%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 15 unt; 3 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
! [A] :
( subgroup_member(j(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [A] :
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f43,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f51,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f54,plain,
! [X0] :
( subgroup_member(j(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ product(X0,j(X0),j(X0))
| ~ product(j(X0),X0,j(X0)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
subgroup_member(j(a)),
inference(resolution,[status(thm)],[f54,f53]) ).
fof(f59,plain,
subgroup_member(j(j(a))),
inference(resolution,[status(thm)],[f58,f54]) ).
fof(f61,plain,
subgroup_member(j(j(j(a)))),
inference(resolution,[status(thm)],[f59,f54]) ).
fof(f63,plain,
subgroup_member(j(j(j(j(a))))),
inference(resolution,[status(thm)],[f61,f54]) ).
fof(f96,definition,
( sQ1_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f135,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f52,f43]) ).
fof(f145,definition,
! [X0] :
( sQ4_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ4_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f135,f145,f96]) ).
fof(f149,plain,
! [X0] :
( ~ sQ4_spl
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f146]) ).
fof(f150,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f149]) ).
fof(f155,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f156,plain,
( ~ subgroup_member(identity)
| ~ product(identity,j(identity),j(identity)) ),
inference(resolution,[status(thm)],[f55,f41]) ).
fof(f157,definition,
( sQ5_spl
<=> product(identity,j(identity),j(identity)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ5_spl
| ~ product(identity,j(identity),j(identity)) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f156,f157,f96]) ).
fof(f161,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f40]) ).
fof(f162,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f148,f155,f160,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n017.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 19:49:42 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.075837 seconds
% 0.15/0.51 % CPU time: 0.198640 seconds
% 0.15/0.51 % Total memory used: 56.057 MB
% 0.15/0.51 % Net memory used: 55.686 MB
%------------------------------------------------------------------------------