%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET079+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n022.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 03:31:26 PM UTC 2025
% Result : Theorem 2.39s 0.67s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 55 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 17 |; 3 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_to_set_in_its_singleton,plain,
! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(corollary_to_set_in_its_singleton_negated,plain,
~ ! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
inference(negate_conjecture,[status(cth)],[corollary_to_set_in_its_singleton]) ).
cnf(89,plain,
member(sK10,universal_class),
inference(cnf,[status(esa)],[corollary_to_set_in_its_singleton_negated]) ).
cnf(l0,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[89]) ).
fof(complement,plain,
! [X,Z] :
( member(Z,complement(X))
<=> ( member(Z,universal_class)
& ~ member(Z,X) ) ),
file('Axioms/SET005+0.ax',complement) ).
cnf(28,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf,[status(esa)],[complement]) ).
cnf(l1,plain,
( ~ member(sK10,universal_class)
| ~ member(sK10,complement(universal_class)) ),
inference(instantiation,[status(thm)],[28]) ).
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(l2,plain,
( ~ subclass(singleton(sK10),complement(universal_class))
| ~ member(sK10,singleton(sK10))
| member(sK10,complement(universal_class)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l56,plain,
( ~ subclass(unordered_pair(sK10,sK10),singleton(sK10))
| ~ member(sK10,unordered_pair(sK10,sK10))
| member(sK10,singleton(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(5,plain,
( X0 != X1
| subclass(X1,X0) ),
inference(cnf,[status(esa)],[extensionality]) ).
cnf(l57,plain,
( singleton(sK10) != unordered_pair(sK10,sK10)
| subclass(unordered_pair(sK10,sK10),singleton(sK10)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(1,plain,
( subclass(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subclass_defn]) ).
cnf(l22,plain,
( subclass(null_class,complement(universal_class))
| member(sK1(null_class,complement(universal_class)),null_class) ),
inference(instantiation,[status(thm)],[1]) ).
fof(null_class_defn,plain,
! [X] : ~ member(X,null_class),
file('Axioms/SET005+0.ax',null_class_defn) ).
cnf(31,plain,
~ member(X0,null_class),
inference(cnf,[status(esa)],[null_class_defn]) ).
cnf(l51,plain,
~ member(sK1(null_class,complement(universal_class)),null_class),
inference(instantiation,[status(thm)],[31]) ).
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(l58,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
cnf(90,plain,
singleton(sK10) = null_class,
inference(cnf,[status(esa)],[corollary_to_set_in_its_singleton_negated]) ).
cnf(l16,plain,
singleton(sK10) = null_class,
inference(instantiation,[status(thm)],[90]) ).
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(10,plain,
( ~ member(X0,universal_class)
| X0 != X1
| member(X0,unordered_pair(X2,X1)) ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l61,plain,
( ~ member(sK10,universal_class)
| sK10 != sK10
| member(sK10,unordered_pair(sK10,sK10)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l56,l57,l22,l51,l58,l16,l61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET079+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 19:44:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.38 % launching worker at depth: 10
% 2.39/0.67 % SZS status Theorem for theBenchmark
% 2.39/0.67 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------