%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:27:21 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 3
% Syntax : Number of formulae : 159 ( 128 unt; 0 def)
% Number of atoms : 249 ( 248 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 215 ( 125 ~; 90 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 453 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(VAR_0,inverse(double_divide(VAR_1,double_divide(VAR_0,VAR_2))))),VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
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(a4,b4) != multiply(b4,a4)
| 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(a4,b4) != multiply(b4,a4)
| 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_350,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_351,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_350]) ).
cnf(c_352,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_351]) ).
cnf(c_353,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_352]) ).
cnf(c_354,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_353]) ).
cnf(c_355,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_354]) ).
cnf(c_356,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_355]) ).
cnf(c_357,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_356]) ).
cnf(c_358,plain,
( inverse(double_divide(b4,a4)) != multiply(b4,a4)
| 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_357]) ).
cnf(c_359,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| 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_358]) ).
cnf(c_360,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| 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_359]) ).
cnf(c_4,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| 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_360]) ).
cnf(c_361,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = inverse(double_divide(D,inverse(double_divide(B,double_divide(D,double_divide(A,C)))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,D)))))) = inverse(double_divide(inverse(double_divide(C,B)),D)),
inference(copy,[status(thm)],[c_361]) ).
cnf(c_6,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),B))) = D,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_14,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_362,plain,
inverse(double_divide(A,double_divide(B,C))) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(double_divide(E,inverse(double_divide(A,double_divide(E,C))))))),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_21,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,double_divide(C,E))))))) = inverse(double_divide(D,double_divide(B,E))),
inference(copy,[status(thm)],[c_362]) ).
cnf(c_31,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),D)),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_32,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_42,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(A,C))))) = B,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_50,plain,
inverse(inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,B)))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_14,c_14]) ).
cnf(c_55,plain,
inverse(double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B)))) = inverse(double_divide(A,C)),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_60,plain,
inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))),
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_61,plain,
inverse(double_divide(inverse(A),double_divide(B,double_divide(B,inverse(double_divide(C,A)))))) = C,
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_66,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),D))) = double_divide(B,inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_32,c_11]) ).
cnf(c_68,plain,
inverse(double_divide(inverse(A),double_divide(B,double_divide(C,inverse(double_divide(D,A)))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_71,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),D)),double_divide(E,D))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_363,plain,
inverse(double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(inverse(double_divide(D,inverse(double_divide(A,double_divide(D,inverse(C)))))),B)),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_79,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,inverse(C)))))),D)) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(copy,[status(thm)],[c_363]) ).
cnf(c_364,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(inverse(double_divide(A,inverse(D))),C))) = inverse(double_divide(B,D)),
inference(paramod,[status(thm)],[c_55,c_6]) ).
cnf(c_84,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)),
inference(paramod,[status(thm)],[c_60,c_364]) ).
cnf(c_86,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D)) = inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C)))),
inference(paramod,[status(thm)],[c_6,c_55]) ).
cnf(c_92,plain,
double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(inverse(double_divide(B,C)),D)))) = D,
inference(paramod,[status(thm)],[c_55,c_32]) ).
cnf(c_95,plain,
inverse(double_divide(inverse(double_divide(A,inverse(inverse(double_divide(B,C))))),inverse(double_divide(D,B)))) = inverse(double_divide(A,inverse(double_divide(D,inverse(C))))),
inference(paramod,[status(thm)],[c_55,c_55]) ).
cnf(c_97,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_84,c_42]) ).
cnf(c_365,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),double_divide(A,inverse(C)))))) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(paramod,[status(thm)],[c_86,c_79]) ).
cnf(c_98,plain,
inverse(inverse(double_divide(inverse(A),double_divide(B,C)))) = inverse(double_divide(B,inverse(double_divide(C,A)))),
inference(paramod,[status(thm)],[c_84,c_365]) ).
cnf(c_103,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_98,c_50]) ).
cnf(c_118,plain,
inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),double_divide(inverse(inverse(double_divide(C,A))),double_divide(B,D)))) = D,
inference(paramod,[status(thm)],[c_84,c_11]) ).
cnf(c_119,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,D))))) = inverse(double_divide(inverse(D),double_divide(B,C))),
inference(paramod,[status(thm)],[c_84,c_11]) ).
cnf(c_366,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = inverse(double_divide(double_divide(A,C),B)),
inference(paramod,[status(thm)],[c_11,c_84]) ).
cnf(c_121,plain,
inverse(double_divide(double_divide(A,B),C)) = double_divide(inverse(double_divide(A,inverse(C))),B),
inference(copy,[status(thm)],[c_366]) ).
cnf(c_367,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(C,D))))),inverse(double_divide(D,B)))) = double_divide(inverse(double_divide(E,C)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_84,c_14]) ).
cnf(c_368,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(inverse(B),inverse(double_divide(D,B)))),double_divide(C,D))))) = double_divide(inverse(double_divide(E,C)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_86,c_367]) ).
cnf(c_123,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),B)))))) = double_divide(inverse(double_divide(E,D)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_86,c_368]) ).
cnf(c_125,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),D)),double_divide(E,D))) = double_divide(inverse(double_divide(B,E)),inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_84,c_14]) ).
cnf(c_369,plain,
double_divide(A,inverse(inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,C))))) = inverse(double_divide(B,double_divide(A,D))),
inference(paramod,[status(thm)],[c_14,c_84]) ).
cnf(c_129,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(D,C)))))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_98,c_369]) ).
cnf(c_132,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B))) = double_divide(A,C),
inference(paramod,[status(thm)],[c_84,c_32]) ).
cnf(c_370,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = inverse(double_divide(double_divide(A,inverse(double_divide(B,D))),C)),
inference(paramod,[status(thm)],[c_32,c_84]) ).
cnf(c_371,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(B,D))),
inference(paramod,[status(thm)],[c_121,c_370]) ).
cnf(c_133,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,D))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(inverse(B),D))),
inference(copy,[status(thm)],[c_371]) ).
cnf(c_372,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))) = inverse(double_divide(inverse(double_divide(inverse(D),double_divide(A,C))),B)),
inference(paramod,[status(thm)],[c_84,c_84]) ).
cnf(c_137,plain,
inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),D)) = double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),
inference(copy,[status(thm)],[c_372]) ).
cnf(c_373,plain,
inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(B,C))),double_divide(E,D))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_121,c_71]) ).
cnf(c_374,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(E,D)))),inverse(double_divide(B,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_121,c_373]) ).
cnf(c_375,plain,
double_divide(inverse(double_divide(A,E)),inverse(double_divide(B,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_132,c_374]) ).
cnf(c_143,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),D) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D))),
inference(copy,[status(thm)],[c_375]) ).
cnf(c_376,plain,
inverse(double_divide(double_divide(inverse(double_divide(inverse(double_divide(A,B)),inverse(D))),double_divide(A,C)),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_121,c_31]) ).
cnf(c_377,plain,
inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(B,double_divide(A,C)))),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_143,c_376]) ).
cnf(c_378,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(inverse(double_divide(C,E)),D)))),inverse(double_divide(B,double_divide(A,C)))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_121,c_377]) ).
cnf(c_149,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(A,B)))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_132,c_378]) ).
cnf(c_379,plain,
inverse(double_divide(double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),double_divide(E,D))) = double_divide(inverse(double_divide(B,E)),inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_137,c_125]) ).
cnf(c_157,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(inverse(C),inverse(double_divide(D,E))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_121,c_379]) ).
cnf(c_380,plain,
double_divide(B,inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(C,A))),double_divide(B,D))),inverse(double_divide(C,A))))) = D,
inference(paramod,[status(thm)],[c_137,c_118]) ).
cnf(c_158,plain,
double_divide(A,double_divide(A,inverse(double_divide(inverse(inverse(double_divide(B,C))),inverse(double_divide(D,inverse(double_divide(B,C)))))))) = D,
inference(paramod,[status(thm)],[c_137,c_380]) ).
cnf(c_381,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,D))))) = double_divide(B,inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_143,c_66]) ).
cnf(c_164,plain,
inverse(double_divide(inverse(A),double_divide(B,C))) = double_divide(B,inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_119,c_381]) ).
cnf(c_382,plain,
inverse(double_divide(double_divide(B,inverse(double_divide(C,A))),D)) = double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),
inference(paramod,[status(thm)],[c_164,c_137]) ).
cnf(c_176,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,D))) = double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))),
inference(paramod,[status(thm)],[c_121,c_382]) ).
cnf(c_191,plain,
double_divide(A,double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(B,C)),
inference(paramod,[status(thm)],[c_164,c_84]) ).
cnf(c_383,plain,
double_divide(B,inverse(double_divide(double_divide(C,inverse(double_divide(D,A))),A))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_164,c_68]) ).
cnf(c_384,plain,
double_divide(B,double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(D,A)))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_121,c_383]) ).
cnf(c_385,plain,
double_divide(B,double_divide(C,D)) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_132,c_384]) ).
cnf(c_193,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,D)))) = double_divide(B,double_divide(C,D)),
inference(copy,[status(thm)],[c_385]) ).
cnf(c_194,plain,
inverse(double_divide(inverse(A),inverse(double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_191,c_61]) ).
cnf(c_386,plain,
double_divide(C,inverse(double_divide(B,double_divide(A,B)))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_164,c_14]) ).
cnf(c_202,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = double_divide(B,inverse(double_divide(D,double_divide(C,D)))),
inference(copy,[status(thm)],[c_386]) ).
cnf(c_387,plain,
double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),inverse(double_divide(B,double_divide(A,B)))) = D,
inference(paramod,[status(thm)],[c_164,c_7]) ).
cnf(c_388,plain,
double_divide(C,inverse(double_divide(inverse(double_divide(A,double_divide(C,D))),inverse(double_divide(B,double_divide(A,B)))))) = D,
inference(paramod,[status(thm)],[c_176,c_387]) ).
cnf(c_203,plain,
inverse(double_divide(A,double_divide(B,inverse(double_divide(A,double_divide(B,C)))))) = C,
inference(paramod,[status(thm)],[c_129,c_388]) ).
cnf(c_205,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(inverse(C),inverse(double_divide(D,E))))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_176,c_157]) ).
cnf(c_207,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(D,double_divide(A,B)))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_176,c_149]) ).
cnf(c_389,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_176,c_133]) ).
cnf(c_211,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = double_divide(A,inverse(double_divide(inverse(C),inverse(double_divide(B,D))))),
inference(copy,[status(thm)],[c_389]) ).
cnf(c_212,plain,
inverse(double_divide(A,inverse(double_divide(inverse(inverse(double_divide(B,C))),inverse(double_divide(D,B)))))) = inverse(double_divide(A,inverse(double_divide(D,inverse(C))))),
inference(paramod,[status(thm)],[c_176,c_95]) ).
cnf(c_390,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(inverse(C),D)))))) = D,
inference(paramod,[status(thm)],[c_211,c_92]) ).
cnf(c_391,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(double_divide(C,D)))))))) = D,
inference(paramod,[status(thm)],[c_211,c_390]) ).
cnf(c_213,plain,
inverse(double_divide(inverse(A),inverse(double_divide(A,B)))) = B,
inference(paramod,[status(thm)],[c_32,c_391]) ).
cnf(c_216,plain,
double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,D))))) = inverse(double_divide(C,double_divide(A,D))),
inference(paramod,[status(thm)],[c_193,c_21]) ).
cnf(c_218,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_194,c_158]) ).
cnf(c_223,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(C,B))))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_194,c_123]) ).
cnf(c_392,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(double_divide(C,inverse(double_divide(D,E))))))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_211,c_205]) ).
cnf(c_393,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(D,E))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_213,c_392]) ).
cnf(c_227,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,D))) = double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),
inference(copy,[status(thm)],[c_393]) ).
cnf(c_394,plain,
inverse(inverse(double_divide(A,double_divide(A,C)))) = C,
inference(paramod,[status(thm)],[c_216,c_203]) ).
cnf(c_229,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_218,c_394]) ).
cnf(c_246,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,inverse(double_divide(D,double_divide(A,B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_227,c_207]) ).
cnf(c_395,plain,
inverse(double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(D,B)))))) = inverse(double_divide(A,inverse(double_divide(D,inverse(C))))),
inference(paramod,[status(thm)],[c_229,c_212]) ).
cnf(c_396,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,inverse(inverse(double_divide(D,B))))),C))) = inverse(double_divide(A,inverse(double_divide(D,inverse(C))))),
inference(paramod,[status(thm)],[c_121,c_395]) ).
cnf(c_262,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,double_divide(C,B))),D))) = inverse(double_divide(A,inverse(double_divide(C,inverse(D))))),
inference(paramod,[status(thm)],[c_229,c_396]) ).
cnf(c_267,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_229,c_97]) ).
cnf(c_397,plain,
inverse(double_divide(A,double_divide(inverse(C),D))) = inverse(double_divide(A,inverse(double_divide(C,inverse(D))))),
inference(paramod,[status(thm)],[c_267,c_262]) ).
cnf(c_276,plain,
inverse(double_divide(A,inverse(double_divide(B,inverse(C))))) = inverse(double_divide(A,double_divide(inverse(B),C))),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_398,plain,
inverse(double_divide(A,inverse(C))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_267,c_223]) ).
cnf(c_279,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = inverse(double_divide(C,inverse(B))),
inference(copy,[status(thm)],[c_398]) ).
cnf(c_399,plain,
inverse(double_divide(C,inverse(B))) = double_divide(B,inverse(double_divide(D,double_divide(C,D)))),
inference(paramod,[status(thm)],[c_279,c_202]) ).
cnf(c_280,plain,
inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_267,c_399]) ).
cnf(c_400,plain,
double_divide(A,inverse(double_divide(B,inverse(D)))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_267,c_129]) ).
cnf(c_401,plain,
double_divide(A,double_divide(D,inverse(B))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_280,c_400]) ).
cnf(c_285,plain,
inverse(double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,inverse(C))),
inference(copy,[status(thm)],[c_401]) ).
cnf(c_402,plain,
inverse(double_divide(A,inverse(A))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_267,c_103]) ).
cnf(c_403,plain,
double_divide(A,inverse(A)) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_280,c_402]) ).
cnf(c_404,plain,
double_divide(A,inverse(A)) = inverse(double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_279,c_403]) ).
cnf(c_286,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_280,c_404]) ).
cnf(c_405,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,double_divide(D,inverse(B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_246]) ).
cnf(c_406,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,inverse(double_divide(D,inverse(B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_405]) ).
cnf(c_407,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,double_divide(B,inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_280,c_406]) ).
cnf(c_408,plain,
double_divide(A,double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_407]) ).
cnf(c_409,plain,
double_divide(A,double_divide(A,double_divide(B,double_divide(B,double_divide(C,inverse(inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_408]) ).
cnf(c_410,plain,
double_divide(A,double_divide(A,double_divide(B,double_divide(B,double_divide(C,D))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_229,c_409]) ).
cnf(c_411,plain,
double_divide(A,double_divide(A,double_divide(C,D))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_218,c_410]) ).
cnf(c_291,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_218,c_411]) ).
cnf(c_412,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| 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
| double_divide(b1,inverse(b1)) != inverse(double_divide(a1,inverse(a1))) ),
inference(paramod,[status(thm)],[c_280,c_4]) ).
cnf(c_413,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| 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
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_280,c_412]) ).
cnf(c_414,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,double_divide(b2,inverse(b2)))) != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_280,c_413]) ).
cnf(c_415,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| double_divide(b2,double_divide(a2,inverse(inverse(b2)))) != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_285,c_414]) ).
cnf(c_416,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| double_divide(b2,double_divide(a2,b2)) != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_229,c_415]) ).
cnf(c_417,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_267,c_416]) ).
cnf(c_418,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(b3,c3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_417]) ).
cnf(c_419,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(a3,inverse(double_divide(b3,c3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_418]) ).
cnf(c_420,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| double_divide(double_divide(b3,c3),inverse(a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_280,c_419]) ).
cnf(c_421,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(a3),double_divide(b3,c3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_420]) ).
cnf(c_422,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(a3),double_divide(b3,c3)) != inverse(double_divide(c3,inverse(double_divide(a3,b3))))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_421]) ).
cnf(c_423,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(double_divide(a3,b3),inverse(c3))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_280,c_422]) ).
cnf(c_424,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_423]) ).
cnf(c_425,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_291,c_424]) ).
cnf(c_426,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3))
| a2 != a2
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_425]) ).
cnf(c_427,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3))
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_426]) ).
cnf(c_428,plain,
( double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3))
| double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_427]) ).
cnf(c_296,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(resolve,[status(thm)],[c_286,c_428]) ).
cnf(c_429,plain,
inverse(double_divide(A,double_divide(C,inverse(B)))) = inverse(double_divide(A,double_divide(inverse(B),C))),
inference(paramod,[status(thm)],[c_280,c_276]) ).
cnf(c_430,plain,
double_divide(C,double_divide(A,inverse(inverse(B)))) = inverse(double_divide(A,double_divide(inverse(B),C))),
inference(paramod,[status(thm)],[c_285,c_429]) ).
cnf(c_431,plain,
double_divide(C,double_divide(A,B)) = inverse(double_divide(A,double_divide(inverse(B),C))),
inference(paramod,[status(thm)],[c_229,c_430]) ).
cnf(c_432,plain,
double_divide(C,double_divide(A,B)) = double_divide(inverse(B),double_divide(A,inverse(C))),
inference(paramod,[status(thm)],[c_285,c_431]) ).
cnf(c_306,plain,
double_divide(inverse(A),double_divide(B,inverse(C))) = double_divide(C,double_divide(B,A)),
inference(copy,[status(thm)],[c_432]) ).
cnf(c_433,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(c3),double_divide(b3,inverse(inverse(a3)))),
inference(paramod,[status(thm)],[c_306,c_296]) ).
cnf(c_434,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(c3),double_divide(b3,a3)),
inference(paramod,[status(thm)],[c_229,c_433]) ).
cnf(c_435,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(paramod,[status(thm)],[c_291,c_434]) ).
cnf(c_349,plain,
$false,
inference(copy,[status(thm)],[c_435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.43 % Computer : n004.cluster.edu
% 0.18/5.43 % Model : x86_64 x86_64
% 0.18/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.43 % Memory : 8046.5625MB
% 0.18/5.43 % OS : Linux 6.8.0-71-generic
% 0.18/5.43 % CPULimit : 300
% 0.18/5.43 % WCLimit : 300
% 0.18/5.43 % DateTime : Fri Sep 25 14:22:43 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.44 % Process 3362262 was started by sandbox2 on n004,
% 0.18/5.44 % Fri Sep 25 14:22:43 2026
% 0.18/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.44
% 0.18/5.44 % From the command line: assign(max_seconds, 300).
% 0.22/5.55
% 0.22/5.55 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.22/5.55
% 0.22/5.55 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.55
% 0.22/5.55 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.22/5.55 % Length of proof is 70.
% 0.22/5.55 % Level of proof is 21.
% 0.22/5.55 % Maximum clause weight is 85.000.
% 0.22/5.55 % Given clauses 19.
% 0.22/5.55
% 0.22/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
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