%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP582-1 : 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 07:30:25 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 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 : 56 ( 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_121,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_121]) ).
fof(prove_these_axioms_2,axiom,
multiply(identity,a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(identity,a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_7,plain,
double_divide(double_divide(a2,identity),identity) != a2,
inference(paramod,[status(thm)],[c_2,c_6]) ).
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_122,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_123,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_122]) ).
cnf(c_124,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_123]) ).
cnf(c_26,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_124]) ).
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_125,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_125]) ).
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_126,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_126]) ).
cnf(c_127,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_128,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_127]) ).
cnf(c_129,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_128]) ).
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_129]) ).
cnf(c_94,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(a2,identity)))) != a2,
inference(paramod,[status(thm)],[c_65,c_7]) ).
cnf(c_130,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_98,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_130]) ).
cnf(c_131,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_98]) ).
cnf(c_111,plain,
double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
inference(paramod,[status(thm)],[c_46,c_131]) ).
cnf(c_132,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_98,c_45]) ).
cnf(c_133,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_132]) ).
cnf(c_134,plain,
identity = double_divide(double_divide(B,identity),double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_111,c_133]) ).
cnf(c_113,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,identity))) = identity,
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,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_111,c_45]) ).
cnf(c_136,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_135]) ).
cnf(c_137,plain,
double_divide(identity,identity) = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_113,c_136]) ).
cnf(c_138,plain,
identity = double_divide(B,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_26,c_137]) ).
cnf(c_118,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(copy,[status(thm)],[c_138]) ).
cnf(c_139,plain,
double_divide(double_divide(A,double_divide(identity,identity)),identity) = A,
inference(paramod,[status(thm)],[c_118,c_46]) ).
cnf(c_140,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_26,c_139]) ).
cnf(c_119,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_65,c_140]) ).
cnf(c_120,plain,
$false,
inference(resolve,[status(thm)],[c_119,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 15:00:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3484681 was started by sandbox2 on n004,
% 0.17/0.45 % Fri Sep 25 15:00:36 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 24.
% 0.17/0.50 % Level of proof is 11.
% 0.17/0.50 % Maximum clause weight is 17.000.
% 0.17/0.50 % Given clauses 24.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------