%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP033-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:32:20 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [A] :
( subgroup_member(j(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [A] :
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0] :
( subgroup_member(j(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ product(X0,j(X0),j(X0))
| ~ product(j(X0),X0,j(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
subgroup_member(j(a)),
inference(resolution,[status(thm)],[f26,f27]) ).
fof(f30,plain,
subgroup_member(j(j(a))),
inference(resolution,[status(thm)],[f29,f27]) ).
fof(f31,plain,
subgroup_member(j(j(j(a)))),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f32,plain,
subgroup_member(j(j(j(j(a))))),
inference(resolution,[status(thm)],[f31,f27]) ).
fof(f33,plain,
subgroup_member(j(j(j(j(j(a)))))),
inference(resolution,[status(thm)],[f32,f27]) ).
fof(f34,plain,
subgroup_member(j(j(j(j(j(j(a))))))),
inference(resolution,[status(thm)],[f33,f27]) ).
fof(f35,plain,
subgroup_member(j(j(j(j(j(j(j(a)))))))),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f36,plain,
subgroup_member(j(j(j(j(j(j(j(j(a))))))))),
inference(resolution,[status(thm)],[f35,f27]) ).
fof(f37,plain,
subgroup_member(j(j(j(j(j(j(j(j(j(a)))))))))),
inference(resolution,[status(thm)],[f36,f27]) ).
fof(f42,plain,
( ~ subgroup_member(identity)
| ~ product(identity,j(identity),j(identity)) ),
inference(resolution,[status(thm)],[f14,f28]) ).
fof(f46,plain,
~ subgroup_member(identity),
inference(forward_subsumption_resolution,[status(thm)],[f42,f13]) ).
fof(f76,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f25,f16]) ).
fof(f80,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f76]) ).
fof(f81,plain,
! [X0] : ~ subgroup_member(X0),
inference(forward_subsumption_resolution,[status(thm)],[f80,f46]) ).
fof(f93,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f37,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP033-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 20 19:54:20 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 0.18/0.45 % Refutation found
% 0.18/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.48 % Elapsed time: 0.067211 seconds
% 0.18/0.48 % CPU time: 0.114872 seconds
% 0.18/0.48 % Total memory used: 8.360 MB
% 0.18/0.48 % Net memory used: 8.288 MB
%------------------------------------------------------------------------------