%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:32:15 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.55s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 18 unt; 0 def)
% Number of atoms : 51 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 46 ( 46 !; 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(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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(f9,hypothesis,
product(a,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
product(c,b,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,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)],[f7]) ).
fof(f20,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)],[f19]) ).
fof(f23,plain,
product(a,b,identity),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
product(c,b,identity),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f18,f13]) ).
fof(f41,plain,
! [X0,X1,X2] :
( product(c,X1,X2)
| ~ product(identity,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f20,f24]) ).
fof(f42,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(identity,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f46,plain,
! [X0] :
( product(c,identity,X0)
| ~ product(identity,inverse(b),X0) ),
inference(resolution,[status(thm)],[f41,f15]) ).
fof(f124,plain,
product(c,identity,inverse(b)),
inference(resolution,[status(thm)],[f46,f12]) ).
fof(f130,plain,
c = inverse(b),
inference(resolution,[status(thm)],[f124,f31]) ).
fof(f144,plain,
product(b,c,identity),
inference(paramodulation,[status(thm)],[f130,f15]) ).
fof(f148,plain,
! [X0] :
( product(a,identity,X0)
| ~ product(identity,c,X0) ),
inference(resolution,[status(thm)],[f144,f42]) ).
fof(f258,plain,
product(a,identity,c),
inference(resolution,[status(thm)],[f148,f12]) ).
fof(f262,plain,
a = c,
inference(resolution,[status(thm)],[f258,f31]) ).
fof(f271,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f262,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.52 % Computer : n019.cluster.edu
% 0.12/5.52 % Model : x86_64 x86_64
% 0.12/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.52 % Memory : 8046.5625MB
% 0.12/5.52 % OS : Linux 6.8.0-71-generic
% 0.12/5.52 % CPULimit : 300
% 0.12/5.52 % WCLimit : 300
% 0.12/5.52 % DateTime : Sun Sep 20 19:53:41 UTC 2026
% 0.12/5.52 % CPUTime :
% 0.12/5.53 % Drodi V4.1.1
% 0.12/5.55 % Refutation found
% 0.12/5.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.58 % Elapsed time: 0.045959 seconds
% 0.12/5.58 % CPU time: 0.145441 seconds
% 0.12/5.58 % Total memory used: 37.600 MB
% 0.12/5.58 % Net memory used: 37.208 MB
%------------------------------------------------------------------------------