%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [A] : product(A,inverse(A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [A] : product(A,identity,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [A] : ~ product(A,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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(f12,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)],[f11]) ).
fof(f13,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(f14,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)],[f13]) ).
fof(f15,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] : ~ product(X0,a,identity),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( product(X2,X1,X3)
| ~ product(X2,X0,X3)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( product(identity,X1,X3)
| ~ product(X0,X2,X3)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f89,plain,
! [X0,X1] :
( product(identity,inverse(inverse(X0)),X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f29,f15]) ).
fof(f290,plain,
! [X0] : product(identity,inverse(inverse(X0)),X0),
inference(resolution,[status(thm)],[f89,f16]) ).
fof(f296,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(X0,inverse(inverse(X1)),X2) ),
inference(resolution,[status(thm)],[f290,f24]) ).
fof(f1358,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(resolution,[status(thm)],[f296,f15]) ).
fof(f1462,plain,
$false,
inference(resolution,[status(thm)],[f1358,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 19:54:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.39 % Elapsed time: 0.074199 seconds
% 0.08/0.39 % CPU time: 0.405505 seconds
% 0.08/0.39 % Total memory used: 61.814 MB
% 0.08/0.39 % Net memory used: 60.013 MB
%------------------------------------------------------------------------------