%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET515-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 4.28s 1.11s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 22 unt; 0 def)
% Number of atoms : 163 ( 52 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 63 ~; 82 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [X] : intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
member(x,x),
file('/export/starexec/sandbox2/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(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(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(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(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
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(f199,plain,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f245,plain,
member(x,x),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f250,plain,
! [X0] :
( member(x,X0)
| ~ subclass(x,X0) ),
inference(resolution,[status(thm)],[f115,f245]) ).
fof(f251,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[f250,f118]) ).
fof(f261,plain,
! [X0,X1,X2] :
( member(not_subclass_element(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[f116,f115]) ).
fof(f264,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f188,f115]) ).
fof(f271,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f281,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f282,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f281]) ).
fof(f285,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f129,f125]) ).
fof(f289,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f282,f188]) ).
fof(f292,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f142,f188]) ).
fof(f293,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f142,f116]) ).
fof(f333,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f289,f188]) ).
fof(f335,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f333]) ).
fof(f398,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,null_class)
| ~ member(X0,regular(X1))
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f189,f145]) ).
fof(f519,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f271,f264]) ).
fof(f527,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f519]) ).
fof(f534,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f527,f118]) ).
fof(f549,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f534,f146]) ).
fof(f554,plain,
! [X0] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),universal_class) ),
inference(resolution,[status(thm)],[f549,f116]) ).
fof(f941,plain,
! [X0] :
( subclass(null_class,X0)
| ~ subclass(null_class,universal_class)
| subclass(null_class,X0) ),
inference(resolution,[status(thm)],[f261,f554]) ).
fof(f958,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f941]) ).
fof(f959,plain,
! [X0] : subclass(null_class,X0),
inference(forward_subsumption_resolution,[status(thm)],[f958,f118]) ).
fof(f966,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(resolution,[status(thm)],[f959,f121]) ).
fof(f1059,plain,
! [X0] :
( intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = null_class
| member(regular(cantor(X0)),domain_of(X0)) ),
inference(paramodulation,[status(thm)],[f199,f292]) ).
fof(f1067,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| ~ member(X0,cantor(X1)) ),
inference(paramodulation,[status(thm)],[f199,f142]) ).
fof(f1068,plain,
! [X0] :
( cantor(X0) = null_class
| member(regular(cantor(X0)),domain_of(X0)) ),
inference(forward_demodulation,[status(thm)],[f199,f1059]) ).
fof(f1874,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f293,f117]) ).
fof(f1901,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f1874]) ).
fof(f1965,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(resolution,[status(thm)],[f1901,f966]) ).
fof(f2003,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(paramodulation,[status(thm)],[f150,f1965]) ).
fof(f2083,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(resolution,[status(thm)],[f2003,f152]) ).
fof(f2099,plain,
cantor(null_class) = null_class,
inference(resolution,[status(thm)],[f2083,f1068]) ).
fof(f2117,plain,
! [X0] :
( member(X0,domain_of(null_class))
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f2099,f1067]) ).
fof(f2118,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f2117,f2083]) ).
fof(f3048,plain,
! [X0,X1] :
( X1 = null_class
| ~ member(X0,regular(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f2118]) ).
fof(f3066,plain,
! [X0,X1] :
( singleton(X1) = null_class
| singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f289,f3048]) ).
fof(f3068,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f3066]) ).
fof(f3755,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f3068,f335]) ).
fof(f3761,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3755]) ).
fof(f3773,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[f3761,f245]) ).
fof(f3839,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f3773,f285]) ).
fof(f3860,plain,
member(x,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f3839,f251]) ).
fof(f3861,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3860,f2118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET515-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:22:55 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 4.28/1.11 % Refutation found
% 4.28/1.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.28/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.72/1.17 % Elapsed time: 0.693079 seconds
% 1.72/1.17 % CPU time: 4.911846 seconds
% 1.72/1.17 % Total memory used: 158.662 MB
% 1.72/1.17 % Net memory used: 152.658 MB
%------------------------------------------------------------------------------