TSTP Solution File: GRP581-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 10:42:36 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of clauses : 88 ( 47 unt; 0 nHn; 54 RR)
% Number of literals : 147 ( 146 equ; 62 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 : 96 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),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(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_8,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),C) ),[0],$fot(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)))]]) ).
cnf(refute_0_11,plain,
( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)),C) )],[single_axiom,refute_0_11]) ).
cnf(refute_0_13,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,double_divide(X_11,identity)))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_12:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_14,plain,
inverse(X_11) = double_divide(X_11,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_15,plain,
( inverse(X_11) != double_divide(X_11,identity)
| double_divide(X_11,identity) = inverse(X_11) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(double_divide(X_11,identity)))]]) ).
cnf(refute_0_16,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),double_divide(X_11,identity)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,double_divide(X_11,identity)))),inverse(identity)) != X_12
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,inverse(X_11)))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,double_divide(X_11,identity)))),inverse(identity)),X_12) ),[0,0,1,1,1],$fot(inverse(X_11))]]) ).
cnf(refute_0_18,plain,
( double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,double_divide(X_11,identity)))),inverse(identity)) != X_12
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,inverse(X_11)))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,inverse(X_11)))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_11),double_divide(X_12,double_divide(X_11,identity)))),inverse(identity)),X_12) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),double_divide(X_13,inverse(X_13)))),inverse(identity)) = X_13,
inference(subst,[],[refute_0_19:[bind(X_11,$fot(X_13)),bind(X_12,$fot(X_13))]]) ).
cnf(refute_0_21,plain,
identity = double_divide(X_13,inverse(X_13)),
inference(subst,[],[identity:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_22,plain,
( identity != double_divide(X_13,inverse(X_13))
| double_divide(X_13,inverse(X_13)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_13,inverse(X_13))))]]) ).
cnf(refute_0_23,plain,
double_divide(X_13,inverse(X_13)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_13,inverse(X_13))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( double_divide(X_13,inverse(X_13)) != identity
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),double_divide(X_13,inverse(X_13)))),inverse(identity)) != X_13
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),double_divide(X_13,inverse(X_13)))),inverse(identity)),X_13) ),[0,0,1,1],$fot(identity)]]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),double_divide(X_13,inverse(X_13)))),inverse(identity)) != X_13
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = X_13 ),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(X_13)),identity) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = X_13,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),double_divide(X_13,inverse(X_13)))),inverse(identity)),X_13) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_28,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_29,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_32,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
inverse(double_divide(identity,X_13)) = multiply(X_13,identity),
inference(subst,[],[refute_0_32:[bind(A,$fot(X_13)),bind(B,$fot(identity))]]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(identity,X_13),identity) = inverse(double_divide(identity,X_13)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,X_13)))]]) ).
cnf(refute_0_35,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_35]) ).
cnf(refute_0_37,plain,
( double_divide(double_divide(identity,X_13),identity) != inverse(double_divide(identity,X_13))
| inverse(double_divide(identity,X_13)) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(double_divide(double_divide(identity,X_13),identity))),bind(Y,$fot(inverse(double_divide(identity,X_13)))),bind(Z,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_38,plain,
( inverse(double_divide(identity,X_13)) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),identity),inverse(double_divide(identity,X_13))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,X_13)),multiply(X_13,identity)) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
double_divide(identity,double_divide(double_divide(identity,X_13),identity)) = double_divide(identity,double_divide(double_divide(identity,X_13),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(identity,X_13),identity)))]]) ).
cnf(refute_0_41,plain,
( double_divide(double_divide(identity,X_13),identity) != multiply(X_13,identity)
| double_divide(identity,double_divide(double_divide(identity,X_13),identity)) != double_divide(identity,double_divide(double_divide(identity,X_13),identity))
| double_divide(identity,double_divide(double_divide(identity,X_13),identity)) = double_divide(identity,multiply(X_13,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),double_divide(identity,double_divide(double_divide(identity,X_13),identity))) ),[1,1],$fot(multiply(X_13,identity))]]) ).
cnf(refute_0_42,plain,
( double_divide(double_divide(identity,X_13),identity) != multiply(X_13,identity)
| double_divide(identity,double_divide(double_divide(identity,X_13),identity)) = double_divide(identity,multiply(X_13,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),double_divide(identity,double_divide(double_divide(identity,X_13),identity))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
double_divide(identity,double_divide(double_divide(identity,X_13),identity)) = double_divide(identity,multiply(X_13,identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),identity),multiply(X_13,identity)) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)))]]) ).
cnf(refute_0_45,plain,
( double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) != double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity))
| double_divide(identity,double_divide(double_divide(identity,X_13),identity)) != double_divide(identity,multiply(X_13,identity))
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity))) ),[1,0],$fot(double_divide(identity,multiply(X_13,identity)))]]) ).
cnf(refute_0_46,plain,
( double_divide(identity,double_divide(double_divide(identity,X_13),identity)) != double_divide(identity,multiply(X_13,identity))
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),double_divide(identity,multiply(X_13,identity))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) != X_13
| double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity))
| double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),X_13) ),[0],$fot(double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)))]]) ).
cnf(refute_0_49,plain,
( double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)) != X_13
| double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)) = X_13 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
double_divide(double_divide(identity,multiply(X_13,identity)),inverse(identity)) = X_13,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X_13),identity)),inverse(identity)),X_13) )],[refute_0_26,refute_0_49]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)) = inverse(identity),
inference(subst,[],[refute_0_50:[bind(X_13,$fot(inverse(identity)))]]) ).
cnf(refute_0_52,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_30:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_53,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_54,plain,
( identity != double_divide(X_3,inverse(X_3))
| double_divide(X_3,inverse(X_3)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_3,inverse(X_3))))]]) ).
cnf(refute_0_55,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_57,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(subst,[],[refute_0_58:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_60,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| double_divide(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)) != inverse(identity)
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)),inverse(identity)) ),[0,0,1],$fot(inverse(identity))]]) ).
cnf(refute_0_61,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)) != inverse(identity)
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)),inverse(identity)) )],[refute_0_51,refute_0_61]) ).
cnf(refute_0_63,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_64,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_63]) ).
cnf(refute_0_65,plain,
double_divide(identity,inverse(identity)) = identity,
inference(subst,[],[refute_0_64:[bind(A,$fot(identity))]]) ).
cnf(refute_0_66,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = double_divide(double_divide(identity,inverse(identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(identity)),inverse(identity)))]]) ).
cnf(refute_0_67,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != double_divide(double_divide(identity,inverse(identity)),inverse(identity))
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = double_divide(identity,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),double_divide(double_divide(identity,inverse(identity)),inverse(identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_68,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = double_divide(identity,inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),double_divide(double_divide(identity,inverse(identity)),inverse(identity))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = double_divide(identity,inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = identity ),
inference(subst,[],[refute_0_36:[bind(X,$fot(double_divide(double_divide(identity,inverse(identity)),inverse(identity)))),bind(Y,$fot(double_divide(identity,inverse(identity)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_71,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),double_divide(identity,inverse(identity))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_65,refute_0_71]) ).
cnf(refute_0_73,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != identity
| double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)) ),[0],$fot(identity)]]) ).
cnf(refute_0_74,plain,
( double_divide(double_divide(identity,inverse(identity)),inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),identity) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)) )],[refute_0_62,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_58:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_77,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_78,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_78,prove_these_axioms_1]) ).
cnf(refute_0_80,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_81,plain,
identity != inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_80,refute_0_79]) ).
cnf(refute_0_82,plain,
$false,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_75,refute_0_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 04:14:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------