%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD065-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:22:07 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 9 unt; 3 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 31 ~; 29 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
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(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
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(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(f65,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(f66,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)],[f65]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X2,X1)
| ~ sum(additive_inverse(a),X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f66,f70]) ).
fof(f76,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,a,X0)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f75,f35]) ).
fof(f77,definition,
! [X0] :
( sQ0_spl
<=> ( ~ sum(additive_identity,a,X0)
| less_or_equal(additive_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [X0] :
( ~ sQ0_spl
| ~ sum(additive_identity,a,X0)
| less_or_equal(additive_identity,X0) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ1_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( sQ1_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f77,f80]) ).
fof(f85,plain,
( ~ sQ0_spl
| ~ defined(a)
| less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[f78,f34]) ).
fof(f86,definition,
( sQ2_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ2_spl
| less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f85,f86,f80,f77]) ).
fof(f90,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f69]) ).
fof(f91,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f71]) ).
fof(f93,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f94,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f89,f91,f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD065-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 15:45:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.038145 seconds
% 0.12/0.40 % CPU time: 0.084556 seconds
% 0.12/0.40 % Total memory used: 9.785 MB
% 0.12/0.40 % Net memory used: 9.635 MB
%------------------------------------------------------------------------------