%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET411-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 03:32:03 PM UTC 2025
% Result : Unsatisfiable 110.98s 14.29s
% Output : CNFRefutation 110.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_compose_condition_for_singleton_membership1_1)
% Comments :
%------------------------------------------------------------------------------
cnf(112,plain,
member(ordered_pair(x,y),singleton_relation),
inference(cnf,[status(esa)],[prove_compose_condition_for_singleton_membership1_1]) ).
cnf(l0,plain,
member(ordered_pair(x,y),singleton_relation),
inference(instantiation,[status(thm)],[112]) ).
cnf(0,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subclass_members]) ).
cnf(l1,plain,
( ~ subclass(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))
| ~ member(ordered_pair(x,y),singleton_relation)
| member(ordered_pair(x,y),intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(4,plain,
( X0 != X1
| subclass(X0,X1) ),
inference(cnf,[status(esa)],[equal_implies_subclass1]) ).
cnf(l22,plain,
( singleton_relation != intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)
| subclass(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(103,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(cnf,[status(esa)],[compose_can_define_singleton]) ).
cnf(l24,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(instantiation,[status(thm)],[103]) ).
cnf(15,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(cnf,[status(esa)],[cartesian_product3]) ).
cnf(l2,plain,
( ~ member(x,y)
| ~ member(ordered_pair(x,y),intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))
| member(ordered_pair(x,ordered_pair(x,y)),cross_product(y,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l3,plain,
( ~ member(x,universal_class)
| ~ member(ordered_pair(x,ordered_pair(x,y)),cross_product(y,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)))
| member(ordered_pair(x,ordered_pair(x,ordered_pair(x,y))),cross_product(universal_class,cross_product(y,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)))) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(13,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf,[status(esa)],[cartesian_product1]) ).
cnf(l4,plain,
( ~ member(ordered_pair(x,ordered_pair(x,ordered_pair(x,y))),cross_product(universal_class,cross_product(y,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))))
| member(x,universal_class) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(113,plain,
~ member(x,universal_class),
inference(cnf,[status(esa)],[prove_compose_condition_for_singleton_membership1_2]) ).
cnf(l7,plain,
~ member(x,universal_class),
inference(instantiation,[status(thm)],[113]) ).
cnf(l13,plain,
( ~ subclass(y,universal_class)
| ~ member(x,y)
| member(x,universal_class) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l16,plain,
( ~ member(ordered_pair(x,ordered_pair(x,y)),cross_product(y,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)))
| member(x,y) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(3,plain,
subclass(X0,universal_class),
inference(cnf,[status(esa)],[class_elements_are_sets]) ).
cnf(l15,plain,
subclass(y,universal_class),
inference(instantiation,[status(thm)],[3]) ).
cnf(18,plain,
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) ),
inference(cnf,[status(esa)],[element_relation2]) ).
cnf(l99,plain,
( ~ member(ordered_pair(x,y),element_relation)
| member(x,y) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(21,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection2]) ).
cnf(l100,plain,
( ~ member(ordered_pair(x,y),intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))
| member(ordered_pair(x,y),element_relation) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l22,l24,l2,l3,l4,l7,l13,l16,l15,l99,l100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET411-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 21:19:34 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 9
% 0.20/0.36 % launching worker at depth: 10
% 1.82/0.57 % launching worker at depth: 11
% 110.98/14.29 % SZS status Theorem for theBenchmark
% 110.98/14.29 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------