%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP584-1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:30:25 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 5
% Syntax : Number of formulae : 115 ( 115 unt; 0 def)
% Number of atoms : 115 ( 114 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 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 225 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(identity,VAR_1),double_divide(VAR_2,double_divide(VAR_1,VAR_0)))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_163,plain,
identity = double_divide(A,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(copy,[status(thm)],[c_163]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_6,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_164,plain,
double_divide(double_divide(b,a),identity) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_7,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_2,c_164]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_16,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(identity,identity),double_divide(B,A))))),C)),double_divide(identity,identity)) = double_divide(D,double_divide(double_divide(identity,E),double_divide(C,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_22,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),double_divide(identity,identity)) = F,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_25,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_165,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_166,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_165]) ).
cnf(c_167,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_166]) ).
cnf(c_26,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_167]) ).
cnf(c_168,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,A)))),double_divide(C,B))),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_12,c_8]) ).
cnf(c_169,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,A)))),double_divide(C,B))),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_26,c_168]) ).
cnf(c_170,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,A)))),double_divide(C,B))),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_26,c_169]) ).
cnf(c_27,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,A)))),double_divide(C,B))),identity) = C,
inference(paramod,[status(thm)],[c_26,c_170]) ).
cnf(c_171,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,identity)) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_26,c_25]) ).
cnf(c_32,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(double_divide(identity,A),identity)),
inference(paramod,[status(thm)],[c_26,c_171]) ).
cnf(c_172,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),double_divide(identity,identity)) = F,
inference(paramod,[status(thm)],[c_26,c_22]) ).
cnf(c_173,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),double_divide(identity,identity)) = F,
inference(paramod,[status(thm)],[c_26,c_172]) ).
cnf(c_174,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),double_divide(identity,identity)) = F,
inference(paramod,[status(thm)],[c_26,c_173]) ).
cnf(c_35,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),identity) = F,
inference(paramod,[status(thm)],[c_26,c_174]) ).
cnf(c_175,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),
inference(paramod,[status(thm)],[c_26,c_21]) ).
cnf(c_176,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),
inference(paramod,[status(thm)],[c_26,c_175]) ).
cnf(c_177,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),
inference(paramod,[status(thm)],[c_26,c_176]) ).
cnf(c_178,plain,
identity = double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),
inference(paramod,[status(thm)],[c_26,c_177]) ).
cnf(c_36,plain,
double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))) = identity,
inference(copy,[status(thm)],[c_178]) ).
cnf(c_179,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(identity,identity),double_divide(B,A))))),C)),double_divide(identity,identity)) = double_divide(D,double_divide(double_divide(identity,E),double_divide(C,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_26,c_16]) ).
cnf(c_180,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(identity,double_divide(B,A))))),C)),double_divide(identity,identity)) = double_divide(D,double_divide(double_divide(identity,E),double_divide(C,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_26,c_179]) ).
cnf(c_181,plain,
double_divide(double_divide(identity,double_divide(identity,C)),double_divide(identity,identity)) = double_divide(D,double_divide(double_divide(identity,E),double_divide(C,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_36,c_180]) ).
cnf(c_182,plain,
double_divide(double_divide(identity,double_divide(identity,C)),identity) = double_divide(D,double_divide(double_divide(identity,E),double_divide(C,double_divide(E,D)))),
inference(paramod,[status(thm)],[c_26,c_181]) ).
cnf(c_41,plain,
double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(paramod,[status(thm)],[c_32,c_182]) ).
cnf(c_44,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_26,c_12]) ).
cnf(c_45,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_26,c_11]) ).
cnf(c_183,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_26,c_10]) ).
cnf(c_46,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
inference(paramod,[status(thm)],[c_26,c_183]) ).
cnf(c_50,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(paramod,[status(thm)],[c_44,c_5]) ).
cnf(c_184,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_63,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_26,c_184]) ).
cnf(c_185,plain,
double_divide(double_divide(A,double_divide(identity,identity)),identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),identity)),
inference(paramod,[status(thm)],[c_50,c_46]) ).
cnf(c_186,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),identity)),
inference(paramod,[status(thm)],[c_26,c_185]) ).
cnf(c_187,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_63,c_186]) ).
cnf(c_65,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(paramod,[status(thm)],[c_63,c_187]) ).
cnf(c_188,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(paramod,[status(thm)],[c_63,c_41]) ).
cnf(c_86,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_189,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(C,identity)))),double_divide(D,C)))),double_divide(E,D)))),double_divide(F,E))),identity) = F,
inference(paramod,[status(thm)],[c_86,c_35]) ).
cnf(c_89,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A)))),double_divide(C,B)))),double_divide(D,C)),identity)) = D,
inference(paramod,[status(thm)],[c_63,c_189]) ).
cnf(c_190,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A)))),double_divide(C,B))),identity) = C,
inference(paramod,[status(thm)],[c_63,c_27]) ).
cnf(c_93,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A)))),double_divide(C,B)),identity)) = C,
inference(paramod,[status(thm)],[c_63,c_190]) ).
cnf(c_191,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),identity)),identity) = identity,
inference(paramod,[status(thm)],[c_26,c_45]) ).
cnf(c_97,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),identity) = identity,
inference(paramod,[status(thm)],[c_63,c_191]) ).
cnf(c_100,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(double_divide(identity,double_divide(identity,A)),double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_63,c_45]) ).
cnf(c_101,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,identity)))),identity) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_63,c_45]) ).
cnf(c_192,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(double_divide(B,double_divide(identity,double_divide(A,double_divide(identity,B)))),identity))),identity) = identity,
inference(paramod,[status(thm)],[c_46,c_97]) ).
cnf(c_110,plain,
double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
inference(paramod,[status(thm)],[c_46,c_192]) ).
cnf(c_193,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),identity)),identity) = double_divide(double_divide(B,identity),double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_97,c_45]) ).
cnf(c_194,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),identity) = double_divide(double_divide(B,identity),double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_63,c_193]) ).
cnf(c_195,plain,
identity = double_divide(double_divide(B,identity),double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_110,c_194]) ).
cnf(c_112,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))) = identity,
inference(copy,[status(thm)],[c_195]) ).
cnf(c_115,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(identity,double_divide(identity,double_divide(identity,double_divide(B,identity)))))),identity) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_65,c_45]) ).
cnf(c_196,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),identity)),identity) = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_110,c_45]) ).
cnf(c_197,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))),identity) = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_63,c_196]) ).
cnf(c_198,plain,
double_divide(identity,identity) = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_112,c_197]) ).
cnf(c_199,plain,
identity = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_26,c_198]) ).
cnf(c_117,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(copy,[status(thm)],[c_199]) ).
cnf(c_200,plain,
double_divide(double_divide(A,double_divide(identity,identity)),identity) = A,
inference(paramod,[status(thm)],[c_117,c_46]) ).
cnf(c_201,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_26,c_200]) ).
cnf(c_118,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_65,c_201]) ).
cnf(c_202,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_117,c_45]) ).
cnf(c_203,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_26,c_202]) ).
cnf(c_204,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_26,c_203]) ).
cnf(c_205,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_63,c_204]) ).
cnf(c_206,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_63,c_205]) ).
cnf(c_207,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))))) = A,
inference(paramod,[status(thm)],[c_65,c_206]) ).
cnf(c_119,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_118,c_207]) ).
cnf(c_208,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,identity)))),identity) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_119,c_115]) ).
cnf(c_121,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_101,c_208]) ).
cnf(c_209,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)))),double_divide(C,B)),identity)) = C,
inference(paramod,[status(thm)],[c_119,c_93]) ).
cnf(c_210,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)),double_divide(C,B)),identity)) = C,
inference(paramod,[status(thm)],[c_119,c_209]) ).
cnf(c_211,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)),double_divide(C,B)))) = C,
inference(paramod,[status(thm)],[c_121,c_210]) ).
cnf(c_125,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)),double_divide(C,B)) = C,
inference(paramod,[status(thm)],[c_119,c_211]) ).
cnf(c_212,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)))),double_divide(C,B)))),double_divide(D,C)),identity)) = D,
inference(paramod,[status(thm)],[c_119,c_89]) ).
cnf(c_213,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)),double_divide(C,B)))),double_divide(D,C)),identity)) = D,
inference(paramod,[status(thm)],[c_119,c_212]) ).
cnf(c_214,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,C)),double_divide(D,C)),identity)) = D,
inference(paramod,[status(thm)],[c_125,c_213]) ).
cnf(c_215,plain,
double_divide(identity,double_divide(double_divide(C,double_divide(D,C)),identity)) = D,
inference(paramod,[status(thm)],[c_119,c_214]) ).
cnf(c_216,plain,
double_divide(identity,double_divide(identity,double_divide(C,double_divide(D,C)))) = D,
inference(paramod,[status(thm)],[c_121,c_215]) ).
cnf(c_128,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_119,c_216]) ).
cnf(c_217,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(identity,A)),double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_128,c_100]) ).
cnf(c_218,plain,
double_divide(double_divide(A,double_divide(A,double_divide(B,identity))),identity) = B,
inference(paramod,[status(thm)],[c_119,c_217]) ).
cnf(c_133,plain,
double_divide(identity,double_divide(A,double_divide(A,double_divide(B,identity)))) = B,
inference(paramod,[status(thm)],[c_121,c_218]) ).
cnf(c_219,plain,
double_divide(identity,double_divide(b,a)) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_121,c_7]) ).
cnf(c_139,plain,
double_divide(identity,double_divide(b,a)) != double_divide(identity,double_divide(a,b)),
inference(paramod,[status(thm)],[c_121,c_219]) ).
cnf(c_142,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_128,c_128]) ).
cnf(c_220,plain,
double_divide(A,identity) = double_divide(B,double_divide(B,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_133,c_142]) ).
cnf(c_152,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_221,plain,
double_divide(A,double_divide(A,B)) = double_divide(double_divide(identity,B),identity),
inference(paramod,[status(thm)],[c_142,c_152]) ).
cnf(c_222,plain,
double_divide(A,double_divide(A,B)) = double_divide(identity,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_121,c_221]) ).
cnf(c_158,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_119,c_222]) ).
cnf(c_161,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_128,c_158]) ).
cnf(c_223,plain,
double_divide(identity,double_divide(a,b)) != double_divide(identity,double_divide(a,b)),
inference(paramod,[status(thm)],[c_161,c_139]) ).
cnf(c_162,plain,
$false,
inference(copy,[status(thm)],[c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP584-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:00:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1895416 was started by sandbox2 on n009,
% 0.09/0.35 % Fri Sep 25 15:00:44 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 49.
% 0.13/0.40 % Level of proof is 19.
% 0.13/0.40 % Maximum clause weight is 47.000.
% 0.13/0.40 % Given clauses 35.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------