%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:41:38 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 39
% Syntax : Number of clauses : 140 ( 73 unt; 0 nHn; 86 RR)
% Number of literals : 237 ( 236 equ; 99 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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 : 175 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,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,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_6,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_8,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_11,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))]]) ).
cnf(refute_0_12,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_13,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))))]]) ).
cnf(refute_0_16,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))) ),[1,1],$fot(double_divide(double_divide(double_divide(A,B),C),inverse(B)))]]) ).
cnf(refute_0_17,plain,
( double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),inverse(B))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)))]]) ).
cnf(refute_0_20,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))) ),[1,0],$fot(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))))]]) ).
cnf(refute_0_21,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)))),bind(Y,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)))),bind(Z,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))))]]) ).
cnf(refute_0_26,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))) )],[refute_0_9,refute_0_26]) ).
cnf(refute_0_28,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),C) ),[0],$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)))]]) ).
cnf(refute_0_29,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),C) )],[single_axiom,refute_0_29]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(inverse(X_10))),bind(C,$fot(X_12))]]) ).
cnf(refute_0_32,plain,
identity = double_divide(X_10,inverse(X_10)),
inference(subst,[],[identity:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_33,plain,
( identity != double_divide(X_10,inverse(X_10))
| double_divide(X_10,inverse(X_10)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_10,inverse(X_10))))]]) ).
cnf(refute_0_34,plain,
double_divide(X_10,inverse(X_10)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_10,inverse(X_10))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( double_divide(X_10,inverse(X_10)) != identity
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) ),[0,0,1,0,0],$fot(identity)]]) ).
cnf(refute_0_36,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(X_10)),identity) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(X_13,double_divide(double_divide(identity,identity),inverse(inverse(X_13)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_37:[bind(X_10,$fot(X_13)),bind(X_12,$fot(identity))]]) ).
cnf(refute_0_39,plain,
( double_divide(double_divide(X_13,double_divide(double_divide(identity,identity),inverse(inverse(X_13)))),inverse(identity)) != identity
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(double_divide(identity,identity),inverse(inverse(X_13)))),inverse(identity)),identity) ),[0,0,1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(X_13,double_divide(double_divide(identity,identity),inverse(inverse(X_13)))),inverse(identity)) != identity
| double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_39]) ).
cnf(refute_0_41,plain,
double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(double_divide(identity,identity),inverse(inverse(X_13)))),inverse(identity)),identity) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_41:[bind(X_13,$fot(identity))]]) ).
cnf(refute_0_43,plain,
identity = double_divide(inverse(identity),inverse(inverse(identity))),
inference(subst,[],[identity:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_44,plain,
( identity != double_divide(inverse(identity),inverse(inverse(identity)))
| double_divide(inverse(identity),inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(inverse(identity),inverse(inverse(identity)))))]]) ).
cnf(refute_0_45,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)),identity) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_47,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),identity) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)),identity) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(double_divide(identity,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),inverse(identity)))]]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(double_divide(identity,identity),inverse(identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(double_divide(identity,identity),inverse(identity))) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_51,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(double_divide(identity,identity),inverse(identity))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_51]) ).
cnf(refute_0_53,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(inverse(identity),inverse(identity))
| double_divide(double_divide(identity,identity),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),identity) ),[0],$fot(double_divide(inverse(identity),inverse(identity)))]]) ).
cnf(refute_0_54,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(inverse(identity),inverse(identity))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),identity) )],[refute_0_48,refute_0_54]) ).
cnf(refute_0_56,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) = inverse(identity),
inference(subst,[],[refute_0_30:[bind(B,$fot(double_divide(inverse(identity),inverse(inverse(A))))),bind(C,$fot(inverse(identity)))]]) ).
cnf(refute_0_57,plain,
double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_41:[bind(X_13,$fot(A))]]) ).
cnf(refute_0_58,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) != inverse(identity)
| double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)) != identity
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)),inverse(identity)) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_59,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) != inverse(identity)
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),identity) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(inverse(identity),inverse(inverse(A)))),inverse(identity)),inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)),inverse(identity)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)),
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(double_divide(X_10,X_11))))]]) ).
cnf(refute_0_62,plain,
identity = double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_63,plain,
( identity != double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))
| double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))))]]) ).
cnf(refute_0_64,plain,
double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) != identity
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_66,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),identity) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_69,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_70,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_70]) ).
cnf(refute_0_72,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_73,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
inverse(double_divide(X_10,X_11)) = multiply(X_11,X_10),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_11)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_75,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| inverse(double_divide(X_10,X_11)) != multiply(X_11,X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_11,X_10)) ),[0],$fot(inverse(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_76,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,X_11)),multiply(X_11,X_10)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) )],[refute_0_67,refute_0_76]) ).
cnf(refute_0_78,plain,
double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) = multiply(double_divide(inverse(identity),inverse(inverse(A))),A),
inference(subst,[],[refute_0_77:[bind(X_10,$fot(A)),bind(X_11,$fot(double_divide(inverse(identity),inverse(inverse(A)))))]]) ).
cnf(refute_0_79,plain,
( double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) != multiply(double_divide(inverse(identity),inverse(inverse(A))),A)
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) != inverse(identity)
| multiply(double_divide(inverse(identity),inverse(inverse(A))),A) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)),inverse(identity)) ),[0],$fot(multiply(double_divide(inverse(identity),inverse(inverse(A))),A))]]) ).
cnf(refute_0_80,plain,
( double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)) != inverse(identity)
| multiply(double_divide(inverse(identity),inverse(inverse(A))),A) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)),multiply(double_divide(inverse(identity),inverse(inverse(A))),A)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(double_divide(inverse(identity),inverse(inverse(A))),A) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(inverse(identity),inverse(inverse(A)))))),inverse(identity)),inverse(identity)) )],[refute_0_60,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(double_divide(inverse(identity),inverse(inverse(identity))),identity) = inverse(identity),
inference(subst,[],[refute_0_81:[bind(A,$fot(identity))]]) ).
cnf(refute_0_83,plain,
( multiply(double_divide(inverse(identity),inverse(inverse(identity))),identity) != inverse(identity)
| double_divide(inverse(identity),inverse(inverse(identity))) != identity
| multiply(identity,identity) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(inverse(identity))),identity),inverse(identity)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_84,plain,
( multiply(double_divide(inverse(identity),inverse(inverse(identity))),identity) != inverse(identity)
| multiply(identity,identity) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),identity) )],[refute_0_45,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(inverse(identity))),identity),inverse(identity)) )],[refute_0_82,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_71:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_87,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_88,plain,
( inverse(X_3) != double_divide(X_3,identity)
| double_divide(X_3,identity) = inverse(X_3) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(double_divide(X_3,identity)))]]) ).
cnf(refute_0_89,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_91,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(identity,identity) = inverse(inverse(identity)),
inference(subst,[],[refute_0_92:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_94,plain,
( multiply(identity,identity) != inverse(identity)
| multiply(identity,identity) != inverse(inverse(identity))
| inverse(inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,identity),inverse(identity)) ),[0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_95,plain,
( multiply(identity,identity) != inverse(identity)
| inverse(inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
inverse(inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(identity)) )],[refute_0_85,refute_0_95]) ).
cnf(refute_0_97,plain,
double_divide(double_divide(X_28,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(identity,X_28),
inference(subst,[],[refute_0_77:[bind(X_10,$fot(X_28)),bind(X_11,$fot(identity))]]) ).
cnf(refute_0_98,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_99,plain,
( identity != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_100,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( double_divide(double_divide(X_28,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(identity,X_28)
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(X_28,identity),inverse(identity)) = multiply(identity,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_28,double_divide(identity,inverse(identity))),inverse(identity)),multiply(identity,X_28)) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_102,plain,
( double_divide(double_divide(X_28,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(identity,X_28)
| double_divide(double_divide(X_28,identity),inverse(identity)) = multiply(identity,X_28) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
double_divide(double_divide(X_28,identity),inverse(identity)) = multiply(identity,X_28),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_28,double_divide(identity,inverse(identity))),inverse(identity)),multiply(identity,X_28)) )],[refute_0_97,refute_0_102]) ).
cnf(refute_0_104,plain,
double_divide(X_28,identity) = inverse(X_28),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_28))]]) ).
cnf(refute_0_105,plain,
double_divide(double_divide(X_28,identity),inverse(identity)) = double_divide(double_divide(X_28,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_28,identity),inverse(identity)))]]) ).
cnf(refute_0_106,plain,
( double_divide(X_28,identity) != inverse(X_28)
| double_divide(double_divide(X_28,identity),inverse(identity)) != double_divide(double_divide(X_28,identity),inverse(identity))
| double_divide(double_divide(X_28,identity),inverse(identity)) = double_divide(inverse(X_28),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_28,identity),inverse(identity)),double_divide(double_divide(X_28,identity),inverse(identity))) ),[1,0],$fot(inverse(X_28))]]) ).
cnf(refute_0_107,plain,
( double_divide(X_28,identity) != inverse(X_28)
| double_divide(double_divide(X_28,identity),inverse(identity)) = double_divide(inverse(X_28),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_28,identity),inverse(identity)),double_divide(double_divide(X_28,identity),inverse(identity))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
double_divide(double_divide(X_28,identity),inverse(identity)) = double_divide(inverse(X_28),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_28,identity),inverse(X_28)) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( double_divide(double_divide(X_28,identity),inverse(identity)) != multiply(identity,X_28)
| double_divide(double_divide(X_28,identity),inverse(identity)) != double_divide(inverse(X_28),inverse(identity))
| double_divide(inverse(X_28),inverse(identity)) = multiply(identity,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_28,identity),inverse(identity)),multiply(identity,X_28)) ),[0],$fot(double_divide(inverse(X_28),inverse(identity)))]]) ).
cnf(refute_0_110,plain,
( double_divide(double_divide(X_28,identity),inverse(identity)) != multiply(identity,X_28)
| double_divide(inverse(X_28),inverse(identity)) = multiply(identity,X_28) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_28,identity),inverse(identity)),double_divide(inverse(X_28),inverse(identity))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(identity,X_28) = inverse(inverse(X_28)),
inference(subst,[],[refute_0_92:[bind(X_3,$fot(X_28))]]) ).
cnf(refute_0_112,plain,
( multiply(identity,X_28) != inverse(inverse(X_28))
| double_divide(inverse(X_28),inverse(identity)) != multiply(identity,X_28)
| double_divide(inverse(X_28),inverse(identity)) = inverse(inverse(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_28),inverse(identity)),multiply(identity,X_28)) ),[1],$fot(inverse(inverse(X_28)))]]) ).
cnf(refute_0_113,plain,
( double_divide(inverse(X_28),inverse(identity)) != multiply(identity,X_28)
| double_divide(inverse(X_28),inverse(identity)) = inverse(inverse(X_28)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_28),inverse(inverse(X_28))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( double_divide(double_divide(X_28,identity),inverse(identity)) != multiply(identity,X_28)
| double_divide(inverse(X_28),inverse(identity)) = inverse(inverse(X_28)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_28),inverse(identity)),multiply(identity,X_28)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
double_divide(inverse(X_28),inverse(identity)) = inverse(inverse(X_28)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_28,identity),inverse(identity)),multiply(identity,X_28)) )],[refute_0_103,refute_0_114]) ).
cnf(refute_0_116,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)),
inference(subst,[],[refute_0_115:[bind(X_28,$fot(identity))]]) ).
cnf(refute_0_117,plain,
( double_divide(inverse(identity),inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) != inverse(identity)
| double_divide(inverse(identity),inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(identity),inverse(identity)))),bind(Y,$fot(inverse(inverse(identity)))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_118,plain,
( inverse(inverse(identity)) != inverse(identity)
| double_divide(inverse(identity),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(identity)) )],[refute_0_96,refute_0_118]) ).
cnf(refute_0_120,plain,
( double_divide(inverse(identity),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(identity)) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_121,plain,
( double_divide(inverse(identity),inverse(identity)) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(identity)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),identity) )],[refute_0_55,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_71:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_124,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_125,plain,
( identity != double_divide(X_3,inverse(X_3))
| double_divide(X_3,inverse(X_3)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_3,inverse(X_3))))]]) ).
cnf(refute_0_126,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_128,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_129:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_131,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_132,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_132,prove_these_axioms_1]) ).
cnf(refute_0_134,plain,
$false,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_122,refute_0_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 11:35:52 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.39
% 0.18/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.42
%------------------------------------------------------------------------------