%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP032-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 12:32:20 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : CNFRefutation 0.15s
% 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(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,negated_conjecture,
~ subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
~ subgroup_member(identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f106,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f24,f15]) ).
fof(f110,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f106]) ).
fof(f111,plain,
! [X0] : ~ subgroup_member(X0),
inference(forward_subsumption_resolution,[status(thm)],[f110,f26]) ).
fof(f113,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f25,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP032-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 20 19:56:43 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.54 % Elapsed time: 0.083549 seconds
% 0.21/0.54 % CPU time: 0.125683 seconds
% 0.21/0.54 % Total memory used: 18.048 MB
% 0.21/0.54 % Net memory used: 17.896 MB
%------------------------------------------------------------------------------