21,$fot(inverse(X_37)))]]) ).
cnf(refute_0_281,plain,
divide(inverse(Y),X_33) = inverse(divide(X_33,inverse(Y))),
inference(subst,[],[refute_0_251:[bind(X_21,$fot(X_33)),bind(X_31,$fot(inverse(Y)))]]) ).
cnf(refute_0_282,plain,
multiply(X_33,Y) = divide(X_33,inverse(Y)),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_283,plain,
( multiply(X_33,Y) != divide(X_33,inverse(Y))
| divide(X_33,inverse(Y)) = multiply(X_33,Y) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_33,Y))),bind(Y0,$fot(divide(X_33,inverse(Y))))]]) ).
cnf(refute_0_284,plain,
divide(X_33,inverse(Y)) = multiply(X_33,Y),
inference(resolve,[$cnf( $equal(multiply(X_33,Y),divide(X_33,inverse(Y))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( divide(X_33,inverse(Y)) != multiply(X_33,Y)
| divide(inverse(Y),X_33) != inverse(divide(X_33,inverse(Y)))
| divide(inverse(Y),X_33) = inverse(multiply(X_33,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(Y),X_33),inverse(divide(X_33,inverse(Y)))) ),[1,0],$fot(multiply(X_33,Y))]]) ).
cnf(refute_0_286,plain,
( divide(inverse(Y),X_33) != inverse(divide(X_33,inverse(Y)))
| divide(inverse(Y),X_33) = inverse(multiply(X_33,Y)) ),
inference(resolve,[$cnf( $equal(divide(X_33,inverse(Y)),multiply(X_33,Y)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
divide(inverse(Y),X_33) = inverse(multiply(X_33,Y)),
inference(resolve,[$cnf( $equal(divide(inverse(Y),X_33),inverse(divide(X_33,inverse(Y)))) )],[refute_0_281,refute_0_286]) ).
cnf(refute_0_288,plain,
divide(inverse(X_37),Y) = inverse(multiply(Y,X_37)),
inference(subst,[],[refute_0_287:[bind(Y,$fot(X_37)),bind(X_33,$fot(Y))]]) ).
cnf(refute_0_289,plain,
( multiply(divide(inverse(X_37),Y),Y) != inverse(X_37)
| divide(inverse(X_37),Y) != inverse(multiply(Y,X_37))
| multiply(inverse(multiply(Y,X_37)),Y) = inverse(X_37) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(inverse(X_37),Y),Y),inverse(X_37)) ),[0,0],$fot(inverse(multiply(Y,X_37)))]]) ).
cnf(refute_0_290,plain,
( multiply(divide(inverse(X_37),Y),Y) != inverse(X_37)
| multiply(inverse(multiply(Y,X_37)),Y) = inverse(X_37) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_37),Y),inverse(multiply(Y,X_37))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
multiply(inverse(multiply(Y,X_37)),Y) = inverse(X_37),
inference(resolve,[$cnf( $equal(multiply(divide(inverse(X_37),Y),Y),inverse(X_37)) )],[refute_0_280,refute_0_290]) ).
cnf(refute_0_292,plain,
multiply(inverse(multiply(X_48,X_37)),X_48) = inverse(X_37),
inference(subst,[],[refute_0_291:[bind(Y,$fot(X_48))]]) ).
cnf(refute_0_293,plain,
( multiply(X_50,multiply(X_48,X_37)) != divide(multiply(X_50,X_48),multiply(inverse(multiply(X_48,X_37)),X_48))
| multiply(inverse(multiply(X_48,X_37)),X_48) != inverse(X_37)
| multiply(X_50,multiply(X_48,X_37)) = divide(multiply(X_50,X_48),inverse(X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_50,multiply(X_48,X_37)),divide(multiply(X_50,X_48),multiply(inverse(multiply(X_48,X_37)),X_48))) ),[1,1],$fot(inverse(X_37))]]) ).
cnf(refute_0_294,plain,
( multiply(X_50,multiply(X_48,X_37)) != divide(multiply(X_50,X_48),multiply(inverse(multiply(X_48,X_37)),X_48))
| multiply(X_50,multiply(X_48,X_37)) = divide(multiply(X_50,X_48),inverse(X_37)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_48,X_37)),X_48),inverse(X_37)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
multiply(X_50,multiply(X_48,X_37)) = divide(multiply(X_50,X_48),inverse(X_37)),
inference(resolve,[$cnf( $equal(multiply(X_50,multiply(X_48,X_37)),divide(multiply(X_50,X_48),multiply(inverse(multiply(X_48,X_37)),X_48))) )],[refute_0_279,refute_0_294]) ).
cnf(refute_0_296,plain,
divide(multiply(X_50,X_48),inverse(X_37)) = multiply(multiply(X_50,X_48),X_37),
inference(subst,[],[refute_0_78:[bind(X,$fot(multiply(X_50,X_48))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_297,plain,
( multiply(X_50,multiply(X_48,X_37)) != divide(multiply(X_50,X_48),inverse(X_37))
| divide(multiply(X_50,X_48),inverse(X_37)) != multiply(multiply(X_50,X_48),X_37)
| multiply(X_50,multiply(X_48,X_37)) = multiply(multiply(X_50,X_48),X_37) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_50,multiply(X_48,X_37)),multiply(multiply(X_50,X_48),X_37)) ),[0],$fot(divide(multiply(X_50,X_48),inverse(X_37)))]]) ).
cnf(refute_0_298,plain,
( multiply(X_50,multiply(X_48,X_37)) != divide(multiply(X_50,X_48),inverse(X_37))
| multiply(X_50,multiply(X_48,X_37)) = multiply(multiply(X_50,X_48),X_37) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_50,X_48),inverse(X_37)),multiply(multiply(X_50,X_48),X_37)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
multiply(X_50,multiply(X_48,X_37)) = multiply(multiply(X_50,X_48),X_37),
inference(resolve,[$cnf( $equal(multiply(X_50,multiply(X_48,X_37)),divide(multiply(X_50,X_48),inverse(X_37))) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
( multiply(X_50,multiply(X_48,X_37)) != multiply(multiply(X_50,X_48),X_37)
| multiply(multiply(X_50,X_48),X_37) = multiply(X_50,multiply(X_48,X_37)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_50,multiply(X_48,X_37)))),bind(Y0,$fot(multiply(multiply(X_50,X_48),X_37)))]]) ).
cnf(refute_0_301,plain,
multiply(multiply(X_50,X_48),X_37) = multiply(X_50,multiply(X_48,X_37)),
inference(resolve,[$cnf( $equal(multiply(X_50,multiply(X_48,X_37)),multiply(multiply(X_50,X_48),X_37)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_301:[bind(X_37,$fot(c3)),bind(X_48,$fot(b3)),bind(X_50,$fot(a3))]]) ).
cnf(refute_0_303,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_304,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_304,refute_0_153]) ).
cnf(refute_0_306,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_307,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_306,refute_0_305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 10:46:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.44
%------------------------------------------------------------------------------