%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET138-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:09:28 PM UTC 2026
% Result : Unsatisfiable 3.50s 0.85s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 95 ( 30 unt; 9 def)
% Number of atoms : 170 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 147 ( 72 ~; 66 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 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(f5,axiom,
! [X,Y] :
( subclass(X,Y)
| X != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X] :
( subclass(image(successor_relation,X),X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [X] :
( subclass(compose(X,inverse(X)),identity_relation)
| ~ single_valued_class(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [X] :
( single_valued_class(X)
| ~ subclass(compose(X,inverse(X)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [Xf] :
( subclass(compose(Xf,inverse(Xf)),identity_relation)
| ~ function(Xf) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ member(u,set_builder(u,set_builder(v,set_builder(w,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f102,plain,
! [X0,X1] :
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f107,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f108,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f125,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f129,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f130,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f131,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f152,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f153,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f155,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f165,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ single_valued_class(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f166,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f168,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f174,plain,
function(choice),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f202,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f203,plain,
member(u,universal_class),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f206,plain,
~ member(u,set_builder(u,set_builder(v,set_builder(w,null_class)))),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f207,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f102]) ).
fof(f213,plain,
! [X0] :
( ~ member(u,X0)
| ~ subclass(X0,set_builder(u,set_builder(v,set_builder(w,null_class)))) ),
inference(resolution,[status(thm)],[f98,f206]) ).
fof(f228,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f112,f108]) ).
fof(f342,definition,
( sQ8_spl
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ8_spl
| ~ member(u,universal_class) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f349,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f203]) ).
fof(f350,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f422,definition,
( sQ16_spl
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ16_spl
| ~ member(null_class,universal_class) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f439,plain,
! [X0] :
( single_valued_class(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[f168,f166]) ).
fof(f442,plain,
single_valued_class(choice),
inference(resolution,[status(thm)],[f439,f174]) ).
fof(f443,plain,
subclass(compose(choice,inverse(choice)),identity_relation),
inference(resolution,[status(thm)],[f442,f165]) ).
fof(f506,definition,
! [X1] :
( sQ25_spl
<=> ~ subclass(X1,identity_relation) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f507,plain,
! [X0] :
( ~ sQ25_spl
| ~ subclass(X0,identity_relation) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f513,plain,
( ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f443,f507]) ).
fof(f530,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f637,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[f152,f155]) ).
fof(f639,plain,
! [X0] :
( ~ subclass(complement(X0),set_builder(u,set_builder(v,set_builder(w,null_class))))
| member(u,X0)
| ~ member(u,universal_class) ),
inference(resolution,[status(thm)],[f130,f213]) ).
fof(f643,definition,
! [X0] :
( sQ26_spl
<=> ( ~ subclass(complement(X0),set_builder(u,set_builder(v,set_builder(w,null_class))))
| member(u,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f644,plain,
! [X0] :
( ~ sQ26_spl
| ~ subclass(complement(X0),set_builder(u,set_builder(v,set_builder(w,null_class))))
| member(u,X0) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( sQ26_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f639,f342,f643]) ).
fof(f663,plain,
! [X0] :
( member(null_class,X0)
| ~ subclass(omega,X0) ),
inference(resolution,[status(thm)],[f637,f98]) ).
fof(f760,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ subclass(union(X0,X1),set_builder(u,set_builder(v,set_builder(w,null_class))))
| member(u,intersection(complement(X0),complement(X1))) ),
inference(paramodulation,[status(thm)],[f131,f644]) ).
fof(f769,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ subclass(set_builder(X0,X1),set_builder(u,set_builder(v,set_builder(w,null_class))))
| member(u,intersection(complement(singleton(X0)),complement(X1))) ),
inference(paramodulation,[status(thm)],[f202,f760]) ).
fof(f771,plain,
( ~ sQ26_spl
| member(u,intersection(complement(singleton(u)),complement(set_builder(v,set_builder(w,null_class))))) ),
inference(resolution,[status(thm)],[f769,f207]) ).
fof(f773,plain,
( ~ sQ26_spl
| member(u,complement(singleton(u))) ),
inference(resolution,[status(thm)],[f771,f125]) ).
fof(f777,plain,
( ~ sQ26_spl
| ~ member(u,singleton(u)) ),
inference(resolution,[status(thm)],[f773,f129]) ).
fof(f1047,definition,
( sQ35_spl
<=> member(null_class,omega) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1049,plain,
( sQ35_spl
| ~ member(null_class,omega) ),
inference(component_clause,[status(thm)],[f1047]) ).
fof(f1054,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1049,f637]) ).
fof(f1055,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1074,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[f663,f101]) ).
fof(f1076,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1074,f424]) ).
fof(f1077,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1076]) ).
fof(f1873,definition,
! [X0] :
( sQ75_spl
<=> ~ member(X0,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1874,plain,
! [X0] :
( ~ sQ75_spl
| ~ member(X0,universal_class) ),
inference(component_clause,[status(thm)],[f1873]) ).
fof(f1916,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f1874]) ).
fof(f1917,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f1916]) ).
fof(f1941,definition,
( sQ78_spl
<=> subclass(image(successor_relation,omega),omega) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1943,plain,
( sQ78_spl
| ~ subclass(image(successor_relation,omega),omega) ),
inference(component_clause,[status(thm)],[f1941]) ).
fof(f1979,definition,
( sQ82_spl
<=> subclass(image(successor_relation,universal_class),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1981,plain,
( sQ82_spl
| ~ subclass(image(successor_relation,universal_class),universal_class) ),
inference(component_clause,[status(thm)],[f1979]) ).
fof(f1983,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1981,f101]) ).
fof(f1984,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1983]) ).
fof(f2741,plain,
( sQ78_spl
| ~ inductive(omega) ),
inference(resolution,[status(thm)],[f1943,f153]) ).
fof(f2742,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2741,f155]) ).
fof(f2743,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f2742]) ).
fof(f2902,definition,
( sQ138_spl
<=> subclass(omega,omega) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2904,plain,
( sQ138_spl
| ~ subclass(omega,omega) ),
inference(component_clause,[status(thm)],[f2902]) ).
fof(f2909,plain,
( sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2904,f207]) ).
fof(f2910,plain,
sQ138_spl,
inference(contradiction_clause,[status(thm)],[f2909]) ).
fof(f3117,plain,
( ~ sQ26_spl
| ~ member(u,universal_class) ),
inference(resolution,[status(thm)],[f228,f777]) ).
fof(f3125,plain,
( ~ sQ26_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3117,f342,f643]) ).
fof(f3143,plain,
$false,
inference(sat_refutation,[status(thm)],[f350,f530,f646,f1055,f1077,f1917,f1984,f2743,f2910,f3125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET138-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 04:55:52 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 3.50/0.85 % Refutation found
% 3.50/0.85 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.50/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.50/0.87 % Elapsed time: 0.563804 seconds
% 3.50/0.87 % CPU time: 4.185209 seconds
% 3.50/0.87 % Total memory used: 204.932 MB
% 3.50/0.87 % Net memory used: 190.824 MB
%------------------------------------------------------------------------------