%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD070-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:22:09 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 14 unt; 4 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 111 ( 57 ~; 50 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox/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/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,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,
~ less_or_equal(additive_identity,add(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f59,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
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(f72,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,add(a,b)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
! [X0] :
( ~ less_or_equal(X0,add(a,b))
| ~ less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f64,f75]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ~ less_or_equal(additive_identity,X3)
| ~ sum(X1,X2,add(a,b))
| ~ sum(X0,X2,X3)
| ~ less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f68,f76]) ).
fof(f110,plain,
! [X0,X1] :
( ~ defined(b)
| ~ defined(a)
| ~ less_or_equal(additive_identity,X1)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f79,f59]) ).
fof(f118,definition,
! [X0,X1] :
( sQ7_spl
<=> ( ~ less_or_equal(additive_identity,X1)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,a) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ less_or_equal(additive_identity,X1)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,a) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ8_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ8_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ9_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( sQ9_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f110,f118,f121,f124]) ).
fof(f128,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f72]) ).
fof(f129,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f130,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f71]) ).
fof(f131,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f259,plain,
! [X0] :
( ~ sQ7_spl
| ~ less_or_equal(additive_identity,X0)
| ~ sum(additive_identity,b,X0) ),
inference(resolution,[status(thm)],[f119,f73]) ).
fof(f264,plain,
( ~ sQ7_spl
| ~ defined(b)
| ~ less_or_equal(additive_identity,b) ),
inference(resolution,[status(thm)],[f259,f36]) ).
fof(f268,definition,
( sQ21_spl
<=> less_or_equal(additive_identity,b) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ21_spl
| ~ less_or_equal(additive_identity,b) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f264,f268,f124,f118]) ).
fof(f276,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f74]) ).
fof(f277,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
$false,
inference(sat_refutation,[status(thm)],[f127,f129,f131,f271,f277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD070-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 15:47:21 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.53 % Elapsed time: 0.080988 seconds
% 0.18/0.53 % CPU time: 0.396306 seconds
% 0.18/0.53 % Total memory used: 20.095 MB
% 0.18/0.53 % Net memory used: 19.677 MB
%------------------------------------------------------------------------------