%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET093+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 03:31:30 PM UTC 2025
% Result : Theorem 2.05s 0.59s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 15 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_2_to_singletons_are_sets,plain,
! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(corollary_2_to_singletons_are_sets_negated,plain,
~ ! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
inference(negate_conjecture,[status(cth)],[corollary_2_to_singletons_are_sets]) ).
cnf(93,plain,
singleton(member_of(sK10)) = sK10,
inference(cnf,[status(esa)],[corollary_2_to_singletons_are_sets_negated]) ).
cnf(l0,plain,
singleton(member_of(sK10)) = sK10,
inference(instantiation,[status(thm)],[93]) ).
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(l4,plain,
member(unordered_pair(member_of(sK10),member_of(sK10)),universal_class),
inference(instantiation,[status(thm)],[11]) ).
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(l16,plain,
singleton(member_of(sK10)) = unordered_pair(member_of(sK10),member_of(sK10)),
inference(instantiation,[status(thm)],[12]) ).
cnf(94,plain,
~ member(sK10,universal_class),
inference(cnf,[status(esa)],[corollary_2_to_singletons_are_sets_negated]) ).
cnf(l6,plain,
~ member(sK10,universal_class),
inference(instantiation,[status(thm)],[94]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l4,l16,l6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET093+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.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 19:50:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.34 % launching worker at depth: 3
% 0.19/0.34 % launching worker at depth: 2
% 0.19/0.34 % launching worker at depth: 4
% 0.19/0.34 % launching worker at depth: 1
% 0.19/0.34 % launching worker at depth: 5
% 0.19/0.34 % launching worker at depth: 8
% 0.19/0.34 % launching worker at depth: 6
% 0.19/0.34 % launching worker at depth: 7
% 0.19/0.34 % launching worker at depth: 9
% 0.19/0.37 % launching worker at depth: 10
% 2.05/0.59 % SZS status Theorem for theBenchmark
% 2.05/0.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------