%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:10:01 PM UTC 2026
% Result : Unsatisfiable 1.66s 0.78s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 17 unt; 0 def)
% Number of atoms : 159 ( 48 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 153 ( 70 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 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(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(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(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(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(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(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(f113,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
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(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(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(f131,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
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,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f253,plain,
member(universal_class,universal_class),
inference(resolution,[status(thm)],[f132,f245]) ).
fof(f254,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f134,f245]) ).
fof(f258,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f118,f115]) ).
fof(f270,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f280,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
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)],[f129,f125]) ).
fof(f286,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f281,f188]) ).
fof(f315,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f286,f189]) ).
fof(f316,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f286,f188]) ).
fof(f317,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f315]) ).
fof(f318,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f316]) ).
fof(f326,plain,
ordered_pair(first(ordered_pair(universal_class,y)),second(ordered_pair(universal_class,y))) = ordered_pair(universal_class,y),
inference(resolution,[status(thm)],[f137,f245]) ).
fof(f330,plain,
! [X0,X1] :
( member(ordered_pair(universal_class,y),cross_product(X0,X1))
| ~ member(second(ordered_pair(universal_class,y)),X1)
| ~ member(first(ordered_pair(universal_class,y)),X0) ),
inference(paramodulation,[status(thm)],[f326,f135]) ).
fof(f331,plain,
! [X0,X1] :
( member(second(ordered_pair(universal_class,y)),X1)
| ~ member(ordered_pair(universal_class,y),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f326,f134]) ).
fof(f332,plain,
! [X0,X1] :
( member(first(ordered_pair(universal_class,y)),X0)
| ~ member(ordered_pair(universal_class,y),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f326,f132]) ).
fof(f381,plain,
! [X0,X1] :
( ~ member(y,X0)
| ~ member(universal_class,X1)
| member(second(ordered_pair(universal_class,y)),X0) ),
inference(resolution,[status(thm)],[f331,f135]) ).
fof(f385,plain,
! [X0,X1] :
( second(ordered_pair(universal_class,y)) = X1
| ~ member(y,singleton(X1))
| ~ member(universal_class,X0) ),
inference(resolution,[status(thm)],[f381,f281]) ).
fof(f389,plain,
! [X0] :
( ~ member(y,universal_class)
| second(ordered_pair(universal_class,y)) = y
| ~ member(universal_class,X0) ),
inference(resolution,[status(thm)],[f385,f283]) ).
fof(f390,plain,
! [X0] :
( second(ordered_pair(universal_class,y)) = y
| ~ member(universal_class,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f254]) ).
fof(f394,plain,
! [X0,X1] :
( member(universal_class,X0)
| ~ member(second(ordered_pair(universal_class,y)),X1)
| ~ member(first(ordered_pair(universal_class,y)),X0) ),
inference(resolution,[status(thm)],[f330,f132]) ).
fof(f396,plain,
second(ordered_pair(universal_class,y)) = y,
inference(resolution,[status(thm)],[f390,f253]) ).
fof(f412,plain,
! [X0,X1] :
( member(universal_class,X0)
| ~ member(y,X1)
| ~ member(first(ordered_pair(universal_class,y)),X0) ),
inference(backward_demodulation,[status(thm)],[f396,f394]) ).
fof(f441,plain,
! [X0] :
( ~ member(first(ordered_pair(universal_class,y)),universal_class)
| member(universal_class,singleton(first(ordered_pair(universal_class,y))))
| ~ member(y,X0) ),
inference(resolution,[status(thm)],[f412,f283]) ).
fof(f448,plain,
member(first(ordered_pair(universal_class,y)),universal_class),
inference(resolution,[status(thm)],[f332,f245]) ).
fof(f452,plain,
! [X0] :
( member(universal_class,singleton(first(ordered_pair(universal_class,y))))
| ~ member(y,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f441,f448]) ).
fof(f511,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f270,f258]) ).
fof(f576,plain,
! [X0] :
( universal_class = first(ordered_pair(universal_class,y))
| ~ member(y,X0) ),
inference(resolution,[status(thm)],[f452,f281]) ).
fof(f578,plain,
universal_class = first(ordered_pair(universal_class,y)),
inference(resolution,[status(thm)],[f576,f254]) ).
fof(f588,plain,
! [X0] :
( member(universal_class,singleton(universal_class))
| ~ member(y,X0) ),
inference(backward_demodulation,[status(thm)],[f578,f452]) ).
fof(f748,plain,
! [X0,X1] :
( singleton(X1) = null_class
| member(X0,null_class)
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f317,f145]) ).
fof(f1309,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f511,f188]) ).
fof(f1321,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f1309]) ).
fof(f1338,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f1321,f146]) ).
fof(f1340,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f748,f1342]) ).
fof(f1342,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1338,f258]) ).
fof(f1690,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f1340,f318]) ).
fof(f1695,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1690]) ).
fof(f1697,plain,
singleton(universal_class) = null_class,
inference(resolution,[status(thm)],[f1695,f253]) ).
fof(f1703,plain,
! [X0] :
( member(universal_class,null_class)
| ~ member(y,X0) ),
inference(backward_demodulation,[status(thm)],[f1697,f588]) ).
fof(f1716,plain,
! [X0] : ~ member(y,X0),
inference(forward_subsumption_resolution,[status(thm)],[f1703,f1342]) ).
fof(f1717,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f254,f1716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:27:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 1.66/0.78 % Refutation found
% 1.66/0.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.66/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.66/0.82 % Elapsed time: 0.447507 seconds
% 1.66/0.82 % CPU time: 3.209462 seconds
% 1.66/0.82 % Total memory used: 141.792 MB
% 1.66/0.82 % Net memory used: 136.677 MB
%------------------------------------------------------------------------------