%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD059-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:22:05 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.54s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 11 unt; 2 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 30 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
sum(a,a,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f63,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,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(f68,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)],[f67]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
sum(a,a,u),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,u),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
! [X0] :
( ~ less_or_equal(a,X0)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f64,f73]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ sum(a,X2,X1)
| ~ sum(additive_identity,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f68,f73]) ).
fof(f172,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f123,f74]) ).
fof(f178,plain,
( ~ defined(a)
| less_or_equal(a,u) ),
inference(resolution,[status(thm)],[f172,f36]) ).
fof(f183,definition,
( sQ9_spl
<=> less_or_equal(a,u) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ9_spl
| less_or_equal(a,u) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ10_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ10_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f178,f183,f186]) ).
fof(f190,plain,
( ~ sQ9_spl
| less_or_equal(additive_identity,u) ),
inference(resolution,[status(thm)],[f184,f76]) ).
fof(f195,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f75]) ).
fof(f196,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f71]) ).
fof(f198,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
$false,
inference(sat_refutation,[status(thm)],[f189,f196,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD059-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % Computer : n019.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 15:44:04 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.52 % Drodi V4.1.1
% 0.24/0.54 % Refutation found
% 0.24/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58 % Elapsed time: 0.072923 seconds
% 0.24/0.58 % CPU time: 0.115211 seconds
% 0.24/0.58 % Total memory used: 3.698 MB
% 0.24/0.58 % Net memory used: 3.652 MB
%------------------------------------------------------------------------------