%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET021-7 : 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 : 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 03:31:09 PM UTC 2025
% Result : Unsatisfiable 7.15s 1.30s
% Output : CNFRefutation 7.15s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_unique_1st_and_2nd_in_pair_of_sets2_1)
% Comments :
%------------------------------------------------------------------------------
cnf(157,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(cnf,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_1]) ).
cnf(l0,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(instantiation,[status(thm)],[157]) ).
cnf(118,plain,
( ~ member(X0,X1)
| ~ member(X2,X1)
| subclass(unordered_pair(X0,X2),X1) ),
inference(cnf,[status(esa)],[unordered_pair_is_subset]) ).
cnf(l1,plain,
( ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| subclass(unordered_pair(ordered_pair(u,v),ordered_pair(u,v)),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[118]) ).
cnf(0,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subclass_members]) ).
cnf(l2,plain,
( ~ subclass(unordered_pair(ordered_pair(u,v),ordered_pair(u,v)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),unordered_pair(ordered_pair(u,v),ordered_pair(u,v)))
| member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(94,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,universal_class) ),
inference(cnf,[status(esa)],[corollary_2_to_cartesian_product]) ).
cnf(l7,plain,
( ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class))
| member(second(ordered_pair(u,v)),universal_class) ),
inference(instantiation,[status(thm)],[94]) ).
cnf(151,plain,
( ~ member(X0,universal_class)
| ordered_pair(X1,X0) != ordered_pair(X2,X3)
| X0 = X3 ),
inference(cnf,[status(esa)],[ordered_pair_determines_components2]) ).
cnf(l8,plain,
( ~ member(second(ordered_pair(u,v)),universal_class)
| ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v)
| second(ordered_pair(u,v)) = v ),
inference(instantiation,[status(thm)],[151]) ).
cnf(16,plain,
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(cnf,[status(esa)],[cartesian_product4]) ).
cnf(l17,plain,
( ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(158,plain,
second(ordered_pair(u,v)) != v,
inference(cnf,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_2]) ).
cnf(l9,plain,
second(ordered_pair(u,v)) != v,
inference(instantiation,[status(thm)],[158]) ).
cnf(121,plain,
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(cnf,[status(esa)],[set_in_its_singleton]) ).
cnf(l28,plain,
( ~ member(ordered_pair(u,v),universal_class)
| member(ordered_pair(u,v),singleton(ordered_pair(u,v))) ),
inference(instantiation,[status(thm)],[121]) ).
cnf(11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf,[status(esa)],[singleton_set]) ).
cnf(l26,plain,
unordered_pair(ordered_pair(u,v),ordered_pair(u,v)) = singleton(ordered_pair(u,v)),
inference(instantiation,[status(thm)],[11]) ).
cnf(144,plain,
member(ordered_pair(X0,X1),universal_class),
inference(cnf,[status(esa)],[ordered_pair_is_set]) ).
cnf(l29,plain,
member(ordered_pair(u,v),universal_class),
inference(instantiation,[status(thm)],[144]) ).
cnf(l6,plain,
( ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l7,l8,l17,l9,l28,l26,l29,l6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET021-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n029.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 19:21:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.19/0.38 % launching worker at depth: 10
% 4.85/1.02 % launching worker at depth: 11
% 7.15/1.30 % SZS status Theorem for theBenchmark
% 7.15/1.30 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------