%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:38:48 PM UTC 2026
% Result : Unsatisfiable 0.24s 5.53s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 7 unt; 4 def)
% Number of atoms : 85 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 34 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f147,axiom,
! [X,Z] :
( function(Z)
| ~ member(X,recursion_equation_functions(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
~ function(z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,negated_conjecture,
recursion_equation_functions(z) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f163,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f168,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f235,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f333,plain,
! [Z] :
( function(Z)
| ! [X] : ~ member(X,recursion_equation_functions(Z)) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f334,plain,
! [X0,X1] :
( function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f348,plain,
~ function(z),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f349,plain,
recursion_equation_functions(z) != null_class,
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f378,plain,
! [X0,X1] :
( function(X0)
| subclass(recursion_equation_functions(X0),X1) ),
inference(resolution,[status(thm)],[f163,f334]) ).
fof(f386,plain,
! [X0,X1] :
( X1 = recursion_equation_functions(X0)
| ~ subclass(X1,recursion_equation_functions(X0))
| function(X0) ),
inference(resolution,[status(thm)],[f378,f168]) ).
fof(f388,plain,
! [X0,X1] :
( function(X1)
| recursion_equation_functions(X1) = recursion_equation_functions(X0)
| function(X0) ),
inference(resolution,[status(thm)],[f386,f378]) ).
fof(f395,plain,
! [X0] :
( function(z)
| function(X0)
| recursion_equation_functions(X0) != null_class ),
inference(paramodulation,[status(thm)],[f388,f349]) ).
fof(f401,plain,
! [X0,X1,X2] :
( function(X2)
| function(X1)
| function(X2)
| ~ member(X0,recursion_equation_functions(X1)) ),
inference(paramodulation,[status(thm)],[f388,f334]) ).
fof(f412,definition,
! [X2] :
( sQ4_spl
<=> ( function(X2)
| function(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f413,plain,
! [X0] :
( ~ sQ4_spl
| function(X0)
| function(X0) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f419,definition,
! [X0] :
( sQ5_spl
<=> ( function(X0)
| recursion_equation_functions(X0) != null_class ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ5_spl
| function(X0)
| recursion_equation_functions(X0) != null_class ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,definition,
( sQ6_spl
<=> function(z) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ6_spl
| function(z) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f395,f419,f422]) ).
fof(f446,definition,
! [X0,X1] :
( sQ12_spl
<=> ( function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0,X1] :
( ~ sQ12_spl
| function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f401,f446,f412]) ).
fof(f457,plain,
! [X0] :
( ~ sQ4_spl
| function(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f413]) ).
fof(f465,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f348,f457]) ).
fof(f467,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f528,plain,
! [X0] :
( ~ sQ12_spl
| function(X0)
| recursion_equation_functions(X0) = null_class ),
inference(resolution,[status(thm)],[f235,f447]) ).
fof(f530,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| function(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f420]) ).
fof(f532,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f348,f530]) ).
fof(f534,plain,
( ~ sQ12_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f423]) ).
fof(f536,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
$false,
inference(sat_refutation,[status(thm)],[f425,f449,f467,f534,f536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.46 % Computer : n015.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Mon Sep 21 02:17:11 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.49 % Drodi V4.1.1
% 0.24/5.53 % Refutation found
% 0.24/5.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/5.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/5.59 % Elapsed time: 0.113300 seconds
% 0.24/5.59 % CPU time: 0.146609 seconds
% 0.24/5.59 % Total memory used: 17.234 MB
% 0.24/5.59 % Net memory used: 17.216 MB
%------------------------------------------------------------------------------