TSTP Solution File: GRP481-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 10:41:37 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 34
% Syntax : Number of clauses : 114 ( 60 unt; 0 nHn; 54 RR)
% Number of literals : 193 ( 192 equ; 82 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 215 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = 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(inverse(identity),inverse(inverse(identity))),
inference(subst,[],[identity:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(C),double_divide(A,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),double_divide(A,identity))
| double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) ),[1,1],$fot(inverse(A))]]) ).
cnf(refute_0_8,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)),
inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
double_divide(C,identity) = inverse(C),
inference(subst,[],[refute_0_5:[bind(A,$fot(C))]]) ).
cnf(refute_0_11,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_12,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_11]) ).
cnf(refute_0_13,plain,
double_divide(D,inverse(D)) = identity,
inference(subst,[],[refute_0_12:[bind(A,$fot(D))]]) ).
cnf(refute_0_14,plain,
double_divide(D,identity) = inverse(D),
inference(subst,[],[refute_0_5:[bind(A,$fot(D))]]) ).
cnf(refute_0_15,plain,
double_divide(D,double_divide(D,identity)) = double_divide(D,double_divide(D,identity)),
introduced(tautology,[refl,[$fot(double_divide(D,double_divide(D,identity)))]]) ).
cnf(refute_0_16,plain,
( double_divide(D,double_divide(D,identity)) != double_divide(D,double_divide(D,identity))
| double_divide(D,identity) != inverse(D)
| double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,double_divide(D,identity))) ),[1,1],$fot(inverse(D))]]) ).
cnf(refute_0_17,plain,
( double_divide(D,identity) != inverse(D)
| double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)) ),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,double_divide(D,identity))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)),
inference(resolve,[$cnf( $equal(double_divide(D,identity),inverse(D)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( double_divide(D,double_divide(D,identity)) != double_divide(D,inverse(D))
| double_divide(D,inverse(D)) != identity
| double_divide(D,double_divide(D,identity)) = identity ),
inference(subst,[],[refute_0_20:[bind(X,$fot(double_divide(D,double_divide(D,identity)))),bind(Y,$fot(double_divide(D,inverse(D)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_22,plain,
( double_divide(D,inverse(D)) != identity
| double_divide(D,double_divide(D,identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,inverse(D))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
double_divide(D,double_divide(D,identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(D,inverse(D)),identity) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,double_divide(D,double_divide(D,identity))),
introduced(tautology,[refl,[$fot(double_divide(C,double_divide(D,double_divide(D,identity))))]]) ).
cnf(refute_0_25,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != double_divide(C,double_divide(D,double_divide(D,identity)))
| double_divide(D,double_divide(D,identity)) != identity
| double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,double_divide(D,double_divide(D,identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_26,plain,
( double_divide(D,double_divide(D,identity)) != identity
| double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity) ),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,double_divide(D,double_divide(D,identity)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),identity) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != double_divide(C,identity)
| double_divide(C,identity) != inverse(C)
| double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(double_divide(C,double_divide(D,double_divide(D,identity))))),bind(Y,$fot(double_divide(C,identity))),bind(Z,$fot(inverse(C)))]]) ).
cnf(refute_0_29,plain,
( double_divide(C,identity) != inverse(C)
| double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C) ),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,identity)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C),
inference(resolve,[$cnf( $equal(double_divide(C,identity),inverse(C)) )],[refute_0_10,refute_0_29]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))]]) ).
cnf(refute_0_32,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != inverse(C)
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),[1,0],$fot(inverse(C))]]) ).
cnf(refute_0_33,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != inverse(C)
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),inverse(C)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),double_divide(A,identity))
| double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))),bind(Y,$fot(double_divide(inverse(C),double_divide(A,identity)))),bind(Z,$fot(double_divide(inverse(C),inverse(A))))]]) ).
cnf(refute_0_36,plain,
( double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)),
inference(resolve,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),inverse(A))) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))]]) ).
cnf(refute_0_39,plain,
( double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) ),[1,1],$fot(double_divide(inverse(C),inverse(A)))]]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(inverse(C),inverse(A))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_5:[bind(A,$fot(B))]]) ).
cnf(refute_0_43,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(B,identity)))]]) ).
cnf(refute_0_44,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,double_divide(B,identity))
| double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_45,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))]]) ).
cnf(refute_0_48,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) ),[1,0],$fot(double_divide(A,inverse(B)))]]) ).
cnf(refute_0_49,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,inverse(B))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))),bind(Y,$fot(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))),bind(Z,$fot(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))))]]) ).
cnf(refute_0_52,plain,
( double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))) )],[refute_0_41,refute_0_52]) ).
cnf(refute_0_54,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B))]]) ).
cnf(refute_0_55,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)) ),[1,0],$fot(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))))]]) ).
cnf(refute_0_56,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
( double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != C
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B)
| double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),C) ),[0],$fot(double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B))]]) ).
cnf(refute_0_59,plain,
( double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != C
| double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),C) )],[single_axiom,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),double_divide(inverse(X_10),inverse(inverse(X_10)))),X_9) = X_10,
inference(subst,[],[refute_0_60:[bind(A,$fot(inverse(X_10))),bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_62,plain,
identity = double_divide(inverse(X_10),inverse(inverse(X_10))),
inference(subst,[],[identity:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_63,plain,
( identity != double_divide(inverse(X_10),inverse(inverse(X_10)))
| double_divide(inverse(X_10),inverse(inverse(X_10))) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(inverse(X_10),inverse(inverse(X_10)))))]]) ).
cnf(refute_0_64,plain,
double_divide(inverse(X_10),inverse(inverse(X_10))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(X_10),inverse(inverse(X_10)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),double_divide(inverse(X_10),inverse(inverse(X_10)))),X_9) != X_10
| double_divide(inverse(X_10),inverse(inverse(X_10))) != identity
| double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),double_divide(inverse(X_10),inverse(inverse(X_10)))),X_9),X_10) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_66,plain,
( double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),double_divide(inverse(X_10),inverse(inverse(X_10)))),X_9) != X_10
| double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),inverse(inverse(X_10))),identity) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),double_divide(inverse(X_10),inverse(inverse(X_10)))),X_9),X_10) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_5:[bind(A,$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( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_70]) ).
cnf(refute_0_72,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$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( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
inverse(double_divide(inverse(X_10),inverse(X_9))) = multiply(inverse(X_9),inverse(X_10)),
inference(subst,[],[refute_0_73:[bind(A,$fot(inverse(X_9))),bind(B,$fot(inverse(X_10)))]]) ).
cnf(refute_0_75,plain,
double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) = inverse(double_divide(inverse(X_10),inverse(X_9))),
inference(subst,[],[refute_0_5:[bind(A,$fot(double_divide(inverse(X_10),inverse(X_9))))]]) ).
cnf(refute_0_76,plain,
( double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) != inverse(double_divide(inverse(X_10),inverse(X_9)))
| inverse(double_divide(inverse(X_10),inverse(X_9))) != multiply(inverse(X_9),inverse(X_10))
| double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) = multiply(inverse(X_9),inverse(X_10)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity))),bind(Y,$fot(inverse(double_divide(inverse(X_10),inverse(X_9))))),bind(Z,$fot(multiply(inverse(X_9),inverse(X_10))))]]) ).
cnf(refute_0_77,plain,
( inverse(double_divide(inverse(X_10),inverse(X_9))) != multiply(inverse(X_9),inverse(X_10))
| double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) = multiply(inverse(X_9),inverse(X_10)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),inverse(double_divide(inverse(X_10),inverse(X_9)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) = multiply(inverse(X_9),inverse(X_10)),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(X_10),inverse(X_9))),multiply(inverse(X_9),inverse(X_10))) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9))]]) ).
cnf(refute_0_80,plain,
( double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) != double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9)
| double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) != multiply(inverse(X_9),inverse(X_10))
| double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = double_divide(multiply(inverse(X_9),inverse(X_10)),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9)) ),[1,0],$fot(multiply(inverse(X_9),inverse(X_10)))]]) ).
cnf(refute_0_81,plain,
( double_divide(double_divide(inverse(X_10),inverse(X_9)),identity) != multiply(inverse(X_9),inverse(X_10))
| double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = double_divide(multiply(inverse(X_9),inverse(X_10)),X_9) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) = double_divide(multiply(inverse(X_9),inverse(X_10)),X_9),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),multiply(inverse(X_9),inverse(X_10))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) != X_10
| double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) != double_divide(multiply(inverse(X_9),inverse(X_10)),X_9)
| double_divide(multiply(inverse(X_9),inverse(X_10)),X_9) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),X_10) ),[0],$fot(double_divide(multiply(inverse(X_9),inverse(X_10)),X_9))]]) ).
cnf(refute_0_84,plain,
( double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9) != X_10
| double_divide(multiply(inverse(X_9),inverse(X_10)),X_9) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),double_divide(multiply(inverse(X_9),inverse(X_10)),X_9)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
double_divide(multiply(inverse(X_9),inverse(X_10)),X_9) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_10),inverse(X_9)),identity),X_9),X_10) )],[refute_0_67,refute_0_84]) ).
cnf(refute_0_86,plain,
double_divide(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(X_11)) = X_11,
inference(subst,[],[refute_0_85:[bind(X_10,$fot(X_11)),bind(X_9,$fot(inverse(X_11)))]]) ).
cnf(refute_0_87,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_71:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_88,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_89,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_90,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_92,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(inverse(X_11)),inverse(X_11)) = inverse(identity),
inference(subst,[],[refute_0_93:[bind(X_3,$fot(inverse(X_11)))]]) ).
cnf(refute_0_95,plain,
( multiply(inverse(inverse(X_11)),inverse(X_11)) != inverse(identity)
| double_divide(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(X_11)) != X_11
| double_divide(inverse(identity),inverse(X_11)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(X_11)),X_11) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_96,plain,
( double_divide(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(X_11)) != X_11
| double_divide(inverse(identity),inverse(X_11)) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(identity)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
double_divide(inverse(identity),inverse(X_11)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(inverse(X_11)),inverse(X_11)),inverse(X_11)),X_11) )],[refute_0_86,refute_0_96]) ).
cnf(refute_0_98,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_97:[bind(X_11,$fot(inverse(identity)))]]) ).
cnf(refute_0_99,plain,
( double_divide(inverse(identity),inverse(inverse(identity))) != inverse(identity)
| identity != double_divide(inverse(identity),inverse(inverse(identity)))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_100,plain,
( identity != double_divide(inverse(identity),inverse(inverse(identity)))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) )],[refute_0_0,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_93:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_103,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_104,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_104,prove_these_axioms_1]) ).
cnf(refute_0_106,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_107,plain,
identity != inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
$false,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_101,refute_0_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 09:59:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------