%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:29:53 AM UTC 2026
% Result : Unsatisfiable 1.24s 0.58s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 3
% Syntax : Number of formulae : 128 ( 128 unt; 0 def)
% Number of atoms : 128 ( 127 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 22 ( 22 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 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 : 436 ( 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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_923,plain,
multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(paramod,[status(thm)],[c_2,c_923]) ).
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_924,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_924]) ).
cnf(c_925,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_925]) ).
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_926,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_927,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_926]) ).
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_927]) ).
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_928,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_928]) ).
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_929,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_930,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_929]) ).
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_930]) ).
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_931,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_931]) ).
cnf(c_932,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_932]) ).
cnf(c_933,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_933]) ).
cnf(c_934,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_935,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_934]) ).
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_935]) ).
cnf(c_936,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_311,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_936]) ).
cnf(c_330,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_937,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_330]) ).
cnf(c_339,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_178,c_937]) ).
cnf(c_344,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_330,c_181]) ).
cnf(c_375,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_339,c_11]) ).
cnf(c_376,plain,
double_divide(inverse(A),A) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_339,c_11]) ).
cnf(c_386,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_339,c_339]) ).
cnf(c_388,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(A),A)))) != a2,
inference(paramod,[status(thm)],[c_376,c_4]) ).
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_376,c_103]) ).
cnf(c_423,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_376,c_11]) ).
cnf(c_938,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_376,c_11]) ).
cnf(c_425,plain,
double_divide(A,inverse(inverse(B))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_375,c_938]) ).
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_311]) ).
cnf(c_939,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_386,c_11]) ).
cnf(c_940,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_939]) ).
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_940]) ).
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_376,c_51]) ).
cnf(c_941,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_376,c_51]) ).
cnf(c_942,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_941]) ).
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_942]) ).
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_386,c_51]) ).
cnf(c_489,plain,
inverse(double_divide(a2,inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))))) != a2,
inference(paramod,[status(thm)],[c_91,c_388]) ).
cnf(c_502,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(double_divide(B,A)))))))) != a2,
inference(paramod,[status(thm)],[c_181,c_489]) ).
cnf(c_514,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),inverse(double_divide(inverse(A),inverse(double_divide(inverse(B),B)))))))) != a2,
inference(paramod,[status(thm)],[c_376,c_502]) ).
cnf(c_531,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_632,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_656,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_943,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_944,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_943]) ).
cnf(c_664,plain,
double_divide(A,inverse(double_divide(B,C))) = double_divide(A,double_divide(inverse(C),inverse(B))),
inference(copy,[status(thm)],[c_944]) ).
cnf(c_945,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_664,c_656]) ).
cnf(c_946,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_664,c_945]) ).
cnf(c_947,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_664,c_946]) ).
cnf(c_948,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_947]) ).
cnf(c_949,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_948]) ).
cnf(c_950,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_949]) ).
cnf(c_696,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_950]) ).
cnf(c_951,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_664,c_531]) ).
cnf(c_740,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_951]) ).
cnf(c_952,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),inverse(double_divide(inverse(A),double_divide(inverse(B),inverse(inverse(B))))))))) != a2,
inference(paramod,[status(thm)],[c_664,c_514]) ).
cnf(c_953,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),inverse(double_divide(inverse(A),double_divide(inverse(B),B))))))) != a2,
inference(paramod,[status(thm)],[c_425,c_952]) ).
cnf(c_954,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),double_divide(inverse(double_divide(inverse(B),B)),inverse(inverse(A))))))) != a2,
inference(paramod,[status(thm)],[c_664,c_953]) ).
cnf(c_955,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),double_divide(inverse(double_divide(inverse(B),B)),A))))) != a2,
inference(paramod,[status(thm)],[c_425,c_954]) ).
cnf(c_956,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),double_divide(double_divide(inverse(B),inverse(inverse(B))),A))))) != a2,
inference(paramod,[status(thm)],[c_236,c_955]) ).
cnf(c_957,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(inverse(A)),double_divide(double_divide(inverse(B),B),A))))) != a2,
inference(paramod,[status(thm)],[c_425,c_956]) ).
cnf(c_958,plain,
inverse(double_divide(a2,double_divide(inverse(double_divide(double_divide(inverse(B),B),A)),inverse(inverse(inverse(A)))))) != a2,
inference(paramod,[status(thm)],[c_664,c_957]) ).
cnf(c_959,plain,
inverse(double_divide(a2,double_divide(inverse(double_divide(double_divide(inverse(B),B),A)),inverse(A)))) != a2,
inference(paramod,[status(thm)],[c_425,c_958]) ).
cnf(c_960,plain,
inverse(double_divide(a2,double_divide(double_divide(inverse(A),inverse(double_divide(inverse(B),B))),inverse(A)))) != a2,
inference(paramod,[status(thm)],[c_236,c_959]) ).
cnf(c_961,plain,
inverse(double_divide(a2,double_divide(double_divide(inverse(A),double_divide(inverse(B),inverse(inverse(B)))),inverse(A)))) != a2,
inference(paramod,[status(thm)],[c_664,c_960]) ).
cnf(c_746,plain,
inverse(double_divide(a2,double_divide(double_divide(inverse(A),double_divide(inverse(B),B)),inverse(A)))) != a2,
inference(paramod,[status(thm)],[c_425,c_961]) ).
cnf(c_962,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_664,c_458]) ).
cnf(c_757,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_962]) ).
cnf(c_963,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_664,c_418]) ).
cnf(c_768,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_963]) ).
cnf(c_964,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_664,c_344]) ).
cnf(c_965,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_664,c_964]) ).
cnf(c_966,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_965]) ).
cnf(c_967,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_966]) ).
cnf(c_780,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_967]) ).
cnf(c_968,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_757,c_482]) ).
cnf(c_833,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_968]) ).
cnf(c_969,plain,
double_divide(B,inverse(inverse(D))) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_833,c_632]) ).
cnf(c_970,plain,
double_divide(B,D) = double_divide(E,double_divide(double_divide(B,D),E)),
inference(paramod,[status(thm)],[c_425,c_969]) ).
cnf(c_837,plain,
double_divide(A,double_divide(double_divide(B,C),A)) = double_divide(B,C),
inference(copy,[status(thm)],[c_970]) ).
cnf(c_862,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_837,c_483]) ).
cnf(c_971,plain,
double_divide(inverse(inverse(A)),D) = double_divide(E,double_divide(double_divide(A,D),E)),
inference(paramod,[status(thm)],[c_862,c_479]) ).
cnf(c_863,plain,
double_divide(inverse(inverse(A)),B) = double_divide(A,B),
inference(paramod,[status(thm)],[c_837,c_971]) ).
cnf(c_867,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_837,c_437]) ).
cnf(c_972,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_863,c_780]) ).
cnf(c_973,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_863,c_972]) ).
cnf(c_974,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_863,c_973]) ).
cnf(c_889,plain,
double_divide(A,double_divide(double_divide(B,C),B)) = double_divide(A,C),
inference(paramod,[status(thm)],[c_837,c_974]) ).
cnf(c_975,plain,
double_divide(double_divide(A,inverse(A)),C) = double_divide(inverse(inverse(C)),double_divide(inverse(D),D)),
inference(paramod,[status(thm)],[c_889,c_768]) ).
cnf(c_903,plain,
double_divide(double_divide(A,inverse(A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_867,c_975]) ).
cnf(c_976,plain,
double_divide(double_divide(A,inverse(A)),C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_889,c_740]) ).
cnf(c_977,plain,
inverse(C) = double_divide(inverse(inverse(C)),double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_903,c_976]) ).
cnf(c_978,plain,
inverse(C) = double_divide(C,double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_863,c_977]) ).
cnf(c_912,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(copy,[status(thm)],[c_978]) ).
cnf(c_979,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_863,c_696]) ).
cnf(c_980,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_863,c_979]) ).
cnf(c_981,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_889,c_980]) ).
cnf(c_916,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_912,c_981]) ).
cnf(c_982,plain,
inverse(double_divide(a2,double_divide(A,inverse(A)))) != a2,
inference(paramod,[status(thm)],[c_867,c_746]) ).
cnf(c_983,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_912,c_982]) ).
cnf(c_984,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_916,c_983]) ).
cnf(c_922,plain,
$false,
inference(copy,[status(thm)],[c_984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:57:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3475452 was started by sandbox2 on n004,
% 0.08/0.36 % Fri Sep 25 14:57:07 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 1.24/0.58
% 1.24/0.58 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.24/0.58
% 1.24/0.58 % SZS status Unsatisfiable for theBenchmark
% 1.24/0.58
% 1.24/0.58 % Proof 1 at 0.15 (+ 0.05) seconds.
% 1.24/0.58 % Length of proof is 63.
% 1.24/0.58 % Level of proof is 25.
% 1.24/0.58 % Maximum clause weight is 97.000.
% 1.24/0.58 % Given clauses 35.
% 1.24/0.58
% 1.24/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------