%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET516-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 95 ( 34 unt; 0 def)
% Number of atoms : 182 ( 69 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 : 11 ( 11 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(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f123,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f125,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f130,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f169,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f174,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f189,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f245,plain,
singleton(x) = x,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f254,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f129,f128]) ).
fof(f255,plain,
member(x,universal_class),
inference(paramodulation,[status(thm)],[f245,f254]) ).
fof(f262,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f263,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f262]) ).
fof(f265,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f129,f125]) ).
fof(f270,plain,
! [X0] :
( ~ inductive(singleton(X0))
| null_class = X0 ),
inference(resolution,[status(thm)],[f263,f169]) ).
fof(f272,plain,
! [X0] :
( X0 = x
| ~ member(X0,x) ),
inference(paramodulation,[status(thm)],[f245,f263]) ).
fof(f274,plain,
! [X0] :
( subclass(x,X0)
| not_subclass_element(x,X0) = x ),
inference(resolution,[status(thm)],[f272,f116]) ).
fof(f275,plain,
! [X0] :
( subclass(x,X0)
| subclass(x,X0)
| ~ member(x,X0) ),
inference(paramodulation,[status(thm)],[f274,f117]) ).
fof(f277,plain,
! [X0] :
( subclass(x,X0)
| ~ member(x,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f275]) ).
fof(f279,plain,
! [X0] :
( X0 = x
| ~ subclass(X0,x)
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[f277,f121]) ).
fof(f289,plain,
( regular(x) = x
| x = null_class ),
inference(resolution,[status(thm)],[f188,f272]) ).
fof(f300,plain,
! [X0] : unordered_pair(x,unordered_pair(x,singleton(X0))) = ordered_pair(x,X0),
inference(paramodulation,[status(thm)],[f245,f130]) ).
fof(f313,plain,
unordered_pair(x,unordered_pair(x,x)) = ordered_pair(x,x),
inference(paramodulation,[status(thm)],[f245,f300]) ).
fof(f315,plain,
! [X0] :
( member(x,ordered_pair(x,X0))
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f300,f125]) ).
fof(f318,plain,
unordered_pair(x,singleton(x)) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f129,f313]) ).
fof(f319,plain,
unordered_pair(x,x) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f245,f318]) ).
fof(f320,plain,
singleton(x) = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f129,f319]) ).
fof(f321,plain,
x = ordered_pair(x,x),
inference(forward_demodulation,[status(thm)],[f245,f320]) ).
fof(f323,plain,
! [X0] : member(x,ordered_pair(x,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f315,f255]) ).
fof(f326,plain,
member(x,x),
inference(paramodulation,[status(thm)],[f321,f323]) ).
fof(f447,plain,
( x = null_class
| intersection(x,x) = null_class
| x = null_class ),
inference(paramodulation,[status(thm)],[f289,f189]) ).
fof(f449,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f189,f142]) ).
fof(f451,plain,
( intersection(x,x) = null_class
| x = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f447]) ).
fof(f478,plain,
! [X0] :
( x = null_class
| member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,x) ),
inference(paramodulation,[status(thm)],[f451,f145]) ).
fof(f479,plain,
! [X0] :
( x = null_class
| member(X0,x)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f451,f144]) ).
fof(f481,plain,
! [X0] :
( x = null_class
| member(X0,null_class)
| ~ member(X0,x) ),
inference(duplicate_literals_removal,[status(thm)],[f478]) ).
fof(f484,plain,
( x = null_class
| member(x,null_class) ),
inference(resolution,[status(thm)],[f481,f326]) ).
fof(f498,plain,
! [X0] :
( X0 = x
| x = null_class
| ~ member(X0,null_class) ),
inference(resolution,[status(thm)],[f479,f272]) ).
fof(f503,plain,
! [X0] :
( subclass(null_class,X0)
| not_subclass_element(null_class,X0) = x
| x = null_class ),
inference(resolution,[status(thm)],[f498,f116]) ).
fof(f694,plain,
! [X0] :
( subclass(null_class,X0)
| x = null_class
| subclass(null_class,X0)
| ~ member(x,X0) ),
inference(paramodulation,[status(thm)],[f503,f117]) ).
fof(f696,plain,
! [X0] :
( x = null_class
| subclass(null_class,X0)
| ~ member(x,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f694]) ).
fof(f699,plain,
( null_class = x
| ~ member(x,null_class)
| x = null_class
| ~ member(x,x) ),
inference(resolution,[status(thm)],[f696,f279]) ).
fof(f702,plain,
( ~ member(x,null_class)
| x = null_class
| ~ member(x,x) ),
inference(duplicate_literals_removal,[status(thm)],[f699]) ).
fof(f703,plain,
( ~ member(x,null_class)
| x = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f702,f326]) ).
fof(f749,plain,
member(x,null_class),
inference(backward_demodulation,[status(thm)],[f762,f326]) ).
fof(f759,plain,
! [X0] :
( X0 = null_class
| ~ member(X0,x) ),
inference(backward_demodulation,[status(thm)],[f762,f272]) ).
fof(f760,plain,
member(null_class,universal_class),
inference(backward_demodulation,[status(thm)],[f762,f255]) ).
fof(f762,plain,
x = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f703,f484]) ).
fof(f807,plain,
member(null_class,null_class),
inference(forward_demodulation,[status(thm)],[f762,f749]) ).
fof(f820,plain,
! [X0] :
( X0 = null_class
| ~ member(X0,null_class) ),
inference(forward_demodulation,[status(thm)],[f762,f759]) ).
fof(f902,plain,
! [X0] :
( X0 = null_class
| member(null_class,X0) ),
inference(resolution,[status(thm)],[f449,f807]) ).
fof(f912,plain,
! [X0] :
( null_class = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f902,f263]) ).
fof(f923,plain,
! [X0] :
( null_class = X0
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f912,f265]) ).
fof(f928,plain,
! [X0] :
( null_class = X0
| ~ inductive(null_class)
| null_class = X0 ),
inference(paramodulation,[status(thm)],[f912,f270]) ).
fof(f932,plain,
! [X0] :
( null_class = X0
| ~ member(X0,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f923,f820]) ).
fof(f934,plain,
! [X0] :
( ~ inductive(null_class)
| null_class = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f928]) ).
fof(f955,plain,
null_class = omega,
inference(resolution,[status(thm)],[f932,f174]) ).
fof(f961,plain,
inductive(null_class),
inference(backward_demodulation,[status(thm)],[f955,f172]) ).
fof(f963,plain,
! [X0] : null_class = X0,
inference(backward_subsumption_resolution,[status(thm)],[f934,f961]) ).
fof(f968,plain,
! [X0,X1] : X0 = X1,
inference(paramodulation,[status(thm)],[f963,f963]) ).
fof(f981,plain,
! [X0] : member(X0,universal_class),
inference(paramodulation,[status(thm)],[f963,f760]) ).
fof(f1000,plain,
! [X0,X1] : member(X0,X1),
inference(paramodulation,[status(thm)],[f968,f981]) ).
fof(f1003,plain,
! [X0,X1] : ~ member(X0,complement(X1)),
inference(backward_subsumption_resolution,[status(thm)],[f146,f1000]) ).
fof(f1005,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1003,f1000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET516-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:22:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.078417 seconds
% 0.13/0.43 % CPU time: 0.286274 seconds
% 0.13/0.43 % Total memory used: 110.451 MB
% 0.13/0.43 % Net memory used: 110.052 MB
%------------------------------------------------------------------------------