%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 42 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
product(a,b,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ product(b,a,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,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(f19,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)],[f18]) ).
fof(f22,plain,
product(a,b,identity),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
~ product(b,a,identity),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f17,f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(identity,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f19,f22]) ).
fof(f56,plain,
! [X0] :
( product(a,identity,X0)
| ~ product(identity,inverse(b),X0) ),
inference(resolution,[status(thm)],[f14,f32]) ).
fof(f182,plain,
product(a,identity,inverse(b)),
inference(resolution,[status(thm)],[f56,f11]) ).
fof(f186,plain,
a = inverse(b),
inference(resolution,[status(thm)],[f182,f26]) ).
fof(f207,plain,
product(b,a,identity),
inference(paramodulation,[status(thm)],[f186,f14]) ).
fof(f209,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f207,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 19:54:19 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.39 % Refutation found
% 0.07/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.061065 seconds
% 0.12/0.43 % CPU time: 0.161568 seconds
% 0.12/0.43 % Total memory used: 44.615 MB
% 0.12/0.43 % Net memory used: 44.059 MB
%------------------------------------------------------------------------------