%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP485-1 : 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 : n017.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 07:29:51 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 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 : 93 ( 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(double_divide(VAR_0,VAR_1),VAR_2),double_divide(VAR_1,identity))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),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_94,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_94]) ).
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_8,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(double_divide(C,D),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,B),identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_25,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_29,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),double_divide(D,double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_95,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_96,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_95]) ).
cnf(c_97,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_25,c_96]) ).
cnf(c_31,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,A),double_divide(double_divide(identity,identity),identity))),double_divide(double_divide(A,B),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_25,c_8]) ).
cnf(c_99,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(double_divide(identity,identity),identity))),double_divide(double_divide(A,B),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_31,c_98]) ).
cnf(c_100,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(identity,identity))),double_divide(double_divide(A,B),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_31,c_99]) ).
cnf(c_101,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(double_divide(A,B),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_31,c_100]) ).
cnf(c_102,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(double_divide(A,B),double_divide(identity,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_31,c_101]) ).
cnf(c_103,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(double_divide(A,B),identity)),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_31,c_102]) ).
cnf(c_32,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(double_divide(A,B),identity)),identity) = B,
inference(paramod,[status(thm)],[c_31,c_103]) ).
cnf(c_104,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(double_divide(double_divide(identity,identity),A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_25,c_8]) ).
cnf(c_105,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,identity),A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_104]) ).
cnf(c_106,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,identity),A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_105]) ).
cnf(c_107,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_106]) ).
cnf(c_108,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_107]) ).
cnf(c_109,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(identity,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_108]) ).
cnf(c_110,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_31,c_109]) ).
cnf(c_33,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_31,c_110]) ).
cnf(c_111,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),double_divide(D,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_31,c_29]) ).
cnf(c_112,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),double_divide(D,identity)),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_31,c_111]) ).
cnf(c_113,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),double_divide(D,identity)),identity) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_31,c_112]) ).
cnf(c_35,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),double_divide(D,identity)),identity) = identity,
inference(paramod,[status(thm)],[c_31,c_113]) ).
cnf(c_50,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(A,B),identity),
inference(paramod,[status(thm)],[c_31,c_12]) ).
cnf(c_51,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),identity) = B,
inference(paramod,[status(thm)],[c_31,c_11]) ).
cnf(c_55,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),identity) = C,
inference(paramod,[status(thm)],[c_31,c_1]) ).
cnf(c_56,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(paramod,[status(thm)],[c_33,c_5]) ).
cnf(c_58,plain,
double_divide(double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(double_divide(identity,A),identity),B),identity)),identity) = B,
inference(paramod,[status(thm)],[c_33,c_32]) ).
cnf(c_114,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),identity)),double_divide(identity,identity)),identity) = A,
inference(paramod,[status(thm)],[c_56,c_32]) ).
cnf(c_115,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),identity)),double_divide(identity,identity)),identity) = A,
inference(paramod,[status(thm)],[c_50,c_114]) ).
cnf(c_116,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),identity)),identity),identity) = A,
inference(paramod,[status(thm)],[c_31,c_115]) ).
cnf(c_62,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(paramod,[status(thm)],[c_33,c_116]) ).
cnf(c_65,plain,
double_divide(double_divide(double_divide(identity,A),double_divide(double_divide(A,B),identity)),identity) = B,
inference(paramod,[status(thm)],[c_62,c_58]) ).
cnf(c_117,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity)))),identity),identity) = double_divide(D,identity),
inference(paramod,[status(thm)],[c_35,c_65]) ).
cnf(c_118,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),double_divide(C,double_divide(double_divide(identity,D),double_divide(double_divide(C,identity),identity)))),double_divide(B,identity))),identity) = double_divide(D,identity),
inference(paramod,[status(thm)],[c_62,c_117]) ).
cnf(c_80,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_55,c_118]) ).
cnf(c_92,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_80,c_51]) ).
cnf(c_93,plain,
$false,
inference(resolve,[status(thm)],[c_92,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP485-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 14:52:04 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2569317 was started by sandbox2 on n017,
% 0.09/0.38 % Fri Sep 25 14:52:04 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 26.
% 0.09/0.40 % Level of proof is 11.
% 0.09/0.40 % Maximum clause weight is 37.000.
% 0.09/0.40 % Given clauses 16.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------