%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP493-1 : 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 : n018.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 07:29:52 AM UTC 2026
% Result : Unsatisfiable 0.25s 5.50s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 21 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(identity,VAR_0),double_divide(double_divide(double_divide(VAR_1,VAR_2),double_divide(identity,identity)),double_divide(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B,
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_38,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_38]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != identity,
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_6,plain,
multiply(inverse(a1),a1) != identity,
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_39,plain,
multiply(double_divide(a1,identity),a1) != identity,
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_40,plain,
double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity,
inference(paramod,[status(thm)],[c_2,c_39]) ).
cnf(c_7,plain,
double_divide(identity,identity) != identity,
inference(paramod,[status(thm)],[c_5,c_40]) ).
cnf(c_41,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(A,double_divide(B,identity)))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(B,identity)))) = B,
inference(paramod,[status(thm)],[c_5,c_41]) ).
cnf(c_27,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_42,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_27]) ).
cnf(c_43,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_42]) ).
cnf(c_36,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_43]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP493-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/5.47 % Computer : n018.cluster.edu
% 0.21/5.47 % Model : x86_64 x86_64
% 0.21/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.47 % Memory : 8046.5625MB
% 0.21/5.47 % OS : Linux 6.8.0-71-generic
% 0.21/5.47 % CPULimit : 300
% 0.21/5.47 % WCLimit : 300
% 0.21/5.47 % DateTime : Fri Sep 25 14:59:11 UTC 2026
% 0.21/5.47 % CPUTime :
% 0.21/5.48 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/5.48 % Process 2241169 was started by sandbox2 on n018,
% 0.21/5.48 % Fri Sep 25 14:59:11 2026
% 0.21/5.48 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/5.48
% 0.21/5.48 % From the command line: assign(max_seconds, 300).
% 0.25/5.50
% 0.25/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.25/5.50
% 0.25/5.50 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.25/5.50 % Length of proof is 11.
% 0.25/5.50 % Level of proof is 5.
% 0.25/5.50 % Maximum clause weight is 17.000.
% 0.25/5.50 % Given clauses 8.
% 0.25/5.50
% 0.25/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------