%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:09:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 41 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 6 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f111,axiom,
! [Y,X] :
( unordered_pair(X,Y) = singleton(X)
| member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [X,Y] :
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,axiom,
! [X,Y] :
( member(Y,universal_class)
| member(X,universal_class)
| unordered_pair(X,Y) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f148,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f149,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f150,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f280,plain,
! [Y] :
( ! [X] : unordered_pair(X,Y) = singleton(X)
| member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f281,plain,
! [X0,X1] :
( unordered_pair(X1,X0) = singleton(X1)
| member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f282,plain,
! [X] :
( ! [Y] : unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f283,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f284,plain,
! [Y] :
( member(Y,universal_class)
| ! [X] :
( member(X,universal_class)
| unordered_pair(X,Y) = null_class ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f285,plain,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f326,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f327,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f328,plain,
~ member(y,universal_class),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f406,plain,
! [X0] : unordered_pair(X0,x) = singleton(X0),
inference(resolution,[status(thm)],[f281,f327]) ).
fof(f418,plain,
! [X0] : unordered_pair(x,X0) = singleton(X0),
inference(resolution,[status(thm)],[f283,f327]) ).
fof(f420,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,x) = null_class ),
inference(resolution,[status(thm)],[f285,f327]) ).
fof(f460,plain,
! [X0] : unordered_pair(singleton(x),singleton(singleton(X0))) = ordered_pair(x,X0),
inference(paramodulation,[status(thm)],[f418,f167]) ).
fof(f517,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(forward_demodulation,[status(thm)],[f406,f420]) ).
fof(f518,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[f517,f327]) ).
fof(f519,plain,
singleton(y) = null_class,
inference(resolution,[status(thm)],[f517,f328]) ).
fof(f656,plain,
! [X0] : unordered_pair(null_class,singleton(singleton(X0))) = ordered_pair(x,X0),
inference(forward_demodulation,[status(thm)],[f518,f460]) ).
fof(f659,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(x,y),
inference(paramodulation,[status(thm)],[f519,f656]) ).
fof(f670,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f659,f326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:58:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.45 % Refutation found
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.101727 seconds
% 0.13/0.48 % CPU time: 0.474803 seconds
% 0.13/0.48 % Total memory used: 95.484 MB
% 0.13/0.48 % Net memory used: 95.072 MB
%------------------------------------------------------------------------------