TSTP Solution File: GRP589-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 10:42:41 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of clauses : 85 ( 47 unt; 0 nHn; 39 RR)
% Number of literals : 142 ( 141 equ; 59 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 : 209 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C ).
cnf(multiply,axiom,
multiply(A,B) = inverse(double_divide(B,A)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
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( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_4,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[multiply,refute_0_3]) ).
cnf(refute_0_5,plain,
inverse(double_divide(A,inverse(C))) = multiply(inverse(C),A),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(C))),bind(B,$fot(A))]]) ).
cnf(refute_0_6,plain,
multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) = multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)),
introduced(tautology,[refl,[$fot(multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)))]]) ).
cnf(refute_0_7,plain,
( multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) != multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B))
| inverse(double_divide(A,inverse(C))) != multiply(inverse(C),A)
| multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) = multiply(multiply(inverse(C),A),double_divide(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)),multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B))) ),[1,0],$fot(multiply(inverse(C),A))]]) ).
cnf(refute_0_8,plain,
( inverse(double_divide(A,inverse(C))) != multiply(inverse(C),A)
| multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) = multiply(multiply(inverse(C),A),double_divide(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)),multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) = multiply(multiply(inverse(C),A),double_divide(A,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,inverse(C))),multiply(inverse(C),A)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) = multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(double_divide(A,inverse(C))))),bind(B,$fot(double_divide(A,B)))]]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) != multiply(multiply(inverse(C),A),double_divide(A,B))
| inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) != multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B))
| inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) = multiply(multiply(inverse(C),A),double_divide(A,B)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))))),bind(Y,$fot(multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)))),bind(Z,$fot(multiply(multiply(inverse(C),A),double_divide(A,B))))]]) ).
cnf(refute_0_14,plain,
( multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)) != multiply(multiply(inverse(C),A),double_divide(A,B))
| inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) = multiply(multiply(inverse(C),A),double_divide(A,B)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) = multiply(multiply(inverse(C),A),double_divide(A,B)),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(A,inverse(C))),double_divide(A,B)),multiply(multiply(inverse(C),A),double_divide(A,B))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B))]]) ).
cnf(refute_0_17,plain,
( double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) != double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)
| inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) != multiply(multiply(inverse(C),A),double_divide(A,B))
| double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)) ),[1,0],$fot(multiply(multiply(inverse(C),A),double_divide(A,B)))]]) ).
cnf(refute_0_18,plain,
( inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))) != multiply(multiply(inverse(C),A),double_divide(A,B))
| double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B),
inference(resolve,[$cnf( $equal(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),multiply(multiply(inverse(C),A),double_divide(A,B))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) != C
| double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) != double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B)
| double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),C) ),[0],$fot(double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B))]]) ).
cnf(refute_0_21,plain,
( double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) != C
| double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B) = C ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(multiply(multiply(inverse(C),A),double_divide(A,B)),B) = C,
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B),C) )],[single_axiom,refute_0_21]) ).
cnf(refute_0_23,plain,
double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B)),B) = C,
inference(subst,[],[refute_0_22:[bind(A,$fot(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))))]]) ).
cnf(refute_0_24,plain,
double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B) = X_4,
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_25,plain,
( double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B)),B) != C
| double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B) != X_4
| double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),X_4),B) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B)),B),C) ),[0,0,1],$fot(X_4)]]) ).
cnf(refute_0_26,plain,
( double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B)),B) != C
| double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),X_4),B) = C ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B),X_4) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),X_4),B) = C,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B))),double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,B)),B)),B),C) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
double_divide(multiply(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),X_15),inverse(X_13)) = X_13,
inference(subst,[],[refute_0_27:[bind(B,$fot(inverse(X_13))),bind(C,$fot(X_13)),bind(X_2,$fot(X_14)),bind(X_4,$fot(X_15))]]) ).
cnf(refute_0_29,plain,
multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) = inverse(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A)),
inference(subst,[],[multiply:[bind(B,$fot(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))))]]) ).
cnf(refute_0_30,plain,
double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A) = X_4,
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2)),bind(B,$fot(A)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_31,plain,
( multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) != inverse(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A))
| double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A) != X_4
| multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) = inverse(X_4) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))),inverse(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A))) ),[1,0],$fot(X_4)]]) ).
cnf(refute_0_32,plain,
( multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) != inverse(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A))
| multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) = inverse(X_4) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A),X_4) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))) = inverse(X_4),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A))),inverse(double_divide(multiply(multiply(inverse(X_4),X_2),double_divide(X_2,A)),A))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))) = inverse(X_15),
inference(subst,[],[refute_0_33:[bind(A,$fot(inverse(X_13))),bind(X_2,$fot(X_14)),bind(X_4,$fot(X_15))]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))) != inverse(X_15)
| double_divide(multiply(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),X_15),inverse(X_13)) != X_13
| double_divide(multiply(inverse(X_15),X_15),inverse(X_13)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),X_15),inverse(X_13)),X_13) ),[0,0,0],$fot(inverse(X_15))]]) ).
cnf(refute_0_36,plain,
( double_divide(multiply(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),X_15),inverse(X_13)) != X_13
| double_divide(multiply(inverse(X_15),X_15),inverse(X_13)) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),inverse(X_15)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(multiply(inverse(X_15),X_15),inverse(X_13)) = X_13,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(X_13),multiply(multiply(inverse(X_15),X_14),double_divide(X_14,inverse(X_13)))),X_15),inverse(X_13)),X_13) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(X_13)) = X_13,
inference(subst,[],[refute_0_37:[bind(X_15,$fot(multiply(inverse(X_19),X_19)))]]) ).
cnf(refute_0_39,plain,
multiply(inverse(X_16),multiply(inverse(X_17),X_17)) = inverse(double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),
inference(subst,[],[multiply:[bind(A,$fot(inverse(X_16))),bind(B,$fot(multiply(inverse(X_17),X_17)))]]) ).
cnf(refute_0_40,plain,
double_divide(multiply(inverse(X_17),X_17),inverse(X_16)) = X_16,
inference(subst,[],[refute_0_37:[bind(X_13,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_16),multiply(inverse(X_17),X_17)) != inverse(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)))
| double_divide(multiply(inverse(X_17),X_17),inverse(X_16)) != X_16
| multiply(inverse(X_16),multiply(inverse(X_17),X_17)) = inverse(X_16) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_16),multiply(inverse(X_17),X_17)),inverse(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)))) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(X_16),multiply(inverse(X_17),X_17)) != inverse(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)))
| multiply(inverse(X_16),multiply(inverse(X_17),X_17)) = inverse(X_16) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)),X_16) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(X_16),multiply(inverse(X_17),X_17)) = inverse(X_16),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),multiply(inverse(X_17),X_17)),inverse(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)) = inverse(multiply(inverse(X_19),X_19)),
inference(subst,[],[refute_0_43:[bind(X_16,$fot(multiply(inverse(X_19),X_19))),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)) != inverse(multiply(inverse(X_19),X_19))
| double_divide(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(X_13)) != X_13
| double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(X_13)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(X_13)),X_13) ),[0,0],$fot(inverse(multiply(inverse(X_19),X_19)))]]) ).
cnf(refute_0_46,plain,
( double_divide(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(X_13)) != X_13
| double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(X_13)) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_19),X_19))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(X_13)) = X_13,
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(multiply(inverse(X_19),X_19)),multiply(inverse(X_19),X_19)),inverse(X_13)),X_13) )],[refute_0_38,refute_0_46]) ).
cnf(refute_0_48,plain,
double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))) = multiply(inverse(X_39),X_39),
inference(subst,[],[refute_0_47:[bind(X_13,$fot(multiply(inverse(X_39),X_39)))]]) ).
cnf(refute_0_49,plain,
double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),inverse(X_16)) = C,
inference(subst,[],[refute_0_22:[bind(A,$fot(multiply(inverse(X_17),X_17))),bind(B,$fot(inverse(X_16)))]]) ).
cnf(refute_0_50,plain,
( double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),inverse(X_16)) != C
| double_divide(multiply(inverse(X_17),X_17),inverse(X_16)) != X_16
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),inverse(X_16)),C) ),[0,0,1],$fot(X_16)]]) ).
cnf(refute_0_51,plain,
( double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),inverse(X_16)) != C
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = C ),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_17),X_17),inverse(X_16)),X_16) )],[refute_0_40,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = C,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),double_divide(multiply(inverse(X_17),X_17),inverse(X_16))),inverse(X_16)),C) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(inverse(C),multiply(inverse(X_17),X_17)) = inverse(C),
inference(subst,[],[refute_0_43:[bind(X_16,$fot(C))]]) ).
cnf(refute_0_54,plain,
multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) = multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16))]]) ).
cnf(refute_0_55,plain,
( multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) != multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16)
| multiply(inverse(C),multiply(inverse(X_17),X_17)) != inverse(C)
| multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) = multiply(inverse(C),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16)) ),[1,0],$fot(inverse(C))]]) ).
cnf(refute_0_56,plain,
( multiply(inverse(C),multiply(inverse(X_17),X_17)) != inverse(C)
| multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) = multiply(inverse(C),X_16) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) = multiply(inverse(C),X_16),
inference(resolve,[$cnf( $equal(multiply(inverse(C),multiply(inverse(X_17),X_17)),inverse(C)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),
introduced(tautology,[refl,[$fot(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)))]]) ).
cnf(refute_0_59,plain,
( multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) != multiply(inverse(C),X_16)
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) != double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16))
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = double_divide(multiply(inverse(C),X_16),inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16))) ),[1,0],$fot(multiply(inverse(C),X_16))]]) ).
cnf(refute_0_60,plain,
( multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16) != multiply(inverse(C),X_16)
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = double_divide(multiply(inverse(C),X_16),inverse(X_16)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) = double_divide(multiply(inverse(C),X_16),inverse(X_16)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),multiply(inverse(C),X_16)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) != C
| double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) != double_divide(multiply(inverse(C),X_16),inverse(X_16))
| double_divide(multiply(inverse(C),X_16),inverse(X_16)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),C) ),[0],$fot(double_divide(multiply(inverse(C),X_16),inverse(X_16)))]]) ).
cnf(refute_0_63,plain,
( double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)) != C
| double_divide(multiply(inverse(C),X_16),inverse(X_16)) = C ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),double_divide(multiply(inverse(C),X_16),inverse(X_16))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
double_divide(multiply(inverse(C),X_16),inverse(X_16)) = C,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(inverse(C),multiply(inverse(X_17),X_17)),X_16),inverse(X_16)),C) )],[refute_0_52,refute_0_63]) ).
cnf(refute_0_65,plain,
double_divide(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(multiply(inverse(X_17),X_17))) = X_37,
inference(subst,[],[refute_0_64:[bind(C,$fot(X_37)),bind(X_16,$fot(multiply(inverse(X_17),X_17)))]]) ).
cnf(refute_0_66,plain,
multiply(inverse(X_37),multiply(inverse(X_17),X_17)) = inverse(X_37),
inference(subst,[],[refute_0_43:[bind(X_16,$fot(X_37))]]) ).
cnf(refute_0_67,plain,
( multiply(inverse(X_37),multiply(inverse(X_17),X_17)) != inverse(X_37)
| double_divide(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(multiply(inverse(X_17),X_17))) != X_37
| double_divide(inverse(X_37),inverse(multiply(inverse(X_17),X_17))) = X_37 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(multiply(inverse(X_17),X_17))),X_37) ),[0,0],$fot(inverse(X_37))]]) ).
cnf(refute_0_68,plain,
( double_divide(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(multiply(inverse(X_17),X_17))) != X_37
| double_divide(inverse(X_37),inverse(multiply(inverse(X_17),X_17))) = X_37 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(X_37)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(inverse(X_37),inverse(multiply(inverse(X_17),X_17))) = X_37,
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_37),multiply(inverse(X_17),X_17)),inverse(multiply(inverse(X_17),X_17))),X_37) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))) = multiply(inverse(X_19),X_19),
inference(subst,[],[refute_0_69:[bind(X_17,$fot(X_39)),bind(X_37,$fot(multiply(inverse(X_19),X_19)))]]) ).
cnf(refute_0_71,plain,
( double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))) != multiply(inverse(X_19),X_19)
| double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))) != multiply(inverse(X_39),X_39)
| multiply(inverse(X_19),X_19) = multiply(inverse(X_39),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))),multiply(inverse(X_39),X_39)) ),[0],$fot(multiply(inverse(X_19),X_19))]]) ).
cnf(refute_0_72,plain,
( double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))) != multiply(inverse(X_39),X_39)
| multiply(inverse(X_19),X_19) = multiply(inverse(X_39),X_39) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))),multiply(inverse(X_19),X_19)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_19),X_19) = multiply(inverse(X_39),X_39),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(inverse(X_19),X_19)),inverse(multiply(inverse(X_39),X_39))),multiply(inverse(X_39),X_39)) )],[refute_0_48,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(a1),a1) = multiply(inverse(X_44),X_44),
inference(subst,[],[refute_0_73:[bind(X_19,$fot(a1)),bind(X_39,$fot(X_44))]]) ).
cnf(refute_0_75,plain,
( multiply(inverse(X_44),X_44) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != multiply(inverse(X_44),X_44)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(X_44),X_44)) ),[1],$fot(multiply(inverse(b1),b1))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(X_44),X_44) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(X_44),X_44)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(inverse(X_44),X_44) != multiply(inverse(b1),b1),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_76,prove_these_axioms_1]) ).
cnf(refute_0_78,plain,
( multiply(inverse(X_19),X_19) != multiply(inverse(X_39),X_39)
| multiply(inverse(X_39),X_39) = multiply(inverse(X_19),X_19) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(inverse(X_19),X_19))),bind(Y,$fot(multiply(inverse(X_39),X_39)))]]) ).
cnf(refute_0_79,plain,
multiply(inverse(X_39),X_39) = multiply(inverse(X_19),X_19),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),X_19),multiply(inverse(X_39),X_39)) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(inverse(X_44),X_44) = multiply(inverse(b1),b1),
inference(subst,[],[refute_0_79:[bind(X_19,$fot(b1)),bind(X_39,$fot(X_44))]]) ).
cnf(refute_0_81,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),X_44),multiply(inverse(b1),b1)) )],[refute_0_80,refute_0_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:45:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.45
%------------------------------------------------------------------------------