%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD061-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:22:06 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 22 unt; 10 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 248 ( 123 ~; 115 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
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(f23,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
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(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
less_or_equal(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ less_or_equal(add(a,c),add(d,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f53,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f60,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f61,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f65,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(f66,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f68,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,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(f70,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)],[f69]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
defined(d),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
less_or_equal(c,d),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
~ less_or_equal(add(a,c),add(d,b)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
! [X0] :
( ~ less_or_equal(X0,add(d,b))
| ~ less_or_equal(add(a,c),X0) ),
inference(resolution,[status(thm)],[f66,f79]) ).
fof(f88,definition,
( sQ2_spl
<=> defined(add(a,c)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ2_spl
| ~ defined(add(a,c)) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f92,plain,
( sQ2_spl
| ~ defined(c)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f90,f53]) ).
fof(f93,definition,
( sQ3_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ3_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ4_spl
<=> defined(c) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ4_spl
| ~ defined(c) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f92,f93,f96,f88]) ).
fof(f100,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f75]) ).
fof(f101,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f102,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f73]) ).
fof(f103,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(add(a,c),X1)
| ~ less_or_equal(X0,add(d,b)) ),
inference(resolution,[status(thm)],[f80,f66]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ~ defined(X2)
| ~ defined(X1)
| ~ sum(X3,X2,X0)
| ~ less_or_equal(X3,X1)
| less_or_equal(X0,add(X1,X2)) ),
inference(resolution,[status(thm)],[f70,f61]) ).
fof(f123,definition,
( sQ8_spl
<=> defined(d) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( sQ8_spl
| ~ defined(d) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ9_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ9_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f130,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f74]) ).
fof(f131,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f76]) ).
fof(f133,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f152,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(X1)
| sum(X0,X1,add(X1,X0)) ),
inference(resolution,[status(thm)],[f40,f61]) ).
fof(f226,definition,
( sQ21_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ21_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f238,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f54]) ).
fof(f239,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(add(a,c),X2)
| ~ defined(b)
| ~ defined(d)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,d) ),
inference(resolution,[status(thm)],[f121,f105]) ).
fof(f322,definition,
! [X0,X1,X2] :
( sQ38_spl
<=> ( ~ less_or_equal(X2,X1)
| ~ less_or_equal(add(a,c),X2)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,d) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f323,plain,
! [X0,X1,X2] :
( ~ sQ38_spl
| ~ less_or_equal(X2,X1)
| ~ less_or_equal(add(a,c),X2)
| ~ sum(X0,b,X1)
| ~ less_or_equal(X0,d) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f309,f322,f123,f126]) ).
fof(f350,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(add(a,c),X1)
| ~ sum(c,b,X0) ),
inference(resolution,[status(thm)],[f323,f78]) ).
fof(f375,plain,
! [X0] :
( ~ sQ38_spl
| ~ defined(c)
| ~ defined(b)
| ~ less_or_equal(X0,add(b,c))
| ~ less_or_equal(add(a,c),X0) ),
inference(resolution,[status(thm)],[f350,f152]) ).
fof(f379,definition,
! [X0] :
( sQ49_spl
<=> ( ~ less_or_equal(X0,add(b,c))
| ~ less_or_equal(add(a,c),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f380,plain,
! [X0] :
( ~ sQ49_spl
| ~ less_or_equal(X0,add(b,c))
| ~ less_or_equal(add(a,c),X0) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( ~ sQ38_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f375,f379,f126,f96,f322]) ).
fof(f390,plain,
! [X0,X1] :
( ~ sQ49_spl
| ~ defined(c)
| ~ defined(b)
| ~ sum(X1,c,X0)
| ~ less_or_equal(X1,b)
| ~ less_or_equal(add(a,c),X0) ),
inference(resolution,[status(thm)],[f380,f121]) ).
fof(f408,definition,
! [X0,X1] :
( sQ55_spl
<=> ( ~ sum(X1,c,X0)
| ~ less_or_equal(X1,b)
| ~ less_or_equal(add(a,c),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f409,plain,
! [X0,X1] :
( ~ sQ55_spl
| ~ sum(X1,c,X0)
| ~ less_or_equal(X1,b)
| ~ less_or_equal(add(a,c),X0) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,plain,
( ~ sQ49_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f390,f408,f126,f96,f379]) ).
fof(f449,plain,
! [X0] :
( ~ sQ55_spl
| ~ sum(a,c,X0)
| ~ less_or_equal(add(a,c),X0) ),
inference(resolution,[status(thm)],[f409,f77]) ).
fof(f475,plain,
( ~ sQ55_spl
| ~ defined(c)
| ~ defined(a)
| ~ less_or_equal(add(a,c),add(a,c)) ),
inference(resolution,[status(thm)],[f449,f61]) ).
fof(f482,definition,
( sQ69_spl
<=> less_or_equal(add(a,c),add(a,c)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ69_spl
| ~ less_or_equal(add(a,c),add(a,c)) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( ~ sQ55_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f475,f482,f93,f96,f408]) ).
fof(f504,plain,
( sQ69_spl
| ~ defined(add(a,c))
| ~ defined(add(a,c))
| less_or_equal(add(a,c),add(a,c)) ),
inference(resolution,[status(thm)],[f484,f68]) ).
fof(f513,plain,
( ~ sQ2_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f504,f482,f88]) ).
fof(f514,plain,
$false,
inference(sat_refutation,[status(thm)],[f99,f101,f103,f131,f133,f239,f325,f382,f411,f485,f513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD061-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 15:43:49 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.085764 seconds
% 0.12/0.43 % CPU time: 0.471596 seconds
% 0.12/0.43 % Total memory used: 22.409 MB
% 0.12/0.43 % Net memory used: 21.612 MB
%------------------------------------------------------------------------------