%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD055-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:22:04 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 11 unt; 2 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 32 ~; 29 |; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,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(f30,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
sum(additive_identity,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ less_or_equal(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f72,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
sum(additive_identity,b,c),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
~ less_or_equal(a,c),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f69,f75]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f81,f39]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ sum(X2,a,X0)
| ~ sum(X2,b,X1)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f82,f39]) ).
fof(f87,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,b,X0)
| less_or_equal(a,X0) ),
inference(resolution,[status(thm)],[f84,f37]) ).
fof(f90,definition,
! [X0] :
( sQ0_spl
<=> ( ~ sum(additive_identity,b,X0)
| less_or_equal(a,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ0_spl
| ~ sum(additive_identity,b,X0)
| less_or_equal(a,X0) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ1_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ1_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f87,f90,f93]) ).
fof(f97,plain,
( ~ sQ0_spl
| ~ sum(additive_identity,b,c) ),
inference(resolution,[status(thm)],[f91,f77]) ).
fof(f104,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f76]) ).
fof(f105,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f72]) ).
fof(f107,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f105,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD055-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n013.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 15:41:52 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.55 % Elapsed time: 0.091662 seconds
% 0.24/0.55 % CPU time: 0.115010 seconds
% 0.24/0.55 % Total memory used: 4.181 MB
% 0.24/0.55 % Net memory used: 4.141 MB
%------------------------------------------------------------------------------