%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:07:28 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 82 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 48 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f12,axiom,
! [X] : defined(X,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(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X,Y] :
( defined(X,Y)
| ! [Z] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [Y,Z] :
( defined(Y,Z)
| ! [Xy] :
( ~ defined(Xy,Z)
| ! [X] : ~ product(X,Y,Xy) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f38,plain,
! [X0] : identity_map(domain(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
! [X0] : defined(X0,domain(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
! [X0] : product(X0,domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
defined(b,a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
domain(compose(b,a)) != domain(a),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| ~ defined(X0,X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f45]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f23]) ).
fof(f85,plain,
! [X0,X1] :
( ~ identity_map(X1)
| ~ defined(X1,X0)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f61,f44]) ).
fof(f99,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f25,f42]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ defined(X0,X1)
| defined(X1,X2)
| ~ defined(compose(X0,X1),X2) ),
inference(resolution,[status(thm)],[f25,f21]) ).
fof(f103,plain,
! [X0,X1] :
( ~ identity_map(domain(X0))
| ~ identity_map(X1)
| X1 = domain(X0)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f99,f85]) ).
fof(f104,plain,
! [X0,X1] :
( ~ identity_map(X1)
| X1 = domain(X0)
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f38]) ).
fof(f137,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| defined(X0,domain(compose(X1,X0))) ),
inference(resolution,[status(thm)],[f100,f40]) ).
fof(f141,plain,
! [X0,X1] :
( ~ identity_map(domain(compose(X0,X1)))
| domain(compose(X0,X1)) = domain(X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f137,f104]) ).
fof(f145,plain,
! [X0,X1] :
( domain(compose(X0,X1)) = domain(X1)
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f38]) ).
fof(f147,plain,
~ defined(b,a),
inference(resolution,[status(thm)],[f145,f49]) ).
fof(f150,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f147,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:55:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.043659 seconds
% 0.14/0.41 % CPU time: 0.151695 seconds
% 0.14/0.41 % Total memory used: 28.511 MB
% 0.14/0.41 % Net memory used: 28.277 MB
%------------------------------------------------------------------------------