%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET479-6 : 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 02:09:59 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.75s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 25 unt; 0 def)
% Number of atoms : 159 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 136 ( 60 ~; 76 |; 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 : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 135 ( 135 !; 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(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
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(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ 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(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(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [X] :
( member(ordered_pair(X,domain_of(X)),domain_relation)
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ member(domain_of(x),universal_class),
file('/export/starexec/sandbox2/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(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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(f134,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
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(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(f226,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f228,plain,
! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f246,plain,
member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
~ member(domain_of(x),universal_class),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f255,plain,
! [X0] :
( ~ member(domain_of(x),X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f116,f247]) ).
fof(f256,plain,
! [X0] : ~ member(domain_of(x),X0),
inference(forward_subsumption_resolution,[status(thm)],[f255,f119]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ subclass(X2,complement(X1))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f147,f116]) ).
fof(f278,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f130,f124]) ).
fof(f279,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f278]) ).
fof(f280,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f279,f189]) ).
fof(f298,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f143,f189]) ).
fof(f303,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f145,f189]) ).
fof(f318,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f280,f190]) ).
fof(f319,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f280,f189]) ).
fof(f320,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f318]) ).
fof(f321,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f319]) ).
fof(f328,plain,
singleton(domain_of(x)) = null_class,
inference(resolution,[status(thm)],[f321,f256]) ).
fof(f334,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,domain_of(x)),
inference(paramodulation,[status(thm)],[f328,f131]) ).
fof(f337,plain,
! [X0] :
( X0 = domain_of(x)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f328,f279]) ).
fof(f618,plain,
! [X0,X1] :
( singleton(X1) = null_class
| member(X0,null_class)
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f320,f146]) ).
fof(f847,plain,
! [X0] :
( regular(intersection(null_class,X0)) = domain_of(x)
| intersection(null_class,X0) = null_class ),
inference(resolution,[status(thm)],[f298,f337]) ).
fof(f934,plain,
! [X0] :
( intersection(null_class,X0) = null_class
| intersection(null_class,X0) = null_class
| member(domain_of(x),X0) ),
inference(paramodulation,[status(thm)],[f847,f303]) ).
fof(f939,plain,
! [X0] :
( intersection(null_class,X0) = null_class
| member(domain_of(x),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f934]) ).
fof(f945,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f939,f256]) ).
fof(f958,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f945,f145]) ).
fof(f969,plain,
! [X0,X1] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(resolution,[status(thm)],[f958,f117]) ).
fof(f1006,plain,
! [X0] :
( subclass(null_class,X0)
| subclass(null_class,X0) ),
inference(resolution,[status(thm)],[f969,f118]) ).
fof(f1023,plain,
! [X0] : subclass(null_class,X0),
inference(duplicate_literals_removal,[status(thm)],[f1006]) ).
fof(f1032,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f1023,f271]) ).
fof(f1042,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f618,f1044]) ).
fof(f1044,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1032,f958]) ).
fof(f1281,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f1042,f321]) ).
fof(f1287,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1281]) ).
fof(f1294,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ subclass(X1,X0)
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f1287,f116]) ).
fof(f1357,plain,
! [X0] :
( ~ member(universal_class,X0)
| singleton(universal_class) = null_class ),
inference(resolution,[status(thm)],[f1294,f119]) ).
fof(f1363,plain,
( singleton(universal_class) = null_class
| singleton(universal_class) = null_class ),
inference(resolution,[status(thm)],[f1357,f321]) ).
fof(f1370,plain,
singleton(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f1363]) ).
fof(f1400,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,universal_class),
inference(paramodulation,[status(thm)],[f1370,f131]) ).
fof(f1524,plain,
! [X0] : ordered_pair(X0,domain_of(x)) = ordered_pair(X0,universal_class),
inference(forward_demodulation,[status(thm)],[f334,f1400]) ).
fof(f1672,plain,
( member(ordered_pair(x,universal_class),domain_relation)
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f1524,f228]) ).
fof(f1683,plain,
! [X0,X1,X2] :
( member(domain_of(x),X2)
| ~ member(ordered_pair(X0,universal_class),cross_product(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1524,f135]) ).
fof(f1702,plain,
member(ordered_pair(x,universal_class),domain_relation),
inference(forward_subsumption_resolution,[status(thm)],[f1672,f246]) ).
fof(f1708,plain,
! [X0,X1,X2] : ~ member(ordered_pair(X0,universal_class),cross_product(X1,X2)),
inference(forward_subsumption_resolution,[status(thm)],[f1683,f256]) ).
fof(f1777,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X3,universal_class),X0)
| ~ subclass(X0,cross_product(X1,X2)) ),
inference(resolution,[status(thm)],[f1708,f116]) ).
fof(f2047,plain,
! [X0] : ~ member(ordered_pair(X0,universal_class),domain_relation),
inference(resolution,[status(thm)],[f1777,f226]) ).
fof(f2053,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1702,f2047]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET479-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n011.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 05:20:11 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.25/0.75 % Refutation found
% 0.25/0.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.25/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.81 % Elapsed time: 0.343874 seconds
% 0.25/0.81 % CPU time: 1.968883 seconds
% 0.25/0.81 % Total memory used: 131.175 MB
% 0.25/0.81 % Net memory used: 128.394 MB
%------------------------------------------------------------------------------