%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET082+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 : n027.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 215.63s 27.43s
% Output : CNFRefutation 215.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 55 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 19 ~; 18 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_is_null_class,plain,
! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(singleton_is_null_class_negated,plain,
~ ! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
inference(negate_conjecture,[status(cth)],[singleton_is_null_class]) ).
cnf(89,plain,
~ member(sK10,universal_class),
inference(cnf,[status(esa)],[singleton_is_null_class_negated]) ).
cnf(l0,plain,
~ member(sK10,universal_class),
inference(instantiation,[status(thm)],[89]) ).
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(l2,plain,
( ~ member(sK8(unordered_pair(sK10,sK10)),unordered_pair(sK10,sK10))
| sK8(unordered_pair(sK10,sK10)) = sK10
| sK8(unordered_pair(sK10,sK10)) = sK10 ),
inference(instantiation,[status(thm)],[8]) ).
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(l45,plain,
( ~ subclass(unordered_pair(sK10,sK10),universal_class)
| ~ member(sK8(unordered_pair(sK10,sK10)),unordered_pair(sK10,sK10))
| member(sK8(unordered_pair(sK10,sK10)),universal_class) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(2,plain,
( ~ member(sK1(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf,[status(esa)],[subclass_defn]) ).
cnf(l49,plain,
( ~ member(sK1(unordered_pair(sK10,sK10),universal_class),universal_class)
| subclass(unordered_pair(sK10,sK10),universal_class) ),
inference(instantiation,[status(thm)],[2]) ).
fof(regularity,plain,
! [X] :
( X != null_class
=> ? [U] :
( member(U,universal_class)
& member(U,X)
& disjoint(U,X) ) ),
file('Axioms/SET005+0.ax',regularity) ).
cnf(84,plain,
( member(sK8(X0),X0)
| X0 = null_class ),
inference(cnf,[status(esa)],[regularity]) ).
cnf(l3,plain,
( member(sK8(unordered_pair(sK10,sK10)),unordered_pair(sK10,sK10))
| unordered_pair(sK10,sK10) = null_class ),
inference(instantiation,[status(thm)],[84]) ).
cnf(7,plain,
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l56,plain,
( ~ member(sK1(unordered_pair(sK10,sK10),universal_class),unordered_pair(sK10,sK10))
| member(sK1(unordered_pair(sK10,sK10),universal_class),universal_class) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(1,plain,
( subclass(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subclass_defn]) ).
cnf(l57,plain,
( subclass(unordered_pair(sK10,sK10),universal_class)
| member(sK1(unordered_pair(sK10,sK10),universal_class),unordered_pair(sK10,sK10)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l105,plain,
( member(sK8(unordered_pair(sK10,sK10)),unordered_pair(sK10,sK10))
| unordered_pair(sK10,sK10) = null_class ),
inference(instantiation,[status(thm)],[84]) ).
cnf(90,plain,
singleton(sK10) != null_class,
inference(cnf,[status(esa)],[singleton_is_null_class_negated]) ).
cnf(l107,plain,
singleton(sK10) != null_class,
inference(instantiation,[status(thm)],[90]) ).
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(l134,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
cnf(l9,plain,
singleton(sK10) != null_class,
inference(instantiation,[status(thm)],[90]) ).
cnf(l11,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l45,l49,l3,l56,l57,l105,l107,l134,l9,l11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET082+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.10/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 19:45:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.19/0.44 % launching worker at depth: 11
% 20.56/2.98 % launching worker at depth: 12
% 215.63/27.43 % SZS status Theorem for theBenchmark
% 215.63/27.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------