%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET497-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:10:00 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.81s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 74 ( 20 unt; 0 def)
% Number of atoms : 146 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 127 ( 55 ~; 72 |; 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 : 15 ( 15 usr; 5 con; 0-3 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(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(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ 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(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [Z,X] :
( member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) = null_class
| ~ 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(f76,axiom,
! [Xr] : complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
member(z,diagonalise(element_relation)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
member(z,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(f130,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(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(f151,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f154,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| restrict(X1,singleton(X0),universal_class) = null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
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(f199,plain,
! [X0] : complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f246,plain,
member(z,diagonalise(element_relation)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
member(z,z),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f257,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f119,f116]) ).
fof(f268,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f147,f189]) ).
fof(f269,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f147,f117]) ).
fof(f270,plain,
! [X0,X1] :
( ~ member(X0,domain_of(intersection(X1,identity_relation)))
| ~ member(X0,diagonalise(X1)) ),
inference(paramodulation,[status(thm)],[f199,f147]) ).
fof(f280,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f130,f124]) ).
fof(f281,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f280]) ).
fof(f283,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f130,f126]) ).
fof(f286,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f281,f189]) ).
fof(f308,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f286,f190]) ).
fof(f309,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f286,f189]) ).
fof(f310,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f308]) ).
fof(f311,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f309]) ).
fof(f322,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f151,f143]) ).
fof(f410,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f268,f257]) ).
fof(f483,plain,
! [X0,X1] :
( singleton(X1) = null_class
| member(X0,null_class)
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f310,f146]) ).
fof(f694,plain,
! [X0,X1] :
( ~ member(X0,diagonalise(X1))
| restrict(intersection(X1,identity_relation),singleton(X0),universal_class) = null_class
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f154,f270]) ).
fof(f700,plain,
! [X0,X1] :
( ~ member(X1,diagonalise(X0))
| restrict(intersection(X0,identity_relation),singleton(X1),universal_class) = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f694,f257]) ).
fof(f705,plain,
restrict(intersection(element_relation,identity_relation),singleton(z),universal_class) = null_class,
inference(resolution,[status(thm)],[f700,f246]) ).
fof(f708,plain,
! [X0] :
( member(X0,intersection(element_relation,identity_relation))
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f705,f322]) ).
fof(f710,plain,
! [X0] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,identity_relation)) ),
inference(resolution,[status(thm)],[f708,f117]) ).
fof(f714,plain,
! [X0] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(null_class,X0) ),
inference(resolution,[status(thm)],[f710,f143]) ).
fof(f799,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(universal_class),X0),X1)
| subclass(complement(universal_class),X0) ),
inference(resolution,[status(thm)],[f269,f257]) ).
fof(f918,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f410,f189]) ).
fof(f933,plain,
! [X0,X1] :
( ~ member(not_subclass_element(null_class,X0),X1)
| subclass(complement(universal_class),X0) ),
inference(backward_demodulation,[status(thm)],[f934,f799]) ).
fof(f934,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f918]) ).
fof(f935,plain,
! [X0] : subclass(null_class,X0),
inference(backward_subsumption_resolution,[status(thm)],[f714,f942]) ).
fof(f942,plain,
! [X0,X1] :
( ~ member(not_subclass_element(null_class,X0),X1)
| subclass(null_class,X0) ),
inference(forward_demodulation,[status(thm)],[f934,f933]) ).
fof(f944,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(resolution,[status(thm)],[f935,f116]) ).
fof(f955,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f934,f147]) ).
fof(f958,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f483,f959]) ).
fof(f959,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f955,f944]) ).
fof(f1129,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f958,f311]) ).
fof(f1133,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1129]) ).
fof(f1134,plain,
singleton(z) = null_class,
inference(resolution,[status(thm)],[f1133,f247]) ).
fof(f1166,plain,
( member(z,null_class)
| ~ member(z,universal_class) ),
inference(paramodulation,[status(thm)],[f1134,f283]) ).
fof(f1191,plain,
~ member(z,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f1166,f959]) ).
fof(f1192,plain,
! [X0] : ~ member(z,X0),
inference(resolution,[status(thm)],[f1191,f257]) ).
fof(f1194,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f246,f1192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET497-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n003.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Mon Sep 21 05:23:16 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.13/0.81 % Refutation found
% 0.13/0.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.85 % Elapsed time: 0.274772 seconds
% 0.13/0.85 % CPU time: 1.808994 seconds
% 0.13/0.85 % Total memory used: 143.664 MB
% 0.13/0.85 % Net memory used: 140.269 MB
%------------------------------------------------------------------------------