%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 44 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,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(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
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(f11,hypothesis,
! [A] :
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
identity != another_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f28,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0] :
( product(X0,another_identity,X0)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
subgroup_member(another_identity),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
identity != another_identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
! [X0,X1] :
( X0 = X1
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f23,f17]) ).
fof(f107,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f29,f20]) ).
fof(f110,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f107]) ).
fof(f176,plain,
subgroup_member(identity),
inference(resolution,[status(thm)],[f110,f35]) ).
fof(f180,plain,
product(identity,another_identity,identity),
inference(resolution,[status(thm)],[f176,f31]) ).
fof(f202,plain,
another_identity = identity,
inference(resolution,[status(thm)],[f180,f63]) ).
fof(f208,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f202,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:55:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.046956 seconds
% 0.13/0.40 % CPU time: 0.150977 seconds
% 0.13/0.40 % Total memory used: 44.606 MB
% 0.13/0.40 % Net memory used: 44.195 MB
%------------------------------------------------------------------------------