%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:07:26 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 70 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : identity_map(domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,domain(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
defined(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
identity_map(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X,Y] :
( defined(X,Y)
| ! [Z] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [Y,Z] :
( defined(Y,Z)
| ! [Xy] :
( ~ defined(Xy,Z)
| ! [X] : ~ product(X,Y,Xy) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f39,plain,
! [X0] : identity_map(domain(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
! [X0] : product(X0,domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
defined(a,d),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
identity_map(d),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
domain(a) != d,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| ~ defined(X0,X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f48,f46]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f24]) ).
fof(f73,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f26,f43]) ).
fof(f93,plain,
! [X0,X1] :
( ~ identity_map(X1)
| ~ defined(X1,X0)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f103,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| ~ identity_map(domain(X1))
| ~ identity_map(X0)
| X0 = domain(X1) ),
inference(resolution,[status(thm)],[f93,f73]) ).
fof(f107,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| ~ identity_map(X0)
| X0 = domain(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f39]) ).
fof(f111,plain,
( ~ identity_map(d)
| d = domain(a) ),
inference(resolution,[status(thm)],[f107,f49]) ).
fof(f113,plain,
~ identity_map(d),
inference(forward_subsumption_resolution,[status(thm)],[f111,f51]) ).
fof(f114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f113,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n001.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 14:01:15 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.09/0.59 % Refutation found
% 0.09/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.62 % Elapsed time: 0.046384 seconds
% 0.09/0.62 % CPU time: 0.140884 seconds
% 0.09/0.62 % Total memory used: 34.867 MB
% 0.09/0.62 % Net memory used: 34.605 MB
%------------------------------------------------------------------------------