%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET081+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 : n029.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 03:31:27 PM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 11 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(only_member_in_singleton,plain,
! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(only_member_in_singleton_negated,plain,
~ ! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
inference(negate_conjecture,[status(cth)],[only_member_in_singleton]) ).
cnf(89,plain,
member(sK11,singleton(sK10)),
inference(cnf,[status(esa)],[only_member_in_singleton_negated]) ).
cnf(l0,plain,
member(sK11,singleton(sK10)),
inference(instantiation,[status(thm)],[89]) ).
fof(subclass_defn,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('Axioms/SET005+0.ax',subclass_defn) ).
cnf(0,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subclass_defn]) ).
cnf(l1,plain,
( ~ subclass(singleton(sK10),unordered_pair(sK10,sK10))
| ~ member(sK11,singleton(sK10))
| member(sK11,unordered_pair(sK10,sK10)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(extensionality,plain,
! [X,Y] :
( X = Y
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('Axioms/SET005+0.ax',extensionality) ).
cnf(4,plain,
( X0 != X1
| subclass(X0,X1) ),
inference(cnf,[status(esa)],[extensionality]) ).
cnf(l11,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(l12,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(8,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l3,plain,
( ~ member(sK11,unordered_pair(sK10,sK10))
| sK11 = sK10
| sK11 = sK10 ),
inference(instantiation,[status(thm)],[8]) ).
cnf(90,plain,
sK11 != sK10,
inference(cnf,[status(esa)],[only_member_in_singleton_negated]) ).
cnf(l5,plain,
sK11 != sK10,
inference(instantiation,[status(thm)],[90]) ).
cnf(l8,plain,
sK11 != sK10,
inference(instantiation,[status(thm)],[90]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l11,l12,l3,l5,l8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.08 % Problem : SET081+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.08/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n029.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 19:44:49 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------