%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:32:12 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
! [X] : product(X,X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] : product(X0,X0,identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( product(X0,X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f25,plain,
! [X0,X1,X2] :
( product(c,X0,X2)
| ~ product(a,X1,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f39,plain,
! [X0] :
( product(a,c,X0)
| ~ product(identity,b,X0) ),
inference(resolution,[status(thm)],[f19,f15]) ).
fof(f51,plain,
product(a,c,b),
inference(resolution,[status(thm)],[f39,f8]) ).
fof(f53,plain,
! [X0,X1,X2] :
( product(b,X0,X2)
| ~ product(a,X1,X2)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f51,f13]) ).
fof(f58,plain,
! [X0] :
( product(c,b,X0)
| ~ product(a,identity,X0) ),
inference(resolution,[status(thm)],[f25,f14]) ).
fof(f67,plain,
product(c,b,a),
inference(resolution,[status(thm)],[f58,f9]) ).
fof(f70,plain,
! [X0] :
( product(c,a,X0)
| ~ product(identity,b,X0) ),
inference(resolution,[status(thm)],[f67,f19]) ).
fof(f78,plain,
product(c,a,b),
inference(resolution,[status(thm)],[f70,f8]) ).
fof(f93,plain,
! [X0] :
( product(b,a,X0)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f53,f78]) ).
fof(f97,plain,
product(b,a,c),
inference(resolution,[status(thm)],[f93,f15]) ).
fof(f98,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f97,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:54:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.041672 seconds
% 0.13/0.42 % CPU time: 0.146042 seconds
% 0.13/0.42 % Total memory used: 55.676 MB
% 0.13/0.42 % Net memory used: 55.165 MB
%------------------------------------------------------------------------------