%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:08:52 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.84s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 18 unt; 0 def)
% Number of atoms : 59 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
w != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f106,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f111,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f200,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(w,universal_class),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
w != y,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f206,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f110,f109]) ).
fof(f212,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f213,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f212]) ).
fof(f215,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f110,f106]) ).
fof(f222,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(paramodulation,[status(thm)],[f111,f106]) ).
fof(f223,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,singleton(X2))
| X0 = singleton(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(paramodulation,[status(thm)],[f111,f104]) ).
fof(f227,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f222,f206]) ).
fof(f1009,plain,
! [X0] :
( X0 = unordered_pair(w,singleton(x))
| X0 = singleton(w)
| ~ member(X0,ordered_pair(y,z)) ),
inference(paramodulation,[status(thm)],[f200,f223]) ).
fof(f1053,plain,
( singleton(y) = unordered_pair(w,singleton(x))
| singleton(y) = singleton(w) ),
inference(resolution,[status(thm)],[f1009,f227]) ).
fof(f1271,plain,
( singleton(y) = singleton(w)
| member(w,singleton(y))
| ~ member(w,universal_class) ),
inference(paramodulation,[status(thm)],[f1053,f106]) ).
fof(f1277,plain,
( singleton(y) = singleton(w)
| member(w,singleton(y)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1271,f201]) ).
fof(f1278,plain,
( w = y
| singleton(y) = singleton(w) ),
inference(resolution,[status(thm)],[f1277,f213]) ).
fof(f1281,plain,
singleton(y) = singleton(w),
inference(forward_subsumption_resolution,[status(thm)],[f1278,f202]) ).
fof(f1325,plain,
( member(w,singleton(y))
| ~ member(w,universal_class) ),
inference(paramodulation,[status(thm)],[f1281,f215]) ).
fof(f1345,plain,
member(w,singleton(y)),
inference(forward_subsumption_resolution,[status(thm)],[f1325,f201]) ).
fof(f1347,plain,
w = y,
inference(resolution,[status(thm)],[f1345,f213]) ).
fof(f1350,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1347,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n008.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 04:43:23 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.26/0.84 % Refutation found
% 0.26/0.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.26/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.87 % Elapsed time: 0.431102 seconds
% 0.26/0.87 % CPU time: 3.029906 seconds
% 0.26/0.87 % Total memory used: 140.705 MB
% 0.26/0.87 % Net memory used: 135.871 MB
%------------------------------------------------------------------------------