%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD019-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:21:54 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 9 unt; 3 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 36 ~; 34 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
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(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
sum(additive_identity,additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_inverse(a),X1)
| ~ sum(X0,additive_identity,X2)
| sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f31,f70]) ).
fof(f79,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f36,f34]) ).
fof(f90,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f35,f36]) ).
fof(f240,plain,
! [X0] :
( ~ defined(a)
| ~ sum(X0,additive_identity,a)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f73,f90]) ).
fof(f257,definition,
! [X0] :
( sQ18_spl
<=> ( ~ sum(X0,additive_identity,a)
| sum(X0,additive_identity,additive_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f258,plain,
! [X0] :
( ~ sQ18_spl
| ~ sum(X0,additive_identity,a)
| sum(X0,additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ19_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ19_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f240,f257,f260]) ).
fof(f385,plain,
( ~ sQ18_spl
| ~ defined(a)
| sum(a,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f258,f79]) ).
fof(f387,definition,
( sQ31_spl
<=> sum(a,additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ31_spl
| sum(a,additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f385,f387,f260,f257]) ).
fof(f391,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f69]) ).
fof(f392,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f399,plain,
( ~ sQ31_spl
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f388,f36]) ).
fof(f405,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f71]) ).
fof(f406,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f407,plain,
$false,
inference(sat_refutation,[status(thm)],[f263,f390,f392,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD019-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 15:38:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.073999 seconds
% 0.14/0.46 % CPU time: 0.378911 seconds
% 0.14/0.46 % Total memory used: 20.920 MB
% 0.14/0.46 % Net memory used: 20.458 MB
%------------------------------------------------------------------------------