%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:09:21 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 11 unt; 4 def)
% Number of atoms : 103 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 99 ( 49 ~; 46 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [X] :
( member(X,singleton(X))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f126,axiom,
! [X] :
( singleton(X) = null_class
| member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [X] :
( X = null_class
| singleton(not_subclass_element(X,null_class)) = X
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f142,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f146,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f172,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f173,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f175,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f177,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f293,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f294,plain,
! [X0] :
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f297,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f313,plain,
! [X0] :
( X0 = null_class
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f314,plain,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f315,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f316,plain,
x != null_class,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f334,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f146,f149]) ).
fof(f377,definition,
( sQ7_spl
<=> member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ7_spl
| member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f450,definition,
( sQ9_spl
<=> x = null_class ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ9_spl
| x = null_class ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f455,definition,
( sQ10_spl
<=> member(not_subclass_element(x,null_class),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ10_spl
| ~ member(not_subclass_element(x,null_class),universal_class) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f462,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f316]) ).
fof(f463,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f545,plain,
! [X0,X1] :
( singleton(X0) != null_class
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f334,f294]) ).
fof(f578,plain,
( ~ sQ7_spl
| member(not_subclass_element(x,null_class),x) ),
inference(resolution,[status(thm)],[f378,f175]) ).
fof(f579,plain,
( ~ sQ7_spl
| member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))) ),
inference(resolution,[status(thm)],[f378,f173]) ).
fof(f581,plain,
( ~ sQ7_spl
| singleton(not_subclass_element(x,null_class)) != null_class ),
inference(resolution,[status(thm)],[f578,f545]) ).
fof(f749,plain,
( sQ10_spl
| singleton(not_subclass_element(x,null_class)) = null_class ),
inference(resolution,[status(thm)],[f297,f457]) ).
fof(f751,plain,
( sQ10_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f749,f581]) ).
fof(f752,plain,
( sQ10_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f751]) ).
fof(f801,plain,
( ~ sQ7_spl
| ~ member(not_subclass_element(x,null_class),singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f579,f177]) ).
fof(f841,plain,
( x = null_class
| singleton(not_subclass_element(x,null_class)) = x
| member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(paramodulation,[status(thm)],[f314,f313]) ).
fof(f844,definition,
( sQ46_spl
<=> singleton(not_subclass_element(x,null_class)) = x ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f845,plain,
( ~ sQ46_spl
| singleton(not_subclass_element(x,null_class)) = x ),
inference(component_clause,[status(thm)],[f844]) ).
fof(f847,plain,
( sQ9_spl
| sQ46_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f841,f377,f844,f450]) ).
fof(f919,plain,
( ~ sQ7_spl
| ~ member(not_subclass_element(x,null_class),universal_class) ),
inference(resolution,[status(thm)],[f801,f293]) ).
fof(f921,plain,
( ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f919,f455,f377]) ).
fof(f924,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f845,f315]) ).
fof(f925,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f926,plain,
$false,
inference(sat_refutation,[status(thm)],[f463,f752,f847,f921,f925]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:52:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.16/0.39 % Drodi V4.1.1
% 0.16/0.41 % Refutation found
% 0.16/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.45 % Elapsed time: 0.066533 seconds
% 0.16/0.45 % CPU time: 0.226966 seconds
% 0.16/0.45 % Total memory used: 108.969 MB
% 0.16/0.45 % Net memory used: 108.744 MB
%------------------------------------------------------------------------------