TSTP Solution File: GRP496-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP496-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 10:41:44 EDT 2022
% Result : Unsatisfiable 0.09s 0.28s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of clauses : 76 ( 41 unt; 0 nHn; 41 RR)
% Number of literals : 127 ( 126 equ; 54 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ).
cnf(multiply,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity) ).
cnf(inverse,axiom,
inverse(A) = double_divide(A,identity) ).
cnf(identity,axiom,
identity = double_divide(A,inverse(A)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity ).
cnf(refute_0_0,plain,
identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_2,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_3,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_5,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_5:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_7,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| double_divide(double_divide(B,A),identity) != inverse(double_divide(B,A))
| multiply(A,B) = inverse(double_divide(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),inverse(double_divide(B,A))) ),[0],$fot(double_divide(double_divide(B,A),identity))]]) ).
cnf(refute_0_8,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_11,plain,
( multiply(X_2,X_3) != inverse(double_divide(X_3,X_2))
| inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_2,X_3))),bind(Y,$fot(inverse(double_divide(X_3,X_2))))]]) ).
cnf(refute_0_12,plain,
inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_14,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_0,refute_0_14]) ).
cnf(refute_0_16,plain,
identity = double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),
inference(subst,[],[refute_0_15:[bind(X_2,$fot(double_divide(inverse(identity),inverse(identity)))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_17,plain,
double_divide(double_divide(B,double_divide(C,A)),identity) = inverse(double_divide(B,double_divide(C,A))),
inference(subst,[],[refute_0_5:[bind(A,$fot(double_divide(B,double_divide(C,A))))]]) ).
cnf(refute_0_18,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).
cnf(refute_0_19,plain,
( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,1],$fot(inverse(double_divide(B,double_divide(C,A))))]]) ).
cnf(refute_0_20,plain,
( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,double_divide(C,A)),identity),inverse(double_divide(B,double_divide(C,A)))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_5:[bind(A,$fot(B))]]) ).
cnf(refute_0_23,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(B,identity)))]]) ).
cnf(refute_0_24,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,double_divide(B,identity))
| double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_25,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(A,double_divide(B,identity))))]]) ).
cnf(refute_0_28,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,double_divide(B,identity)))
| double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) ),[1,1],$fot(double_divide(A,inverse(B)))]]) ).
cnf(refute_0_29,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,inverse(B))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).
cnf(refute_0_32,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,0],$fot(double_divide(identity,double_divide(A,inverse(B))))]]) ).
cnf(refute_0_33,plain,
( double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,inverse(B)))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_35]) ).
cnf(refute_0_37,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Y,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Z,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))))]]) ).
cnf(refute_0_38,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_21,refute_0_38]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).
cnf(refute_0_41,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) )],[single_axiom,refute_0_41]) ).
cnf(refute_0_43,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_44,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_9,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(double_divide(B,double_divide(C,A))) = multiply(double_divide(C,A),B),
inference(subst,[],[refute_0_44:[bind(A,$fot(double_divide(C,A)))]]) ).
cnf(refute_0_46,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).
cnf(refute_0_47,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) ),[1,1],$fot(multiply(double_divide(C,A),B))]]) ).
cnf(refute_0_48,plain,
( inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,double_divide(C,A))),multiply(double_divide(C,A),B)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)))]]) ).
cnf(refute_0_51,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) = inverse(identity),
inference(subst,[],[refute_0_52:[bind(A,$fot(inverse(identity))),bind(B,$fot(identity)),bind(C,$fot(inverse(identity)))]]) ).
cnf(refute_0_54,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) != inverse(identity)
| identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_55,plain,
( identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),inverse(identity)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) )],[refute_0_16,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_9:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_58,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_59,plain,
( identity != double_divide(X_3,inverse(X_3))
| double_divide(X_3,inverse(X_3)) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_3,inverse(X_3))))]]) ).
cnf(refute_0_60,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_62,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| multiply(inverse(X_3),X_3) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_63:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_65,plain,
( multiply(inverse(a1),a1) != inverse(identity)
| inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_66,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_66,prove_these_axioms_1]) ).
cnf(refute_0_68,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_69,plain,
identity != inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_68,refute_0_67]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_56,refute_0_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GRP496-1 : TPTP v8.1.0. Released v2.6.0.
% 0.02/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 600
% 0.09/0.27 % DateTime : Mon Jun 13 21:45:12 EDT 2022
% 0.09/0.27 % CPUTime :
% 0.09/0.28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.28
% 0.09/0.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.09/0.29
%------------------------------------------------------------------------------