%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP082-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:27:07 AM UTC 2026
% Result : Unsatisfiable 0.92s 0.55s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 3
% Syntax : Number of formulae : 163 ( 134 unt; 0 def)
% Number of atoms : 205 ( 204 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 114 ( 72 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 518 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : double_divide(inverse(VAR_0),inverse(double_divide(inverse(double_divide(VAR_0,double_divide(VAR_1,VAR_2))),double_divide(VAR_3,double_divide(VAR_1,VAR_3))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D))))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_3,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_858,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_859,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_858]) ).
cnf(c_860,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_859]) ).
cnf(c_861,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_860]) ).
cnf(c_862,plain,
( multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_861]) ).
cnf(c_863,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_862]) ).
cnf(c_864,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3)))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_863]) ).
cnf(c_865,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_864]) ).
cnf(c_866,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(copy,[status(thm)],[c_865]) ).
cnf(c_4,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(copy,[status(thm)],[c_866]) ).
cnf(c_5,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C))))) = inverse(double_divide(inverse(double_divide(D,double_divide(E,B))),double_divide(F,double_divide(E,F)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C)))),double_divide(D,double_divide(B,D)))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
double_divide(inverse(A),double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(inverse(A),D)))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(D,double_divide(E,D))))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_867,plain,
double_divide(inverse(A),double_divide(inverse(inverse(double_divide(B,double_divide(C,double_divide(inverse(B),D))))),inverse(double_divide(D,double_divide(E,double_divide(inverse(A),E)))))) = double_divide(F,double_divide(C,F)),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_14,plain,
double_divide(inverse(A),double_divide(B,inverse(A))) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_11,c_867]) ).
cnf(c_868,plain,
double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(C,double_divide(D,double_divide(inverse(C),A)))),double_divide(E,double_divide(D,E)))))) = double_divide(F,double_divide(B,F)),
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_30,plain,
double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_6,c_868]) ).
cnf(c_33,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(E,D))))) = double_divide(C,E),
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_34,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),double_divide(D,double_divide(C,D))))) = A,
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_40,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))) = double_divide(D,double_divide(B,D)),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_869,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(inverse(E),D))))) = inverse(double_divide(inverse(double_divide(E,double_divide(F,double_divide(V6,F)))),double_divide(V7,double_divide(double_divide(C,V6),V7)))),
inference(paramod,[status(thm)],[c_40,c_5]) ).
cnf(c_870,plain,
double_divide(C,inverse(E)) = inverse(double_divide(inverse(double_divide(E,double_divide(F,double_divide(V6,F)))),double_divide(V7,double_divide(double_divide(C,V6),V7)))),
inference(paramod,[status(thm)],[c_33,c_869]) ).
cnf(c_49,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(double_divide(E,C),D)))) = double_divide(E,inverse(A)),
inference(copy,[status(thm)],[c_870]) ).
cnf(c_51,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(C,double_divide(D,C))) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_40,c_30]) ).
cnf(c_871,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(double_divide(B,double_divide(C,B)),double_divide(D,double_divide(E,D)))),double_divide(F,double_divide(double_divide(C,E),F))))) = A,
inference(paramod,[status(thm)],[c_40,c_34]) ).
cnf(c_91,plain,
double_divide(inverse(A),double_divide(B,inverse(double_divide(C,double_divide(B,C))))) = A,
inference(paramod,[status(thm)],[c_49,c_871]) ).
cnf(c_100,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C)))) = inverse(double_divide(D,double_divide(inverse(A),D))),
inference(paramod,[status(thm)],[c_91,c_6]) ).
cnf(c_103,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C) = double_divide(D,double_divide(inverse(C),D)),
inference(paramod,[status(thm)],[c_91,c_30]) ).
cnf(c_872,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),A))),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),double_divide(E,double_divide(D,E))))) = double_divide(inverse(double_divide(B,F)),double_divide(V6,double_divide(inverse(F),V6))),
inference(paramod,[status(thm)],[c_100,c_34]) ).
cnf(c_873,plain,
double_divide(A,double_divide(inverse(B),A)) = double_divide(inverse(double_divide(B,F)),double_divide(V6,double_divide(inverse(F),V6))),
inference(paramod,[status(thm)],[c_34,c_872]) ).
cnf(c_162,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C))) = double_divide(D,double_divide(inverse(A),D)),
inference(copy,[status(thm)],[c_873]) ).
cnf(c_175,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(C,B))))),inverse(double_divide(double_divide(D,inverse(A)),double_divide(E,double_divide(F,E))))) = double_divide(double_divide(D,C),F),
inference(paramod,[status(thm)],[c_40,c_11]) ).
cnf(c_874,plain,
double_divide(A,B) = inverse(double_divide(C,double_divide(A,double_divide(inverse(C),inverse(double_divide(D,double_divide(B,D))))))),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_176,plain,
inverse(double_divide(A,double_divide(B,double_divide(inverse(A),inverse(double_divide(C,double_divide(D,C))))))) = double_divide(B,D),
inference(copy,[status(thm)],[c_874]) ).
cnf(c_875,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(D,double_divide(inverse(double_divide(E,double_divide(F,inverse(double_divide(V6,double_divide(F,V6)))))),D))))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_103,c_11]) ).
cnf(c_178,plain,
double_divide(A,inverse(double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(C,D))))))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_11,c_875]) ).
cnf(c_876,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(C),B)))),double_divide(D,double_divide(inverse(double_divide(C,E)),D))))) = double_divide(F,double_divide(inverse(E),F)),
inference(paramod,[status(thm)],[c_162,c_1]) ).
cnf(c_181,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = double_divide(C,double_divide(inverse(B),C)),
inference(paramod,[status(thm)],[c_33,c_876]) ).
cnf(c_877,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),double_divide(C,D)) = double_divide(double_divide(E,double_divide(inverse(D),E)),double_divide(F,double_divide(inverse(C),F))),
inference(paramod,[status(thm)],[c_162,c_103]) ).
cnf(c_224,plain,
double_divide(double_divide(A,double_divide(inverse(B),A)),double_divide(C,double_divide(inverse(D),C))) = double_divide(double_divide(E,inverse(double_divide(F,double_divide(E,F)))),double_divide(D,B)),
inference(copy,[status(thm)],[c_877]) ).
cnf(c_878,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(C),B))))),inverse(double_divide(double_divide(inverse(D),inverse(A)),double_divide(E,double_divide(F,E))))) = double_divide(inverse(double_divide(C,D)),F),
inference(paramod,[status(thm)],[c_162,c_11]) ).
cnf(c_879,plain,
double_divide(double_divide(inverse(D),inverse(C)),F) = double_divide(inverse(double_divide(C,D)),F),
inference(paramod,[status(thm)],[c_175,c_878]) ).
cnf(c_236,plain,
double_divide(inverse(double_divide(A,B)),C) = double_divide(double_divide(inverse(B),inverse(A)),C),
inference(copy,[status(thm)],[c_879]) ).
cnf(c_289,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(paramod,[status(thm)],[c_236,c_4]) ).
cnf(c_880,plain,
double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(inverse(C),C)),B))) = A,
inference(paramod,[status(thm)],[c_181,c_91]) ).
cnf(c_312,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(inverse(C),inverse(inverse(C))),B))) = A,
inference(paramod,[status(thm)],[c_236,c_880]) ).
cnf(c_331,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = double_divide(inverse(C),inverse(double_divide(C,B))),
inference(paramod,[status(thm)],[c_181,c_181]) ).
cnf(c_881,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),inverse(double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(C,D))))))),
inference(paramod,[status(thm)],[c_91,c_331]) ).
cnf(c_340,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_178,c_881]) ).
cnf(c_345,plain,
double_divide(inverse(inverse(A)),inverse(double_divide(inverse(B),inverse(double_divide(B,C))))) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_331,c_181]) ).
cnf(c_376,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(inverse(D),double_divide(inverse(E),E))))) = double_divide(B,inverse(inverse(D))),
inference(paramod,[status(thm)],[c_340,c_11]) ).
cnf(c_377,plain,
double_divide(inverse(A),A) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_340,c_11]) ).
cnf(c_387,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_340,c_340]) ).
cnf(c_400,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))) = double_divide(inverse(B),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_377,c_40]) ).
cnf(c_418,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C) = double_divide(inverse(inverse(C)),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_377,c_103]) ).
cnf(c_882,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),inverse(double_divide(C,double_divide(D,double_divide(E,D))))) = double_divide(inverse(double_divide(inverse(A),C)),E),
inference(paramod,[status(thm)],[c_377,c_11]) ).
cnf(c_420,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),inverse(double_divide(C,double_divide(D,double_divide(E,D))))) = double_divide(double_divide(inverse(C),inverse(inverse(A))),E),
inference(paramod,[status(thm)],[c_236,c_882]) ).
cnf(c_423,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_377,c_11]) ).
cnf(c_883,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(inverse(D),double_divide(inverse(E),E))))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_377,c_11]) ).
cnf(c_425,plain,
double_divide(A,inverse(inverse(B))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_376,c_883]) ).
cnf(c_432,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),inverse(double_divide(C,double_divide(D,double_divide(E,D))))) = double_divide(double_divide(inverse(C),A),E),
inference(paramod,[status(thm)],[c_425,c_420]) ).
cnf(c_437,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(inverse(C),C),B))) = A,
inference(paramod,[status(thm)],[c_425,c_312]) ).
cnf(c_884,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),inverse(double_divide(C,double_divide(D,C)))))))),inverse(double_divide(inverse(E),E))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_387,c_11]) ).
cnf(c_885,plain,
double_divide(inverse(double_divide(B,D)),inverse(double_divide(inverse(E),E))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_176,c_884]) ).
cnf(c_458,plain,
double_divide(double_divide(inverse(A),inverse(B)),inverse(double_divide(inverse(C),C))) = double_divide(B,A),
inference(paramod,[status(thm)],[c_236,c_885]) ).
cnf(c_479,plain,
double_divide(double_divide(inverse(A),double_divide(inverse(B),B)),double_divide(C,double_divide(D,C))) = double_divide(E,double_divide(double_divide(A,D),E)),
inference(paramod,[status(thm)],[c_377,c_51]) ).
cnf(c_886,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(C,double_divide(D,C))) = double_divide(inverse(double_divide(B,D)),double_divide(inverse(E),E)),
inference(paramod,[status(thm)],[c_377,c_51]) ).
cnf(c_887,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(C,double_divide(D,C))) = double_divide(double_divide(inverse(D),inverse(B)),double_divide(inverse(E),E)),
inference(paramod,[status(thm)],[c_236,c_886]) ).
cnf(c_482,plain,
double_divide(double_divide(inverse(A),inverse(B)),double_divide(inverse(C),C)) = double_divide(double_divide(D,double_divide(B,D)),double_divide(E,double_divide(A,E))),
inference(copy,[status(thm)],[c_887]) ).
cnf(c_483,plain,
double_divide(double_divide(A,double_divide(inverse(B),B)),double_divide(C,double_divide(D,C))) = double_divide(E,double_divide(double_divide(inverse(A),D),E)),
inference(paramod,[status(thm)],[c_387,c_51]) ).
cnf(c_888,plain,
multiply(inverse(A),A) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_423,c_2]) ).
cnf(c_486,plain,
inverse(double_divide(A,inverse(A))) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_2,c_888]) ).
cnf(c_501,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_423,c_103]) ).
cnf(c_506,plain,
double_divide(double_divide(inverse(A),double_divide(B,inverse(B))),double_divide(C,double_divide(D,C))) = double_divide(E,double_divide(double_divide(A,D),E)),
inference(paramod,[status(thm)],[c_423,c_51]) ).
cnf(c_510,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ),
inference(resolve,[status(thm)],[c_486,c_289]) ).
cnf(c_589,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(C,double_divide(inverse(inverse(D)),C))) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_425,c_51]) ).
cnf(c_610,plain,
double_divide(inverse(A),double_divide(B,inverse(double_divide(double_divide(inverse(C),inverse(D)),double_divide(B,inverse(double_divide(D,C))))))) = A,
inference(paramod,[status(thm)],[c_236,c_91]) ).
cnf(c_889,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(D,double_divide(double_divide(inverse(E),inverse(F)),D))))) = double_divide(B,inverse(double_divide(F,E))),
inference(paramod,[status(thm)],[c_236,c_11]) ).
cnf(c_890,plain,
double_divide(B,double_divide(inverse(E),inverse(F))) = double_divide(B,inverse(double_divide(F,E))),
inference(paramod,[status(thm)],[c_11,c_889]) ).
cnf(c_618,plain,
double_divide(A,inverse(double_divide(B,C))) = double_divide(A,double_divide(inverse(C),inverse(B))),
inference(copy,[status(thm)],[c_890]) ).
cnf(c_891,plain,
double_divide(inverse(A),double_divide(B,inverse(double_divide(double_divide(inverse(C),inverse(D)),double_divide(B,double_divide(inverse(C),inverse(D))))))) = A,
inference(paramod,[status(thm)],[c_618,c_610]) ).
cnf(c_892,plain,
double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(B,double_divide(inverse(C),inverse(D)))),inverse(double_divide(inverse(C),inverse(D)))))) = A,
inference(paramod,[status(thm)],[c_618,c_891]) ).
cnf(c_893,plain,
double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(B,double_divide(inverse(C),inverse(D)))),double_divide(inverse(inverse(D)),inverse(inverse(C)))))) = A,
inference(paramod,[status(thm)],[c_618,c_892]) ).
cnf(c_894,plain,
double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(B,double_divide(inverse(C),inverse(D)))),double_divide(inverse(inverse(D)),C)))) = A,
inference(paramod,[status(thm)],[c_425,c_893]) ).
cnf(c_895,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(inverse(double_divide(inverse(C),inverse(D))),inverse(B)),double_divide(inverse(inverse(D)),C)))) = A,
inference(paramod,[status(thm)],[c_236,c_894]) ).
cnf(c_896,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(double_divide(inverse(inverse(D)),inverse(inverse(C))),inverse(B)),double_divide(inverse(inverse(D)),C)))) = A,
inference(paramod,[status(thm)],[c_236,c_895]) ).
cnf(c_645,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(double_divide(inverse(inverse(C)),D),inverse(B)),double_divide(inverse(inverse(C)),D)))) = A,
inference(paramod,[status(thm)],[c_425,c_896]) ).
cnf(c_897,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,double_divide(inverse(inverse(b2)),inverse(b2)))) != a2 ),
inference(paramod,[status(thm)],[c_618,c_510]) ).
cnf(c_680,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| inverse(double_divide(a2,double_divide(inverse(inverse(b2)),inverse(b2)))) != a2 ),
inference(paramod,[status(thm)],[c_618,c_897]) ).
cnf(c_898,plain,
double_divide(double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(B))),C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_618,c_501]) ).
cnf(c_682,plain,
double_divide(double_divide(A,double_divide(double_divide(inverse(B),inverse(A)),inverse(B))),C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_236,c_898]) ).
cnf(c_899,plain,
double_divide(double_divide(inverse(A),inverse(B)),double_divide(inverse(C),inverse(inverse(C)))) = double_divide(B,A),
inference(paramod,[status(thm)],[c_618,c_458]) ).
cnf(c_688,plain,
double_divide(double_divide(inverse(A),inverse(B)),double_divide(inverse(C),C)) = double_divide(B,A),
inference(paramod,[status(thm)],[c_425,c_899]) ).
cnf(c_900,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),double_divide(inverse(double_divide(D,double_divide(E,D))),inverse(C))) = double_divide(double_divide(inverse(C),A),E),
inference(paramod,[status(thm)],[c_618,c_432]) ).
cnf(c_901,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),double_divide(double_divide(inverse(double_divide(E,D)),inverse(D)),inverse(C))) = double_divide(double_divide(inverse(C),A),E),
inference(paramod,[status(thm)],[c_236,c_900]) ).
cnf(c_698,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,inverse(B))))),double_divide(double_divide(double_divide(inverse(C),inverse(D)),inverse(C)),inverse(E))) = double_divide(double_divide(inverse(E),A),D),
inference(paramod,[status(thm)],[c_236,c_901]) ).
cnf(c_902,plain,
double_divide(double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(B))),C) = double_divide(inverse(inverse(C)),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_618,c_418]) ).
cnf(c_699,plain,
double_divide(double_divide(A,double_divide(double_divide(inverse(B),inverse(A)),inverse(B))),C) = double_divide(inverse(inverse(C)),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_236,c_902]) ).
cnf(c_903,plain,
double_divide(inverse(inverse(A)),inverse(double_divide(inverse(B),double_divide(inverse(C),inverse(B))))) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_618,c_345]) ).
cnf(c_904,plain,
double_divide(inverse(inverse(A)),double_divide(inverse(double_divide(inverse(C),inverse(B))),inverse(inverse(B)))) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_618,c_903]) ).
cnf(c_905,plain,
double_divide(inverse(inverse(A)),double_divide(inverse(double_divide(inverse(C),inverse(B))),B)) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_425,c_904]) ).
cnf(c_906,plain,
double_divide(inverse(inverse(A)),double_divide(double_divide(inverse(inverse(B)),inverse(inverse(C))),B)) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_236,c_905]) ).
cnf(c_711,plain,
double_divide(inverse(inverse(A)),double_divide(double_divide(inverse(inverse(B)),C),B)) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_425,c_906]) ).
cnf(c_907,plain,
double_divide(double_divide(A,double_divide(inverse(B),A)),double_divide(C,double_divide(inverse(D),C))) = double_divide(double_divide(E,double_divide(inverse(double_divide(E,F)),inverse(F))),double_divide(D,B)),
inference(paramod,[status(thm)],[c_618,c_224]) ).
cnf(c_908,plain,
double_divide(double_divide(A,double_divide(inverse(B),A)),double_divide(C,double_divide(inverse(D),C))) = double_divide(double_divide(E,double_divide(double_divide(inverse(F),inverse(E)),inverse(F))),double_divide(D,B)),
inference(paramod,[status(thm)],[c_236,c_907]) ).
cnf(c_742,plain,
double_divide(double_divide(A,double_divide(double_divide(inverse(B),inverse(A)),inverse(B))),double_divide(C,D)) = double_divide(double_divide(E,double_divide(inverse(D),E)),double_divide(F,double_divide(inverse(C),F))),
inference(copy,[status(thm)],[c_908]) ).
cnf(c_909,plain,
double_divide(B,A) = double_divide(double_divide(D,double_divide(B,D)),double_divide(E,double_divide(A,E))),
inference(paramod,[status(thm)],[c_688,c_482]) ).
cnf(c_764,plain,
double_divide(double_divide(A,double_divide(B,A)),double_divide(C,double_divide(D,C))) = double_divide(B,D),
inference(copy,[status(thm)],[c_909]) ).
cnf(c_765,plain,
double_divide(double_divide(A,double_divide(double_divide(inverse(B),inverse(A)),inverse(B))),double_divide(C,D)) = double_divide(inverse(D),inverse(C)),
inference(paramod,[status(thm)],[c_764,c_742]) ).
cnf(c_910,plain,
double_divide(B,inverse(inverse(D))) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_764,c_589]) ).
cnf(c_911,plain,
double_divide(B,D) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_425,c_910]) ).
cnf(c_768,plain,
double_divide(A,double_divide(double_divide(B,C),A)) = double_divide(B,C),
inference(copy,[status(thm)],[c_911]) ).
cnf(c_791,plain,
double_divide(double_divide(inverse(A),double_divide(B,inverse(B))),double_divide(C,double_divide(D,C))) = double_divide(A,D),
inference(paramod,[status(thm)],[c_768,c_506]) ).
cnf(c_793,plain,
double_divide(double_divide(A,double_divide(inverse(B),B)),double_divide(C,double_divide(D,C))) = double_divide(inverse(A),D),
inference(paramod,[status(thm)],[c_768,c_483]) ).
cnf(c_912,plain,
double_divide(inverse(inverse(A)),D) = double_divide(E,double_divide(double_divide(A,D),E)),
inference(paramod,[status(thm)],[c_793,c_479]) ).
cnf(c_794,plain,
double_divide(inverse(inverse(A)),B) = double_divide(A,B),
inference(paramod,[status(thm)],[c_768,c_912]) ).
cnf(c_798,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_768,c_437]) ).
cnf(c_913,plain,
double_divide(inverse(inverse(A)),double_divide(double_divide(B,C),B)) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_794,c_711]) ).
cnf(c_914,plain,
double_divide(A,double_divide(double_divide(B,C),B)) = double_divide(D,double_divide(inverse(inverse(double_divide(A,C))),D)),
inference(paramod,[status(thm)],[c_794,c_913]) ).
cnf(c_915,plain,
double_divide(A,double_divide(double_divide(B,C),B)) = double_divide(D,double_divide(double_divide(A,C),D)),
inference(paramod,[status(thm)],[c_794,c_914]) ).
cnf(c_817,plain,
double_divide(A,double_divide(double_divide(B,C),B)) = double_divide(A,C),
inference(paramod,[status(thm)],[c_768,c_915]) ).
cnf(c_916,plain,
double_divide(double_divide(A,inverse(A)),C) = double_divide(inverse(inverse(C)),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_817,c_699]) ).
cnf(c_830,plain,
double_divide(double_divide(A,inverse(A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_798,c_916]) ).
cnf(c_831,plain,
double_divide(double_divide(A,double_divide(B,inverse(B))),double_divide(double_divide(double_divide(inverse(C),inverse(D)),inverse(C)),inverse(E))) = double_divide(double_divide(inverse(E),A),D),
inference(paramod,[status(thm)],[c_794,c_698]) ).
cnf(c_917,plain,
double_divide(double_divide(A,inverse(A)),C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_817,c_682]) ).
cnf(c_918,plain,
inverse(C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_830,c_917]) ).
cnf(c_919,plain,
inverse(C) = double_divide(C,double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_794,c_918]) ).
cnf(c_836,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(copy,[status(thm)],[c_919]) ).
cnf(c_920,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| inverse(double_divide(a2,double_divide(b2,inverse(b2)))) != a2 ),
inference(paramod,[status(thm)],[c_794,c_680]) ).
cnf(c_838,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| inverse(inverse(a2)) != a2 ),
inference(paramod,[status(thm)],[c_836,c_920]) ).
cnf(c_921,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(double_divide(C,D),inverse(B)),double_divide(inverse(inverse(C)),D)))) = A,
inference(paramod,[status(thm)],[c_794,c_645]) ).
cnf(c_922,plain,
double_divide(inverse(A),double_divide(B,double_divide(double_divide(double_divide(C,D),inverse(B)),double_divide(C,D)))) = A,
inference(paramod,[status(thm)],[c_794,c_921]) ).
cnf(c_923,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_817,c_922]) ).
cnf(c_841,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_836,c_923]) ).
cnf(c_924,plain,
double_divide(inverse(inverse(A)),double_divide(C,double_divide(D,C))) = double_divide(A,D),
inference(paramod,[status(thm)],[c_836,c_791]) ).
cnf(c_846,plain,
double_divide(A,double_divide(B,double_divide(C,B))) = double_divide(A,C),
inference(paramod,[status(thm)],[c_841,c_924]) ).
cnf(c_925,plain,
double_divide(double_divide(A,B),A) = double_divide(inverse(B),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_846,c_400]) ).
cnf(c_850,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_798,c_925]) ).
cnf(c_926,plain,
double_divide(double_divide(A,inverse(A)),double_divide(C,D)) = double_divide(inverse(D),inverse(C)),
inference(paramod,[status(thm)],[c_850,c_765]) ).
cnf(c_852,plain,
inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_830,c_926]) ).
cnf(c_927,plain,
double_divide(inverse(A),double_divide(double_divide(double_divide(inverse(C),inverse(D)),inverse(C)),inverse(E))) = double_divide(double_divide(inverse(E),A),D),
inference(paramod,[status(thm)],[c_836,c_831]) ).
cnf(c_928,plain,
double_divide(inverse(A),double_divide(inverse(D),inverse(E))) = double_divide(double_divide(inverse(E),A),D),
inference(paramod,[status(thm)],[c_850,c_927]) ).
cnf(c_855,plain,
double_divide(double_divide(inverse(A),B),C) = double_divide(inverse(B),double_divide(inverse(C),inverse(A))),
inference(copy,[status(thm)],[c_928]) ).
cnf(c_929,plain,
( inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_838]) ).
cnf(c_930,plain,
( inverse(double_divide(inverse(inverse(c3)),double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_855,c_929]) ).
cnf(c_931,plain,
( inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_930]) ).
cnf(c_932,plain,
( double_divide(inverse(double_divide(inverse(a3),inverse(b3))),inverse(c3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_852,c_931]) ).
cnf(c_933,plain,
( double_divide(double_divide(inverse(inverse(b3)),inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_852,c_932]) ).
cnf(c_934,plain,
( double_divide(double_divide(b3,inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_933]) ).
cnf(c_935,plain,
( double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_934]) ).
cnf(c_936,plain,
( double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(double_divide(inverse(a3),inverse(b3))),inverse(c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_852,c_935]) ).
cnf(c_937,plain,
( double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(inverse(inverse(b3)),inverse(inverse(a3))),inverse(c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_852,c_936]) ).
cnf(c_938,plain,
( double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(b3,inverse(inverse(a3))),inverse(c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_937]) ).
cnf(c_939,plain,
( double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(b3,a3),inverse(c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_841,c_938]) ).
cnf(c_940,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(b3,a3),inverse(c3)),
inference(copy,[status(thm)],[c_939]) ).
cnf(c_857,plain,
$false,
inference(copy,[status(thm)],[c_940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP082-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:21:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1788377 was started by sandbox2 on n009,
% 0.10/0.37 % Fri Sep 25 14:21:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.92/0.55
% 0.92/0.55 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.92/0.55
% 0.92/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.92/0.55
% 0.92/0.55 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.92/0.55 % Length of proof is 77.
% 0.92/0.55 % Level of proof is 28.
% 0.92/0.55 % Maximum clause weight is 98.000.
% 0.92/0.55 % Given clauses 32.
% 0.92/0.55
% 0.92/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
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