%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD060-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:22:05 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 68 ( 21 unt; 8 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 138 ( 61 ~; 69 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
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(f23,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
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,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(a,a,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
sum(b,b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ less_or_equal(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f61,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f62,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,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(f67,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f69,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,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(f71,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)],[f70]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
defined(u),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f78,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
sum(a,a,u),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f80,plain,
sum(b,b,v),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ less_or_equal(u,v),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f71,f78]) ).
fof(f85,plain,
! [X0] :
( ~ sum(a,b,X0)
| less_or_equal(X0,v) ),
inference(resolution,[status(thm)],[f84,f80]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f84,f41]) ).
fof(f93,definition,
( sQ1_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ1_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f97,plain,
( ~ defined(b)
| ~ defined(a)
| less_or_equal(add(a,b),v) ),
inference(resolution,[status(thm)],[f85,f62]) ).
fof(f101,definition,
( sQ2_spl
<=> less_or_equal(add(a,b),v) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| less_or_equal(add(a,b),v) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,definition,
( sQ3_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( sQ3_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f97,f101,f104,f93]) ).
fof(f108,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f75]) ).
fof(f109,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f111,plain,
! [X0] :
( ~ sQ2_spl
| ~ less_or_equal(X0,add(a,b))
| less_or_equal(X0,v) ),
inference(resolution,[status(thm)],[f102,f67]) ).
fof(f121,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f74]) ).
fof(f122,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f130,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(u,X0)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f69,f76]) ).
fof(f131,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f69,f75]) ).
fof(f132,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f69,f74]) ).
fof(f141,definition,
( sQ6_spl
<=> less_or_equal(u,v) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ6_spl
| less_or_equal(u,v) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f162,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f81]) ).
fof(f163,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( less_or_equal(u,u)
| less_or_equal(u,u) ),
inference(resolution,[status(thm)],[f130,f76]) ).
fof(f169,definition,
( sQ12_spl
<=> less_or_equal(u,u) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f172,plain,
sQ12_spl,
inference(split_clause,[status(thm)],[f165,f169]) ).
fof(f189,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f131,f75]) ).
fof(f193,definition,
( sQ17_spl
<=> less_or_equal(b,b) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f196,plain,
sQ17_spl,
inference(split_clause,[status(thm)],[f189,f193]) ).
fof(f207,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f132,f74]) ).
fof(f211,definition,
( sQ20_spl
<=> less_or_equal(a,a) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f214,plain,
sQ20_spl,
inference(split_clause,[status(thm)],[f207,f211]) ).
fof(f215,plain,
! [X0] :
( ~ sum(a,b,X0)
| less_or_equal(u,X0) ),
inference(resolution,[status(thm)],[f88,f79]) ).
fof(f224,plain,
( ~ defined(b)
| ~ defined(a)
| less_or_equal(u,add(a,b)) ),
inference(resolution,[status(thm)],[f215,f62]) ).
fof(f228,definition,
( sQ22_spl
<=> less_or_equal(u,add(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( ~ sQ22_spl
| less_or_equal(u,add(a,b)) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f224,f228,f104,f93]) ).
fof(f232,plain,
( ~ sQ2_spl
| ~ sQ22_spl
| less_or_equal(u,v) ),
inference(resolution,[status(thm)],[f229,f111]) ).
fof(f236,plain,
( ~ sQ2_spl
| ~ sQ22_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f232,f141,f228,f101]) ).
fof(f237,plain,
$false,
inference(sat_refutation,[status(thm)],[f107,f109,f122,f163,f172,f196,f214,f231,f236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD060-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:43:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.080174 seconds
% 0.12/0.45 % CPU time: 0.355072 seconds
% 0.12/0.45 % Total memory used: 19.777 MB
% 0.12/0.45 % Net memory used: 19.375 MB
%------------------------------------------------------------------------------