%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD069-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:22:08 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 29 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f63,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| sum(additive_identity,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f73,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
sum(a,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f88,plain,
( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity) ),
inference(resolution,[status(thm)],[f63,f76]) ).
fof(f89,plain,
~ less_or_equal(b,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f88,f75]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ sum(X1,X2,additive_identity)
| ~ sum(X0,X2,b)
| ~ less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f69,f89]) ).
fof(f127,plain,
! [X0] :
( ~ defined(b)
| ~ sum(X0,b,additive_identity)
| ~ less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f123,f37]) ).
fof(f131,plain,
! [X0] :
( ~ sum(X0,b,additive_identity)
| ~ less_or_equal(additive_identity,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f73]) ).
fof(f134,plain,
~ less_or_equal(additive_identity,a),
inference(resolution,[status(thm)],[f131,f77]) ).
fof(f139,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f134,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD069-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n003.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 15:46:16 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.44 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.059760 seconds
% 0.14/0.50 % CPU time: 0.143496 seconds
% 0.14/0.50 % Total memory used: 4.990 MB
% 0.14/0.50 % Net memory used: 4.946 MB
%------------------------------------------------------------------------------