%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET101+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:31:32 PM UTC 2025
% Result : Theorem 6.05s 1.12s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 51 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 17 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_member_of_ordered_pair,plain,
! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
fof(singleton_member_of_ordered_pair_negated,plain,
~ ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
inference(negate_conjecture,[status(cth)],[singleton_member_of_ordered_pair]) ).
cnf(89,plain,
~ member(singleton(sK10),ordered_pair(sK10,sK11)),
inference(cnf,[status(esa)],[singleton_member_of_ordered_pair_negated]) ).
cnf(l0,plain,
~ member(singleton(sK10),ordered_pair(sK10,sK11)),
inference(instantiation,[status(thm)],[89]) ).
fof(extensionality,plain,
! [X,Y] :
( X = Y
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('Axioms/SET005+0.ax',extensionality) ).
cnf(6,plain,
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf,[status(esa)],[extensionality]) ).
cnf(l2,plain,
( ~ subclass(unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))),ordered_pair(sK10,sK11))
| ~ subclass(ordered_pair(sK10,sK11),unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))))
| unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))) = ordered_pair(sK10,sK11) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(5,plain,
( X0 != X1
| subclass(X1,X0) ),
inference(cnf,[status(esa)],[extensionality]) ).
cnf(l4,plain,
( ordered_pair(sK10,sK11) != unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11)))
| subclass(unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))),ordered_pair(sK10,sK11)) ),
inference(instantiation,[status(thm)],[5]) ).
fof(ordered_pair_defn,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('Axioms/SET005+0.ax',ordered_pair_defn) ).
cnf(13,plain,
ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf,[status(esa)],[ordered_pair_defn]) ).
cnf(l10,plain,
ordered_pair(sK10,sK11) = unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))),
inference(instantiation,[status(thm)],[13]) ).
cnf(4,plain,
( X0 != X1
| subclass(X0,X1) ),
inference(cnf,[status(esa)],[extensionality]) ).
cnf(l5,plain,
( ordered_pair(sK10,sK11) != unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11)))
| subclass(ordered_pair(sK10,sK11),unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11)))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l9,plain,
ordered_pair(sK10,sK11) = unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11))),
inference(instantiation,[status(thm)],[13]) ).
cnf(l12,plain,
( ~ subclass(unordered_pair(sK10,sK10),singleton(sK10))
| ~ subclass(singleton(sK10),unordered_pair(sK10,sK10))
| unordered_pair(sK10,sK10) = singleton(sK10) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l13,plain,
( singleton(sK10) != unordered_pair(sK10,sK10)
| subclass(unordered_pair(sK10,sK10),singleton(sK10)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l16,plain,
( singleton(sK10) != unordered_pair(sK10,sK10)
| subclass(singleton(sK10),unordered_pair(sK10,sK10)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(singleton_set_defn,plain,
! [X] : singleton(X) = unordered_pair(X,X),
file('Axioms/SET005+0.ax',singleton_set_defn) ).
cnf(12,plain,
singleton(X0) = unordered_pair(X0,X0),
inference(cnf,[status(esa)],[singleton_set_defn]) ).
cnf(l15,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
cnf(l17,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
fof(unordered_pair_defn,plain,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('Axioms/SET005+0.ax',unordered_pair_defn) ).
cnf(9,plain,
( ~ member(X0,universal_class)
| X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l3,plain,
( ~ member(unordered_pair(sK10,sK10),universal_class)
| unordered_pair(sK10,sK10) != singleton(sK10)
| member(unordered_pair(sK10,sK10),unordered_pair(singleton(sK10),unordered_pair(sK10,singleton(sK11)))) ),
inference(instantiation,[status(thm)],[9]) ).
fof(unordered_pair,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('Axioms/SET005+0.ax',unordered_pair) ).
cnf(11,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf,[status(esa)],[unordered_pair]) ).
cnf(l6,plain,
member(unordered_pair(sK10,sK10),universal_class),
inference(instantiation,[status(thm)],[11]) ).
cnf(l47,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l4,l10,l5,l9,l12,l13,l16,l15,l17,l3,l6,l47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET101+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 19:54:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.18/0.42 % launching worker at depth: 11
% 6.05/1.12 % SZS status Theorem for theBenchmark
% 6.05/1.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------