%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET504-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.23s 5.78s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 18 unt; 0 def)
% Number of atoms : 125 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 114 ( 52 ~; 62 |; 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 : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 100 !; 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(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(f52,axiom,
member(omega,universal_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(f113,negated_conjecture,
member(ordered_pair(x,universal_class),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(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(f174,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(thm)],[f52]) ).
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(x,universal_class),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f254,plain,
member(universal_class,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(f317,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f315]) ).
fof(f327,plain,
! [X0,X1,X2,X3] :
( ~ member(X1,X3)
| ~ member(X0,X2)
| ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1))) = ordered_pair(X0,X1) ),
inference(resolution,[status(thm)],[f137,f135]) ).
fof(f491,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ordered_pair(first(ordered_pair(X0,universal_class)),second(ordered_pair(X0,universal_class))) = ordered_pair(X0,universal_class) ),
inference(resolution,[status(thm)],[f327,f254]) ).
fof(f543,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f270,f258]) ).
fof(f635,plain,
ordered_pair(first(ordered_pair(omega,universal_class)),second(ordered_pair(omega,universal_class))) = ordered_pair(omega,universal_class),
inference(resolution,[status(thm)],[f491,f174]) ).
fof(f677,plain,
! [X0,X1] :
( member(second(ordered_pair(omega,universal_class)),X1)
| ~ member(ordered_pair(omega,universal_class),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f635,f134]) ).
fof(f752,plain,
! [X0,X1] :
( ~ member(universal_class,X0)
| ~ member(omega,X1)
| member(second(ordered_pair(omega,universal_class)),X0) ),
inference(resolution,[status(thm)],[f677,f135]) ).
fof(f753,plain,
! [X0] :
( ~ member(universal_class,X0)
| member(second(ordered_pair(omega,universal_class)),X0) ),
inference(resolution,[status(thm)],[f752,f174]) ).
fof(f768,plain,
( ~ member(universal_class,universal_class)
| member(second(ordered_pair(omega,universal_class)),singleton(universal_class)) ),
inference(resolution,[status(thm)],[f753,f283]) ).
fof(f775,plain,
member(second(ordered_pair(omega,universal_class)),singleton(universal_class)),
inference(forward_subsumption_resolution,[status(thm)],[f768,f254]) ).
fof(f837,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(f902,plain,
second(ordered_pair(omega,universal_class)) = universal_class,
inference(resolution,[status(thm)],[f775,f281]) ).
fof(f907,plain,
member(universal_class,singleton(universal_class)),
inference(backward_demodulation,[status(thm)],[f902,f775]) ).
fof(f1528,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f543,f188]) ).
fof(f1541,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f1528]) ).
fof(f1559,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f1541,f146]) ).
fof(f1561,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f837,f1563]) ).
fof(f1563,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f1559,f258]) ).
fof(f2064,plain,
( singleton(universal_class) = null_class
| ~ member(universal_class,universal_class) ),
inference(resolution,[status(thm)],[f1561,f907]) ).
fof(f2073,plain,
member(universal_class,null_class),
inference(backward_demodulation,[status(thm)],[f2078,f907]) ).
fof(f2078,plain,
singleton(universal_class) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f2064,f254]) ).
fof(f2080,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2073,f1563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET504-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.49 % Computer : n020.cluster.edu
% 0.18/5.49 % Model : x86_64 x86_64
% 0.18/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.49 % Memory : 8046.5625MB
% 0.18/5.49 % OS : Linux 6.8.0-71-generic
% 0.18/5.49 % CPULimit : 300
% 0.18/5.49 % WCLimit : 300
% 0.18/5.49 % DateTime : Mon Sep 21 05:23:38 UTC 2026
% 0.18/5.49 % CPUTime :
% 0.23/5.51 % Drodi V4.1.1
% 0.23/5.78 % Refutation found
% 0.23/5.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.83 % Elapsed time: 0.319421 seconds
% 0.23/5.83 % CPU time: 2.017095 seconds
% 0.23/5.83 % Total memory used: 129.136 MB
% 0.23/5.83 % Net memory used: 125.526 MB
%------------------------------------------------------------------------------