%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:32:20 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 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 : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ subgroup_member(inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X1,inverse(X0),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
~ subgroup_member(inverse(a)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f23,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f22]) ).
fof(f24,plain,
subgroup_member(identity),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f25,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f11,f19]) ).
fof(f26,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f24]) ).
fof(f27,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[f26,f21]) ).
fof(f28,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f27,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n006.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 20 19:55:12 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.48 % Elapsed time: 0.056613 seconds
% 0.15/0.48 % CPU time: 0.152115 seconds
% 0.15/0.48 % Total memory used: 36.350 MB
% 0.15/0.48 % Net memory used: 36.013 MB
%------------------------------------------------------------------------------