%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET098-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:09:20 PM UTC 2026
% Result : Unsatisfiable 1.23s 0.72s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 79 ( 22 unt; 0 def)
% Number of atoms : 157 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 138 ( 60 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 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(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
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(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f98,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f103,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f122,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f123,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f125,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f127,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f128,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f169,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f170,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f200,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
x != null_class,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f209,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f123,f97]) ).
fof(f210,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f125,f97]) ).
fof(f218,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f209,f98]) ).
fof(f222,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f218]) ).
fof(f223,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[f210,f200]) ).
fof(f224,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f210,f98]) ).
fof(f228,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f224]) ).
fof(f240,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f96,f99]) ).
fof(f242,plain,
! [X0,X1] :
( X0 = intersection(X1,X0)
| ~ subclass(X0,intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f102,f228]) ).
fof(f248,plain,
! [X0,X1,X2] :
( subclass(unordered_pair(X0,X1),X2)
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0 ),
inference(resolution,[status(thm)],[f104,f97]) ).
fof(f251,plain,
( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
| ~ subclass(null_class,intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(resolution,[status(thm)],[f223,f102]) ).
fof(f252,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(resolution,[status(thm)],[f223,f96]) ).
fof(f256,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| member(X0,null_class) ),
inference(resolution,[status(thm)],[f252,f126]) ).
fof(f260,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x)
| member(X0,null_class) ),
inference(resolution,[status(thm)],[f256,f128]) ).
fof(f302,plain,
! [X0,X1] :
( subclass(unordered_pair(X0,X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(unordered_pair(X0,X0),X1) = X0 ),
inference(paramodulation,[status(thm)],[f110,f248]) ).
fof(f309,plain,
! [X0,X1] :
( subclass(unordered_pair(X0,X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f110,f302]) ).
fof(f310,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f110,f309]) ).
fof(f311,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f310]) ).
fof(f442,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f169,f127]) ).
fof(f444,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,x)
| member(X0,null_class) ),
inference(backward_subsumption_resolution,[status(thm)],[f260,f240]) ).
fof(f445,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),universal_class) ),
inference(resolution,[status(thm)],[f240,f169]) ).
fof(f623,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f170,f222]) ).
fof(f630,plain,
null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x),
inference(backward_subsumption_resolution,[status(thm)],[f251,f623]) ).
fof(f744,plain,
( x = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
| ~ subclass(x,null_class) ),
inference(paramodulation,[status(thm)],[f630,f242]) ).
fof(f770,plain,
( x = null_class
| ~ subclass(x,null_class) ),
inference(forward_demodulation,[status(thm)],[f630,f744]) ).
fof(f771,plain,
~ subclass(x,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f770,f202]) ).
fof(f794,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f442,f445]) ).
fof(f798,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f794]) ).
fof(f814,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f798,f127]) ).
fof(f817,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f814,f240]) ).
fof(f819,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(backward_subsumption_resolution,[status(thm)],[f444,f817]) ).
fof(f943,plain,
! [X0] :
( subclass(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x) ),
inference(resolution,[status(thm)],[f819,f98]) ).
fof(f2437,plain,
( subclass(x,singleton(not_subclass_element(x,null_class)))
| subclass(x,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f943,f97]) ).
fof(f2442,plain,
subclass(x,singleton(not_subclass_element(x,null_class))),
inference(duplicate_literals_removal,[status(thm)],[f2437]) ).
fof(f2444,plain,
( singleton(not_subclass_element(x,null_class)) = x
| ~ subclass(singleton(not_subclass_element(x,null_class)),x) ),
inference(resolution,[status(thm)],[f2442,f102]) ).
fof(f2447,plain,
~ subclass(singleton(not_subclass_element(x,null_class)),x),
inference(forward_subsumption_resolution,[status(thm)],[f2444,f201]) ).
fof(f2882,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f311,f98]) ).
fof(f2890,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f2882]) ).
fof(f3009,plain,
~ member(not_subclass_element(x,null_class),x),
inference(resolution,[status(thm)],[f2890,f2447]) ).
fof(f3017,plain,
subclass(x,null_class),
inference(resolution,[status(thm)],[f3009,f97]) ).
fof(f3018,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3017,f771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:50:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.23/0.72 % Refutation found
% 1.23/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.23/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.31/0.76 % Elapsed time: 0.385424 seconds
% 2.31/0.76 % CPU time: 2.690465 seconds
% 2.31/0.76 % Total memory used: 154.007 MB
% 2.31/0.76 % Net memory used: 148.863 MB
%------------------------------------------------------------------------------