%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET068-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:09:10 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.57s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 12 unt; 2 def)
% Number of atoms : 71 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 27 ~; 31 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 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(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,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(f109,negated_conjecture,
~ subclass(singleton(y),unordered_pair(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f111,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f113,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f114,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f118,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f119,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f123,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f237,plain,
~ subclass(singleton(y),unordered_pair(x,y)),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f255,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f125,f119]) ).
fof(f256,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f255]) ).
fof(f274,plain,
member(not_subclass_element(singleton(y),unordered_pair(x,y)),singleton(y)),
inference(resolution,[status(thm)],[f112,f237]) ).
fof(f283,plain,
not_subclass_element(singleton(y),unordered_pair(x,y)) = y,
inference(resolution,[status(thm)],[f256,f274]) ).
fof(f285,plain,
member(y,singleton(y)),
inference(backward_demodulation,[status(thm)],[f283,f274]) ).
fof(f286,plain,
( subclass(singleton(y),unordered_pair(x,y))
| ~ member(y,unordered_pair(x,y)) ),
inference(paramodulation,[status(thm)],[f283,f113]) ).
fof(f287,definition,
( sQ0_spl
<=> member(y,unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ0_spl
| ~ member(y,unordered_pair(x,y)) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ1_spl
<=> subclass(singleton(y),unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ1_spl
| subclass(singleton(y),unordered_pair(x,y)) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f286,f287,f290]) ).
fof(f465,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f111,f114]) ).
fof(f494,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f237]) ).
fof(f495,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f502,plain,
( sQ0_spl
| ~ member(y,universal_class) ),
inference(resolution,[status(thm)],[f123,f289]) ).
fof(f508,plain,
! [X0] :
( sQ0_spl
| ~ member(y,X0) ),
inference(resolution,[status(thm)],[f502,f465]) ).
fof(f509,plain,
( sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f285,f508]) ).
fof(f512,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f513,plain,
$false,
inference(sat_refutation,[status(thm)],[f293,f495,f512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET068-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n009.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 04:49:28 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.54 % Drodi V4.1.1
% 0.15/0.57 % Refutation found
% 0.15/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.60 % Elapsed time: 0.062349 seconds
% 0.15/0.60 % CPU time: 0.189687 seconds
% 0.15/0.60 % Total memory used: 106.416 MB
% 0.15/0.60 % Net memory used: 106.213 MB
%------------------------------------------------------------------------------