%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP020-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:32:17 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 20 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
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(f9,negated_conjecture,
multiply(inverse(a),a) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f21,plain,
multiply(inverse(a),a) != identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0,X1] :
( identity = X1
| ~ product(inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f43,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[f22,f14]) ).
fof(f54,plain,
identity != identity,
inference(backward_demodulation,[status(thm)],[f43,f21]) ).
fof(f59,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP020-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:53:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.39 % Elapsed time: 0.030307 seconds
% 0.14/0.39 % CPU time: 0.069363 seconds
% 0.14/0.39 % Total memory used: 5.546 MB
% 0.14/0.39 % Net memory used: 5.522 MB
%------------------------------------------------------------------------------