%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP128-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:32:47 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 127 ( 53 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [Y,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ! [X] :
( ~ product(X,Z1,Z2)
| product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ~ product(X2,X1,X3)
| ~ product(X0,X2,X3)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| product(X0,X0,X0) ),
inference(factoring,[status(thm)],[f22]) ).
fof(f44,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f28,f38]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f28,f36]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f29,f38]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f31,f38]) ).
fof(f61,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f31,f36]) ).
fof(f68,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f69,plain,
! [X0] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f26]) ).
fof(f70,plain,
! [X0] :
( product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f25]) ).
fof(f72,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f44,f26]) ).
fof(f73,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f44,f25]) ).
fof(f89,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f68,f27]) ).
fof(f92,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f43]) ).
fof(f93,plain,
product(e_3,e_3,e_3),
inference(forward_subsumption_resolution,[status(thm)],[f92,f43]) ).
fof(f96,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f93,f60]) ).
fof(f97,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f93,f54]) ).
fof(f108,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f69,f26]) ).
fof(f110,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f43]) ).
fof(f113,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f70,f25]) ).
fof(f114,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f43]) ).
fof(f115,plain,
product(e_2,e_2,e_2),
inference(forward_subsumption_resolution,[status(thm)],[f110,f43]) ).
fof(f126,plain,
product(e_1,e_1,e_1),
inference(forward_subsumption_resolution,[status(thm)],[f114,f43]) ).
fof(f134,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f96]) ).
fof(f135,plain,
( ~ product(e_1,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f134,f51]) ).
fof(f141,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| product(e_1,X0,e_2)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f134,f22]) ).
fof(f142,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f97]) ).
fof(f143,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f142,f141]) ).
fof(f152,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f135]) ).
fof(f154,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f152,f52]) ).
fof(f162,plain,
product(e_2,e_2,e_3),
inference(forward_subsumption_resolution,[status(thm)],[f154,f126]) ).
fof(f168,plain,
~ product(e_2,e_2,e_2),
inference(resolution,[status(thm)],[f162,f61]) ).
fof(f177,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f168,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP128-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:03:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.047997 seconds
% 0.11/0.42 % CPU time: 0.156173 seconds
% 0.11/0.42 % Total memory used: 17.657 MB
% 0.11/0.42 % Net memory used: 17.277 MB
%------------------------------------------------------------------------------