%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:07:27 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : identity_map(codomain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : product(codomain(X),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
defined(h,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
identity_map(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
codomain(a) != h,
file('/export/starexec/sandbox2/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(f31,plain,
! [Y,X] :
( defined(X,Y)
| ! [Yz] :
( ~ defined(X,Yz)
| ! [Z] : ~ product(Y,Z,Yz) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f40,plain,
! [X0] : identity_map(codomain(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
! [X0] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
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(h,a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
identity_map(h),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
codomain(a) != h,
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(f93,plain,
! [X0,X1] :
( ~ identity_map(X1)
| ~ defined(X1,X0)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f136,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f32,f44]) ).
fof(f142,plain,
! [X0,X1] :
( ~ identity_map(X0)
| ~ identity_map(codomain(X1))
| codomain(X1) = X0
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f136,f93]) ).
fof(f144,plain,
! [X0,X1] :
( ~ identity_map(X0)
| codomain(X1) = X0
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f40]) ).
fof(f146,plain,
( ~ identity_map(h)
| codomain(a) = h ),
inference(resolution,[status(thm)],[f144,f49]) ).
fof(f150,plain,
~ identity_map(h),
inference(forward_subsumption_resolution,[status(thm)],[f146,f51]) ).
fof(f151,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f150,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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 : Mon Sep 21 13:55:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.046819 seconds
% 0.12/0.40 % CPU time: 0.146304 seconds
% 0.12/0.40 % Total memory used: 32.428 MB
% 0.12/0.40 % Net memory used: 32.169 MB
%------------------------------------------------------------------------------