%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 12:32:14 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
an_element(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ an_element(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
an_element(a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [Z] :
( an_element(Z)
| ! [X,Y] :
( ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2] :
( an_element(X2)
| ~ product(X0,inverse(X1),X2)
| ~ an_element(X1)
| ~ an_element(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f21,plain,
~ an_element(identity),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0] :
( an_element(identity)
| ~ an_element(X0)
| ~ an_element(X0) ),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f26,plain,
! [X0] :
( an_element(identity)
| ~ an_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0] : ~ an_element(X0),
inference(forward_subsumption_resolution,[status(thm)],[f26,f21]) ).
fof(f29,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f14,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 19:52:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.053062 seconds
% 0.09/0.44 % CPU time: 0.148691 seconds
% 0.09/0.44 % Total memory used: 55.380 MB
% 0.09/0.44 % Net memory used: 54.842 MB
%------------------------------------------------------------------------------