%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP609-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:30:29 AM UTC 2026
% Result : Unsatisfiable 0.20s 15.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 150 ( 150 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 613 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(inverse(double_divide(VAR_0,VAR_1)),VAR_2)),double_divide(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_469,plain,
inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_470,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(paramod,[status(thm)],[c_2,c_469]) ).
cnf(c_4,plain,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(copy,[status(thm)],[c_470]) ).
cnf(c_5,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,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_1,c_5]) ).
cnf(c_471,plain,
A = double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(B,C)),A)))),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_16,plain,
double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,B)),C)))) = C,
inference(copy,[status(thm)],[c_471]) ).
cnf(c_19,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_21,plain,
inverse(double_divide(inverse(inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(D,double_divide(D,A)))) = C,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_472,plain,
inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(inverse(double_divide(C,A)),D)))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_23,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(inverse(double_divide(C,D)),E)))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))),
inference(copy,[status(thm)],[c_472]) ).
cnf(c_30,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(inverse(double_divide(inverse(double_divide(C,D)),double_divide(A,D)))),B))) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_39,plain,
inverse(double_divide(A,double_divide(B,double_divide(inverse(double_divide(C,D)),double_divide(C,A))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_41,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = double_divide(inverse(double_divide(D,B)),double_divide(D,C)),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_60,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_19,c_6]) ).
cnf(c_473,plain,
double_divide(double_divide(A,B),double_divide(inverse(double_divide(C,D)),E)) = double_divide(inverse(double_divide(F,double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D))),double_divide(F,E)),
inference(paramod,[status(thm)],[c_5,c_41]) ).
cnf(c_79,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),D)),E))),double_divide(A,F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(copy,[status(thm)],[c_473]) ).
cnf(c_474,plain,
double_divide(A,double_divide(B,C)) = double_divide(inverse(double_divide(D,double_divide(inverse(double_divide(E,B)),double_divide(E,A)))),double_divide(D,C)),
inference(paramod,[status(thm)],[c_6,c_41]) ).
cnf(c_81,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,C)),double_divide(B,D)))),double_divide(A,E)) = double_divide(D,double_divide(C,E)),
inference(copy,[status(thm)],[c_474]) ).
cnf(c_84,plain,
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_41,c_10]) ).
cnf(c_475,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),double_divide(A,inverse(double_divide(inverse(double_divide(D,C)),double_divide(D,E))))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_91,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(C,double_divide(C,D))))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_23,c_475]) ).
cnf(c_476,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(B,C)),D)) = double_divide(inverse(double_divide(E,double_divide(B,inverse(double_divide(C,A))))),double_divide(E,D)),
inference(paramod,[status(thm)],[c_19,c_41]) ).
cnf(c_92,plain,
double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,D))))),double_divide(A,E)) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(copy,[status(thm)],[c_476]) ).
cnf(c_162,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,double_divide(inverse(double_divide(D,C)),E))),B))) = double_divide(inverse(E),double_divide(D,A)),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_477,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = inverse(double_divide(D,double_divide(inverse(double_divide(B,D)),C))),
inference(paramod,[status(thm)],[c_16,c_19]) ).
cnf(c_168,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(C))),
inference(copy,[status(thm)],[c_477]) ).
cnf(c_178,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(D),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_478,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,inverse(double_divide(E,double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E)),F))))),C))) = F,
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_479,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,double_divide(inverse(double_divide(A,D)),inverse(double_divide(B,F))))),C))) = F,
inference(paramod,[status(thm)],[c_60,c_478]) ).
cnf(c_179,plain,
double_divide(inverse(inverse(double_divide(A,B))),double_divide(C,double_divide(C,A))) = B,
inference(paramod,[status(thm)],[c_162,c_479]) ).
cnf(c_480,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,B)),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(D,E),
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_182,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,B))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_7,c_480]) ).
cnf(c_481,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,B))),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E))))) = C,
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_186,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(B,C))))) = A,
inference(paramod,[status(thm)],[c_182,c_481]) ).
cnf(c_482,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(double_divide(inverse(double_divide(D,E)),double_divide(D,E)),F)),C))) = double_divide(inverse(double_divide(A,B)),F),
inference(paramod,[status(thm)],[c_84,c_5]) ).
cnf(c_190,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,C)),double_divide(B,C)))),D)),E) = double_divide(inverse(double_divide(A,D)),E),
inference(paramod,[status(thm)],[c_7,c_482]) ).
cnf(c_483,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_84,c_5]) ).
cnf(c_193,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_186,c_483]) ).
cnf(c_484,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E)))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_84,c_6]) ).
cnf(c_199,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(double_divide(C,D)),double_divide(C,D)))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_193,c_484]) ).
cnf(c_485,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E))))) = double_divide(inverse(double_divide(F,inverse(double_divide(B,C)))),double_divide(F,A)),
inference(paramod,[status(thm)],[c_84,c_10]) ).
cnf(c_486,plain,
inverse(double_divide(A,double_divide(B,C))) = double_divide(inverse(double_divide(F,inverse(double_divide(B,C)))),double_divide(F,A)),
inference(paramod,[status(thm)],[c_199,c_485]) ).
cnf(c_206,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),double_divide(A,D)) = inverse(double_divide(D,double_divide(B,C))),
inference(copy,[status(thm)],[c_486]) ).
cnf(c_487,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(D,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),D)),inverse(double_divide(inverse(double_divide(E,F)),double_divide(E,F)))),
inference(paramod,[status(thm)],[c_84,c_10]) ).
cnf(c_208,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(D,C))) = double_divide(inverse(double_divide(A,B)),D),
inference(paramod,[status(thm)],[c_199,c_487]) ).
cnf(c_488,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),double_divide(C,D))),inverse(double_divide(inverse(double_divide(E,F)),double_divide(E,F))))) = double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D),
inference(paramod,[status(thm)],[c_84,c_7]) ).
cnf(c_233,plain,
inverse(double_divide(double_divide(A,B),double_divide(C,D))) = double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D),
inference(paramod,[status(thm)],[c_199,c_488]) ).
cnf(c_489,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(double_divide(A,B),double_divide(double_divide(inverse(double_divide(C,D)),double_divide(C,D)),E)))) = E,
inference(paramod,[status(thm)],[c_84,c_16]) ).
cnf(c_490,plain,
double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(C,D)),double_divide(C,D)))),B)),E)) = E,
inference(paramod,[status(thm)],[c_233,c_489]) ).
cnf(c_238,plain,
double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(A,B)),C)) = C,
inference(paramod,[status(thm)],[c_190,c_490]) ).
cnf(c_243,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,B))) = double_divide(double_divide(inverse(double_divide(C,D)),double_divide(C,D)),double_divide(inverse(double_divide(E,F)),double_divide(E,F))),
inference(paramod,[status(thm)],[c_84,c_84]) ).
cnf(c_491,plain,
double_divide(inverse(double_divide(A,B)),inverse(D)) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))),
inference(paramod,[status(thm)],[c_208,c_178]) ).
cnf(c_492,plain,
double_divide(inverse(double_divide(A,B)),inverse(D)) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_193,c_491]) ).
cnf(c_246,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(B,D)) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(copy,[status(thm)],[c_492]) ).
cnf(c_493,plain,
double_divide(B,C) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(C))),
inference(paramod,[status(thm)],[c_193,c_168]) ).
cnf(c_251,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = double_divide(B,C),
inference(copy,[status(thm)],[c_493]) ).
cnf(c_253,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(inverse(D),double_divide(C,A)),
inference(paramod,[status(thm)],[c_193,c_162]) ).
cnf(c_260,plain,
double_divide(A,double_divide(B,double_divide(B,C))) = double_divide(A,C),
inference(paramod,[status(thm)],[c_193,c_91]) ).
cnf(c_262,plain,
double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))),
inference(paramod,[status(thm)],[c_193,c_60]) ).
cnf(c_494,plain,
double_divide(A,inverse(double_divide(double_divide(B,inverse(double_divide(C,D))),double_divide(A,E)))) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_262,c_92]) ).
cnf(c_495,plain,
double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,D)))),E)) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_233,c_494]) ).
cnf(c_496,plain,
double_divide(A,double_divide(inverse(double_divide(B,inverse(double_divide(A,inverse(double_divide(C,D)))))),E)) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_262,c_495]) ).
cnf(c_497,plain,
double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(A,inverse(double_divide(C,D)))),E)))) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_262,c_496]) ).
cnf(c_498,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(inverse(double_divide(C,D)),E)))))) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_262,c_497]) ).
cnf(c_499,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))))) = double_divide(inverse(D),double_divide(inverse(double_divide(B,C)),E)),
inference(paramod,[status(thm)],[c_262,c_498]) ).
cnf(c_317,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))))) = double_divide(inverse(D),double_divide(B,inverse(double_divide(C,E)))),
inference(paramod,[status(thm)],[c_262,c_499]) ).
cnf(c_500,plain,
double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,D)))))),double_divide(A,E)) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_81]) ).
cnf(c_501,plain,
double_divide(A,inverse(double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,D)))),double_divide(A,E)))) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_500]) ).
cnf(c_502,plain,
double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,double_divide(B,D))))),E)) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_233,c_501]) ).
cnf(c_503,plain,
double_divide(A,double_divide(inverse(double_divide(B,inverse(double_divide(A,inverse(double_divide(C,double_divide(B,D))))))),E)) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_502]) ).
cnf(c_504,plain,
double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(A,inverse(double_divide(C,double_divide(B,D))))),E)))) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_503]) ).
cnf(c_505,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(inverse(double_divide(C,double_divide(B,D))),E)))))) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_504]) ).
cnf(c_506,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(double_divide(B,D),E)))))))) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_262,c_505]) ).
cnf(c_507,plain,
double_divide(inverse(double_divide(B,D)),double_divide(B,inverse(double_divide(C,E)))) = double_divide(D,double_divide(C,E)),
inference(paramod,[status(thm)],[c_317,c_506]) ).
cnf(c_320,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,inverse(double_divide(C,D)))))) = double_divide(B,double_divide(C,D)),
inference(paramod,[status(thm)],[c_262,c_507]) ).
cnf(c_508,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,inverse(double_divide(C,D)))),E))),double_divide(A,F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_79]) ).
cnf(c_509,plain,
double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(C,D)),E))))),double_divide(A,F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_508]) ).
cnf(c_510,plain,
double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,inverse(double_divide(D,E))))))),double_divide(A,F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_509]) ).
cnf(c_511,plain,
double_divide(A,inverse(double_divide(double_divide(B,inverse(double_divide(C,inverse(double_divide(D,E))))),double_divide(A,F)))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_510]) ).
cnf(c_512,plain,
double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,inverse(double_divide(D,E)))))),F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_233,c_511]) ).
cnf(c_513,plain,
double_divide(A,double_divide(inverse(double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))))),F)) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_512]) ).
cnf(c_514,plain,
double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))),F)))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_513]) ).
cnf(c_515,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(double_divide(D,E)))),F)))))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_514]) ).
cnf(c_516,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(inverse(double_divide(D,E)),F)))))))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_515]) ).
cnf(c_517,plain,
double_divide(A,double_divide(B,inverse(double_divide(A,inverse(double_divide(C,inverse(double_divide(D,inverse(double_divide(E,F)))))))))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_262,c_516]) ).
cnf(c_518,plain,
double_divide(inverse(D),double_divide(B,inverse(double_divide(C,inverse(double_divide(E,F)))))) = double_divide(double_divide(B,D),double_divide(inverse(double_divide(C,E)),F)),
inference(paramod,[status(thm)],[c_317,c_517]) ).
cnf(c_519,plain,
double_divide(inverse(D),double_divide(B,inverse(double_divide(C,inverse(double_divide(E,F)))))) = double_divide(double_divide(B,D),double_divide(C,inverse(double_divide(E,F)))),
inference(paramod,[status(thm)],[c_262,c_518]) ).
cnf(c_321,plain,
double_divide(double_divide(A,B),double_divide(C,inverse(double_divide(D,E)))) = double_divide(inverse(B),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))),
inference(copy,[status(thm)],[c_519]) ).
cnf(c_520,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))),
inference(paramod,[status(thm)],[c_262,c_23]) ).
cnf(c_521,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,inverse(double_divide(C,inverse(double_divide(D,E)))))))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))),
inference(paramod,[status(thm)],[c_262,c_520]) ).
cnf(c_522,plain,
double_divide(B,double_divide(C,inverse(double_divide(D,E)))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))),
inference(paramod,[status(thm)],[c_320,c_521]) ).
cnf(c_326,plain,
inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(B,double_divide(C,inverse(double_divide(A,D)))),
inference(copy,[status(thm)],[c_522]) ).
cnf(c_342,plain,
double_divide(inverse(inverse(double_divide(A,B))),A) = B,
inference(paramod,[status(thm)],[c_260,c_179]) ).
cnf(c_523,plain,
inverse(double_divide(inverse(inverse(double_divide(A,inverse(double_divide(B,double_divide(C,B)))))),double_divide(D,double_divide(D,A)))) = C,
inference(paramod,[status(thm)],[c_262,c_21]) ).
cnf(c_524,plain,
inverse(double_divide(inverse(inverse(double_divide(A,inverse(double_divide(B,double_divide(C,B)))))),A)) = C,
inference(paramod,[status(thm)],[c_260,c_523]) ).
cnf(c_346,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_342,c_524]) ).
cnf(c_350,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(double_divide(C,D),B))))) = double_divide(inverse(D),double_divide(C,A)),
inference(paramod,[status(thm)],[c_262,c_253]) ).
cnf(c_351,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,inverse(C))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_262,c_251]) ).
cnf(c_525,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),double_divide(B,D)) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_246]) ).
cnf(c_526,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(B,D)))) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_525]) ).
cnf(c_527,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(B,D)))))) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_526]) ).
cnf(c_356,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(B,D)))))) = double_divide(A,inverse(double_divide(C,inverse(D)))),
inference(paramod,[status(thm)],[c_262,c_527]) ).
cnf(c_528,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(double_divide(inverse(double_divide(C,D)),double_divide(C,D)),double_divide(inverse(double_divide(E,F)),double_divide(E,F))),
inference(paramod,[status(thm)],[c_262,c_243]) ).
cnf(c_529,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),double_divide(inverse(double_divide(E,F)),double_divide(E,F))),
inference(paramod,[status(thm)],[c_262,c_528]) ).
cnf(c_530,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),double_divide(E,inverse(double_divide(F,double_divide(E,F))))),
inference(paramod,[status(thm)],[c_262,c_529]) ).
cnf(c_531,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(inverse(inverse(double_divide(D,double_divide(C,D)))),double_divide(C,inverse(double_divide(E,inverse(double_divide(F,double_divide(E,F))))))),
inference(paramod,[status(thm)],[c_321,c_530]) ).
cnf(c_532,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(C,double_divide(C,inverse(double_divide(E,inverse(double_divide(F,double_divide(E,F))))))),
inference(paramod,[status(thm)],[c_346,c_531]) ).
cnf(c_358,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(C,double_divide(C,inverse(double_divide(D,inverse(D))))),
inference(paramod,[status(thm)],[c_356,c_532]) ).
cnf(c_533,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_262,c_238]) ).
cnf(c_534,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,inverse(double_divide(B,C)))))) = C,
inference(paramod,[status(thm)],[c_262,c_533]) ).
cnf(c_359,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_351,c_534]) ).
cnf(c_535,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(A,D)))) = inverse(double_divide(D,double_divide(B,C))),
inference(paramod,[status(thm)],[c_262,c_206]) ).
cnf(c_370,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,D)))))) = inverse(double_divide(D,double_divide(B,C))),
inference(paramod,[status(thm)],[c_262,c_535]) ).
cnf(c_536,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),double_divide(A,B))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_262,c_182]) ).
cnf(c_537,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(A,B))))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_262,c_536]) ).
cnf(c_538,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,B))))))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_262,c_537]) ).
cnf(c_539,plain,
double_divide(inverse(inverse(double_divide(B,double_divide(B,C)))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_370,c_538]) ).
cnf(c_380,plain,
double_divide(inverse(inverse(A)),B) = double_divide(A,B),
inference(paramod,[status(thm)],[c_359,c_539]) ).
cnf(c_540,plain,
inverse(double_divide(A,double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(C,A))))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_262,c_39]) ).
cnf(c_541,plain,
double_divide(B,double_divide(C,inverse(double_divide(A,inverse(double_divide(D,double_divide(C,A))))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_326,c_540]) ).
cnf(c_542,plain,
double_divide(B,inverse(double_divide(A,double_divide(A,D)))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_370,c_541]) ).
cnf(c_543,plain,
double_divide(B,inverse(D)) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_359,c_542]) ).
cnf(c_544,plain,
double_divide(B,inverse(D)) = double_divide(E,inverse(double_divide(B,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_262,c_543]) ).
cnf(c_402,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,C)))) = double_divide(B,inverse(C)),
inference(copy,[status(thm)],[c_544]) ).
cnf(c_545,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(inverse(double_divide(C,inverse(double_divide(D,double_divide(A,D)))))),B))) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_262,c_30]) ).
cnf(c_546,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,inverse(double_divide(D,double_divide(A,D)))),B))) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_380,c_545]) ).
cnf(c_547,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(double_divide(C,inverse(double_divide(D,double_divide(A,D)))),B))))) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_262,c_546]) ).
cnf(c_548,plain,
double_divide(inverse(inverse(double_divide(D,double_divide(A,D)))),double_divide(C,A)) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_350,c_547]) ).
cnf(c_549,plain,
double_divide(A,double_divide(C,A)) = double_divide(E,double_divide(E,C)),
inference(paramod,[status(thm)],[c_346,c_548]) ).
cnf(c_403,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_359,c_549]) ).
cnf(c_550,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_262,c_10]) ).
cnf(c_551,plain,
inverse(double_divide(A,inverse(C))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_403,c_550]) ).
cnf(c_552,plain,
inverse(double_divide(A,inverse(C))) = double_divide(D,inverse(double_divide(C,double_divide(D,A)))),
inference(paramod,[status(thm)],[c_262,c_551]) ).
cnf(c_409,plain,
inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_402,c_552]) ).
cnf(c_553,plain,
inverse(double_divide(A,inverse(A))) = double_divide(C,double_divide(C,inverse(double_divide(D,inverse(D))))),
inference(paramod,[status(thm)],[c_403,c_358]) ).
cnf(c_554,plain,
double_divide(A,inverse(A)) = double_divide(C,double_divide(C,inverse(double_divide(D,inverse(D))))),
inference(paramod,[status(thm)],[c_409,c_553]) ).
cnf(c_555,plain,
double_divide(A,inverse(A)) = double_divide(C,double_divide(C,double_divide(D,inverse(D)))),
inference(paramod,[status(thm)],[c_409,c_554]) ).
cnf(c_429,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_359,c_555]) ).
cnf(c_556,plain,
double_divide(b1,inverse(b1)) != inverse(double_divide(a1,inverse(a1))),
inference(paramod,[status(thm)],[c_409,c_4]) ).
cnf(c_557,plain,
double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)),
inference(paramod,[status(thm)],[c_409,c_556]) ).
cnf(c_468,plain,
$false,
inference(resolve,[status(thm)],[c_429,c_557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP609-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/15.44 % Computer : n008.cluster.edu
% 0.17/15.44 % Model : x86_64 x86_64
% 0.17/15.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.44 % Memory : 8046.5625MB
% 0.17/15.44 % OS : Linux 6.8.0-71-generic
% 0.17/15.44 % CPULimit : 300
% 0.17/15.44 % WCLimit : 300
% 0.17/15.44 % DateTime : Fri Sep 25 15:03:10 UTC 2026
% 0.17/15.45 % CPUTime :
% 0.17/15.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/15.45 % Process 1345342 was started by sandbox on n008,
% 0.17/15.45 % Fri Sep 25 15:03:10 2026
% 0.17/15.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/15.45
% 0.17/15.45 % From the command line: assign(max_seconds, 300).
% 0.20/15.61
% 0.20/15.61 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.20/15.61
% 0.20/15.61 % SZS status Unsatisfiable for theBenchmark
% 0.20/15.61
% 0.20/15.61 % Proof 1 at 0.09 (+ 0.04) seconds.
% 0.20/15.61 % Length of proof is 58.
% 0.20/15.61 % Level of proof is 16.
% 0.20/15.61 % Maximum clause weight is 92.000.
% 0.20/15.61 % Given clauses 13.
% 0.20/15.61
% 0.20/15.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------