%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:10:02 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 98 ( 37 unt; 0 def)
% Number of atoms : 185 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 145 ( 58 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),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(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
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(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
member(omega,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(f113,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
member_of(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f123,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f124,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f126,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f130,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f131,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f170,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f173,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f175,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f190,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f246,plain,
singleton(member_of(x)) = x,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
member_of(x) = x,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f252,plain,
singleton(x) = x,
inference(forward_demodulation,[status(thm)],[f247,f246]) ).
fof(f257,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f130,f129]) ).
fof(f258,plain,
member(x,universal_class),
inference(paramodulation,[status(thm)],[f252,f257]) ).
fof(f265,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f130,f124]) ).
fof(f266,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f265]) ).
fof(f268,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f130,f126]) ).
fof(f273,plain,
! [X0] :
( ~ inductive(singleton(X0))
| null_class = X0 ),
inference(resolution,[status(thm)],[f266,f170]) ).
fof(f275,plain,
! [X0] :
( X0 = x
| ~ member(X0,x) ),
inference(paramodulation,[status(thm)],[f252,f266]) ).
fof(f277,plain,
! [X0] :
( subclass(x,X0)
| not_subclass_element(x,X0) = x ),
inference(resolution,[status(thm)],[f275,f117]) ).
fof(f278,plain,
! [X0] :
( subclass(x,X0)
| subclass(x,X0)
| ~ member(x,X0) ),
inference(paramodulation,[status(thm)],[f277,f118]) ).
fof(f280,plain,
! [X0] :
( subclass(x,X0)
| ~ member(x,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f278]) ).
fof(f282,plain,
! [X0] :
( X0 = x
| ~ subclass(X0,x)
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[f280,f122]) ).
fof(f288,plain,
( regular(x) = x
| x = null_class ),
inference(resolution,[status(thm)],[f189,f275]) ).
fof(f299,plain,
! [X0] : unordered_pair(x,unordered_pair(x,singleton(X0))) = ordered_pair(x,X0),
inference(paramodulation,[status(thm)],[f252,f131]) ).
fof(f312,plain,
unordered_pair(x,unordered_pair(x,x)) = ordered_pair(x,x),
inference(paramodulation,[status(thm)],[f252,f299]) ).
fof(f314,plain,
! [X0] :
( member(x,ordered_pair(x,X0))
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f299,f126]) ).
fof(f317,plain,
unordered_pair(x,singleton(x)) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f130,f312]) ).
fof(f318,plain,
unordered_pair(x,x) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f252,f317]) ).
fof(f319,plain,
singleton(x) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f130,f318]) ).
fof(f320,plain,
x = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f252,f319]) ).
fof(f322,plain,
! [X0] : member(x,ordered_pair(x,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f314,f258]) ).
fof(f325,plain,
member(x,x),
inference(paramodulation,[status(thm)],[f320,f322]) ).
fof(f438,plain,
( x = null_class
| intersection(x,x) = null_class
| x = null_class ),
inference(paramodulation,[status(thm)],[f288,f190]) ).
fof(f440,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f190,f143]) ).
fof(f441,plain,
( intersection(x,x) = null_class
| x = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f438]) ).
fof(f468,plain,
! [X0] :
( x = null_class
| member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,x) ),
inference(paramodulation,[status(thm)],[f441,f146]) ).
fof(f469,plain,
! [X0] :
( x = null_class
| member(X0,x)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f441,f145]) ).
fof(f471,plain,
! [X0] :
( x = null_class
| member(X0,null_class)
| ~ member(X0,x) ),
inference(duplicate_literals_removal,[status(thm)],[f468]) ).
fof(f474,plain,
( x = null_class
| member(x,null_class) ),
inference(resolution,[status(thm)],[f471,f325]) ).
fof(f495,plain,
! [X0] :
( X0 = x
| x = null_class
| ~ member(X0,null_class) ),
inference(resolution,[status(thm)],[f469,f275]) ).
fof(f500,plain,
! [X0] :
( subclass(null_class,X0)
| not_subclass_element(null_class,X0) = x
| x = null_class ),
inference(resolution,[status(thm)],[f495,f117]) ).
fof(f691,plain,
! [X0] :
( subclass(null_class,X0)
| x = null_class
| subclass(null_class,X0)
| ~ member(x,X0) ),
inference(paramodulation,[status(thm)],[f500,f118]) ).
fof(f693,plain,
! [X0] :
( x = null_class
| subclass(null_class,X0)
| ~ member(x,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f691]) ).
fof(f696,plain,
( null_class = x
| ~ member(x,null_class)
| x = null_class
| ~ member(x,x) ),
inference(resolution,[status(thm)],[f693,f282]) ).
fof(f699,plain,
( ~ member(x,null_class)
| x = null_class
| ~ member(x,x) ),
inference(duplicate_literals_removal,[status(thm)],[f696]) ).
fof(f700,plain,
( ~ member(x,null_class)
| x = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f325]) ).
fof(f746,plain,
member(x,null_class),
inference(backward_demodulation,[status(thm)],[f759,f325]) ).
fof(f755,plain,
! [X0] :
( X0 = null_class
| ~ member(X0,x) ),
inference(backward_demodulation,[status(thm)],[f759,f275]) ).
fof(f756,plain,
member(null_class,universal_class),
inference(backward_demodulation,[status(thm)],[f759,f258]) ).
fof(f759,plain,
x = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f700,f474]) ).
fof(f805,plain,
member(null_class,null_class),
inference(forward_demodulation,[status(thm)],[f759,f746]) ).
fof(f816,plain,
! [X0] :
( X0 = null_class
| ~ member(X0,null_class) ),
inference(forward_demodulation,[status(thm)],[f759,f755]) ).
fof(f884,plain,
! [X0] :
( X0 = null_class
| member(null_class,X0) ),
inference(resolution,[status(thm)],[f440,f805]) ).
fof(f894,plain,
! [X0] :
( null_class = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f884,f266]) ).
fof(f904,plain,
! [X0] :
( null_class = X0
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f894,f268]) ).
fof(f909,plain,
! [X0] :
( null_class = X0
| ~ inductive(null_class)
| null_class = X0 ),
inference(paramodulation,[status(thm)],[f894,f273]) ).
fof(f913,plain,
! [X0] :
( null_class = X0
| ~ member(X0,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f904,f816]) ).
fof(f914,plain,
! [X0] :
( ~ inductive(null_class)
| null_class = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f909]) ).
fof(f935,plain,
null_class = omega,
inference(resolution,[status(thm)],[f913,f175]) ).
fof(f941,plain,
inductive(null_class),
inference(backward_demodulation,[status(thm)],[f935,f173]) ).
fof(f943,plain,
! [X0] : null_class = X0,
inference(backward_subsumption_resolution,[status(thm)],[f914,f941]) ).
fof(f948,plain,
! [X0,X1] : X0 = X1,
inference(paramodulation,[status(thm)],[f943,f943]) ).
fof(f960,plain,
! [X0] : member(X0,universal_class),
inference(paramodulation,[status(thm)],[f943,f756]) ).
fof(f979,plain,
! [X0,X1] : member(X0,X1),
inference(paramodulation,[status(thm)],[f948,f960]) ).
fof(f982,plain,
! [X0,X1] : ~ member(X0,complement(X1)),
inference(backward_subsumption_resolution,[status(thm)],[f147,f979]) ).
fof(f984,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f982,f979]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n009.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 05:22:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.077398 seconds
% 0.12/0.45 % CPU time: 0.315032 seconds
% 0.12/0.45 % Total memory used: 111.039 MB
% 0.12/0.45 % Net memory used: 110.636 MB
%------------------------------------------------------------------------------