%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:32:21 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
product(a,inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
product(a,inverse(b),c),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
~ subgroup_member(c),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
( subgroup_member(c)
| ~ subgroup_member(b)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f28,f33]) ).
fof(f40,plain,
( subgroup_member(c)
| ~ subgroup_member(b) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f31]) ).
fof(f42,plain,
subgroup_member(c),
inference(forward_subsumption_resolution,[status(thm)],[f40,f32]) ).
fof(f43,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f34,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.033260 seconds
% 0.09/0.40 % CPU time: 0.076030 seconds
% 0.09/0.40 % Total memory used: 8.357 MB
% 0.09/0.40 % Net memory used: 8.292 MB
%------------------------------------------------------------------------------