TSTP Solution File: GRP493-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP493-1 : 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 10:41:43 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of clauses : 86 ( 46 unt; 0 nHn; 46 RR)
% Number of literals : 143 ( 142 equ; 60 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ).
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(B,C),double_divide(identity,identity)) = double_divide(double_divide(B,C),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(B,C),double_divide(identity,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(double_divide(B,C),double_divide(identity,identity)) != double_divide(double_divide(B,C),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(B,C),double_divide(identity,identity)) = double_divide(double_divide(B,C),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(double_divide(B,C),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_8,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(B,C),double_divide(identity,identity)) = double_divide(double_divide(B,C),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(double_divide(B,C),double_divide(identity,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(double_divide(B,C),double_divide(identity,identity)) = double_divide(double_divide(B,C),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) = double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))]]) ).
cnf(refute_0_11,plain,
( double_divide(double_divide(B,C),double_divide(identity,identity)) != double_divide(double_divide(B,C),inverse(identity))
| double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) != double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))
| double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) = double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) ),[1,0],$fot(double_divide(double_divide(B,C),inverse(identity)))]]) ).
cnf(refute_0_12,plain,
( double_divide(double_divide(B,C),double_divide(identity,identity)) != double_divide(double_divide(B,C),inverse(identity))
| double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) = double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) = double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(double_divide(B,C),inverse(identity))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))))]]) ).
cnf(refute_0_15,plain,
( double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) != double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) != double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))) ),[1,1],$fot(double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)))]]) ).
cnf(refute_0_16,plain,
( double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)) != double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) != B
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) != double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)))
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),B) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))))]]) ).
cnf(refute_0_19,plain,
( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) != B
| double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) = B ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),inverse(identity)),double_divide(A,C))) = B,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))),B) )],[single_axiom,refute_0_19]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(identity,X_10),double_divide(double_divide(double_divide(X_11,inverse(X_11)),inverse(identity)),double_divide(X_10,inverse(X_11)))) = X_11,
inference(subst,[],[refute_0_20:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(X_11)))]]) ).
cnf(refute_0_22,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_23,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_24,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(double_divide(identity,X_10),double_divide(double_divide(double_divide(X_11,inverse(X_11)),inverse(identity)),double_divide(X_10,inverse(X_11)))) != X_11
| double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(double_divide(X_11,inverse(X_11)),inverse(identity)),double_divide(X_10,inverse(X_11)))),X_11) ),[0,1,0,0],$fot(identity)]]) ).
cnf(refute_0_26,plain,
( double_divide(double_divide(identity,X_10),double_divide(double_divide(double_divide(X_11,inverse(X_11)),inverse(identity)),double_divide(X_10,inverse(X_11)))) != X_11
| double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(double_divide(X_11,inverse(X_11)),inverse(identity)),double_divide(X_10,inverse(X_11)))),X_11) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_29,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(identity,inverse(identity)) = identity,
inference(subst,[],[refute_0_29:[bind(A,$fot(identity))]]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) = double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))))]]) ).
cnf(refute_0_32,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) != double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) = double_divide(identity,double_divide(X_10,inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_33,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) = double_divide(identity,double_divide(X_10,inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) = double_divide(identity,double_divide(X_10,inverse(X_11))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))))]]) ).
cnf(refute_0_36,plain,
( double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) != double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))))
| double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) != double_divide(identity,double_divide(X_10,inverse(X_11)))
| double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))))) ),[1,1],$fot(double_divide(identity,double_divide(X_10,inverse(X_11))))]]) ).
cnf(refute_0_37,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))) != double_divide(identity,double_divide(X_10,inverse(X_11)))
| double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11))),double_divide(identity,double_divide(X_10,inverse(X_11)))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) != X_11
| double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11))))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),X_11) ),[0],$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))))]]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))) != X_11
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11))))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(X_10,inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(double_divide(identity,inverse(identity)),double_divide(X_10,inverse(X_11)))),X_11) )],[refute_0_27,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(double_divide(identity,X_14),double_divide(identity,double_divide(X_14,inverse(X_14)))) = X_14,
inference(subst,[],[refute_0_41:[bind(X_10,$fot(X_14)),bind(X_11,$fot(X_14))]]) ).
cnf(refute_0_43,plain,
identity = double_divide(X_14,inverse(X_14)),
inference(subst,[],[identity:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
( identity != double_divide(X_14,inverse(X_14))
| double_divide(X_14,inverse(X_14)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_14,inverse(X_14))))]]) ).
cnf(refute_0_45,plain,
double_divide(X_14,inverse(X_14)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_14,inverse(X_14))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( double_divide(X_14,inverse(X_14)) != identity
| double_divide(double_divide(identity,X_14),double_divide(identity,double_divide(X_14,inverse(X_14)))) != X_14
| double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,double_divide(X_14,inverse(X_14)))),X_14) ),[0,1,1],$fot(identity)]]) ).
cnf(refute_0_47,plain,
( double_divide(double_divide(identity,X_14),double_divide(identity,double_divide(X_14,inverse(X_14)))) != X_14
| double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(X_14,inverse(X_14)),identity) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,double_divide(X_14,inverse(X_14)))),X_14) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = double_divide(double_divide(identity,X_14),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_14),double_divide(identity,identity)))]]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(identity,X_14),double_divide(identity,identity)) != double_divide(double_divide(identity,X_14),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = double_divide(double_divide(identity,X_14),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,identity)),double_divide(double_divide(identity,X_14),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_51,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = double_divide(double_divide(identity,X_14),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,identity)),double_divide(double_divide(identity,X_14),double_divide(identity,identity))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(identity,X_14),double_divide(identity,identity)) = double_divide(double_divide(identity,X_14),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_51]) ).
cnf(refute_0_53,plain,
( double_divide(double_divide(identity,X_14),double_divide(identity,identity)) != X_14
| double_divide(double_divide(identity,X_14),double_divide(identity,identity)) != double_divide(double_divide(identity,X_14),inverse(identity))
| double_divide(double_divide(identity,X_14),inverse(identity)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,identity)),X_14) ),[0],$fot(double_divide(double_divide(identity,X_14),inverse(identity)))]]) ).
cnf(refute_0_54,plain,
( double_divide(double_divide(identity,X_14),double_divide(identity,identity)) != X_14
| double_divide(double_divide(identity,X_14),inverse(identity)) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,identity)),double_divide(double_divide(identity,X_14),inverse(identity))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
double_divide(double_divide(identity,X_14),inverse(identity)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_14),double_divide(identity,identity)),X_14) )],[refute_0_48,refute_0_54]) ).
cnf(refute_0_56,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(subst,[],[refute_0_55:[bind(X_14,$fot(inverse(identity)))]]) ).
cnf(refute_0_57,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != inverse(identity)
| double_divide(identity,inverse(identity)) != identity
| double_divide(identity,inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_58,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != inverse(identity)
| double_divide(identity,inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_30,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(identity,inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(identity)),inverse(identity)) ),[0],$fot(identity)]]) ).
cnf(refute_0_61,plain,
( double_divide(identity,inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_30,refute_0_60]) ).
cnf(refute_0_62,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),inverse(identity)) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_64,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_65,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_66:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_68,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_69,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_70,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_72,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_73:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_75,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_76,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_76,prove_these_axioms_1]) ).
cnf(refute_0_78,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_79,plain,
identity != inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
$false,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_62,refute_0_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP493-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 13:31:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------