%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:26:08 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_inverse,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_3,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(element_of_set,axiom,
an_element(a),
file('theBenchmark.p',element_of_set) ).
cnf(c_5,plain,
an_element(a),
inference(clausify,[status(thm)],[element_of_set]) ).
fof(condition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( an_element(VAR_2)
| ~ product(VAR_0,inverse(VAR_1),VAR_2)
| ~ an_element(VAR_1)
| ~ an_element(VAR_0) ),
file('theBenchmark.p',condition) ).
cnf(c_6,plain,
( an_element(C)
| ~ product(A,inverse(B),C)
| ~ an_element(B)
| ~ an_element(A) ),
inference(clausify,[status(thm)],[condition]) ).
fof(prove_identity_is_an_element,axiom,
~ an_element(identity),
file('theBenchmark.p',prove_identity_is_an_element) ).
cnf(c_9,plain,
~ an_element(identity),
inference(clausify,[status(thm)],[prove_identity_is_an_element]) ).
cnf(c_12,plain,
( an_element(B)
| ~ product(a,inverse(A),B)
| ~ an_element(A) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_13,plain,
( an_element(A)
| ~ product(a,inverse(a),A) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_10,plain,
an_element(identity),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.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 14:21:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3487172 was started by sandbox2 on n001,
% 0.13/0.36 % Fri Sep 25 14:21:41 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 6.
% 0.13/0.37 % Level of proof is 2.
% 0.13/0.37 % Maximum clause weight is 11.000.
% 0.13/0.37 % Given clauses 6.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------