%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET511-6 : 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 0.22s 6.16s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 93 ( 47 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 35 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 63 ( 63 !; 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(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(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(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(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,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(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(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(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,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f254,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f255,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f254]) ).
fof(f338,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f188,f255]) ).
fof(f341,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f115,f118]) ).
fof(f356,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f338,f188]) ).
fof(f357,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f356]) ).
fof(f457,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f476,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f338,f189]) ).
fof(f480,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f476]) ).
fof(f722,plain,
! [X0,X1] :
( singleton(X1) = null_class
| member(X0,null_class)
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f480,f145]) ).
fof(f949,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f457,f341]) ).
fof(f1690,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f949,f188]) ).
fof(f1726,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f1690]) ).
fof(f1770,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f1726,f146]) ).
fof(f1775,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f722,f1776]) ).
fof(f1776,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1770,f341]) ).
fof(f2036,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f1775,f357]) ).
fof(f2040,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2036]) ).
fof(f2045,plain,
! [X0] :
( ~ member(universal_class,X0)
| singleton(universal_class) = null_class ),
inference(resolution,[status(thm)],[f2040,f341]) ).
fof(f2055,plain,
( singleton(universal_class) = null_class
| singleton(universal_class) = null_class ),
inference(resolution,[status(thm)],[f2045,f357]) ).
fof(f2059,plain,
singleton(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f2055]) ).
fof(f2135,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,universal_class),
inference(paramodulation,[status(thm)],[f2059,f130]) ).
fof(f2233,plain,
ordered_pair(x,universal_class) != ordered_pair(x,universal_class),
inference(backward_demodulation,[status(thm)],[f2135,f245]) ).
fof(f2243,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET511-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n004.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Mon Sep 21 05:22:25 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.22/6.16 % Refutation found
% 0.22/6.16 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/6.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.38/6.19 % Elapsed time: 0.715761 seconds
% 0.38/6.19 % CPU time: 5.390886 seconds
% 0.38/6.19 % Total memory used: 162.862 MB
% 0.38/6.19 % Net memory used: 156.073 MB
%------------------------------------------------------------------------------