%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : TOP021+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 10:10:27 PM UTC 2025
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 6 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kelley_5_19a,plain,
! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_5_19a) ).
fof(kelley_5_19a_negated,plain,
~ ! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
inference(negate_conjecture,[status(cth)],[kelley_5_19a]) ).
cnf(3,plain,
a_locally_compact_top_space(the_product_top_space_over(sK1,sK2)),
inference(cnf,[status(esa)],[kelley_5_19a_negated]) ).
cnf(l0,plain,
a_locally_compact_top_space(the_product_top_space_over(sK1,sK2)),
inference(instantiation,[status(thm)],[3]) ).
fof(kelley_p_147e,plain,
! [F,A,B] :
( ( an_open_function_from_onto(F,A,B)
& a_continuous_function_from_onto(F,A,B)
& a_locally_compact_top_space(A) )
=> a_locally_compact_top_space(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p_147e) ).
cnf(2,plain,
( ~ an_open_function_from_onto(X0,X1,X2)
| ~ a_locally_compact_top_space(X1)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| a_locally_compact_top_space(X2) ),
inference(cnf,[status(esa)],[kelley_p_147e]) ).
cnf(l1,plain,
( ~ an_open_function_from_onto(the_projection_function(sK3,sK1,sK2),the_product_top_space_over(sK1,sK2),apply(sK1,sK3))
| ~ a_locally_compact_top_space(the_product_top_space_over(sK1,sK2))
| ~ a_continuous_function_from_onto(the_projection_function(sK3,sK1,sK2),the_product_top_space_over(sK1,sK2),apply(sK1,sK3))
| a_locally_compact_top_space(apply(sK1,sK3)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(kelley_3_2,plain,
! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_3_2) ).
cnf(1,plain,
an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)),
inference(cnf,[status(esa)],[kelley_3_2]) ).
cnf(l2,plain,
an_open_function_from_onto(the_projection_function(sK3,sK1,sK2),the_product_top_space_over(sK1,sK2),apply(sK1,sK3)),
inference(instantiation,[status(thm)],[1]) ).
fof(kelley_p90a,plain,
! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p90a) ).
cnf(0,plain,
a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)),
inference(cnf,[status(esa)],[kelley_p90a]) ).
cnf(l3,plain,
a_continuous_function_from_onto(the_projection_function(sK3,sK1,sK2),the_product_top_space_over(sK1,sK2),apply(sK1,sK3)),
inference(instantiation,[status(thm)],[0]) ).
cnf(4,plain,
~ a_locally_compact_top_space(apply(sK1,sK3)),
inference(cnf,[status(esa)],[kelley_5_19a_negated]) ).
cnf(l4,plain,
~ a_locally_compact_top_space(apply(sK1,sK3)),
inference(instantiation,[status(thm)],[4]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP021+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n027.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 : Tue Jul 22 21:32:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 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: 2
% 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: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % SZS status Theorem for theBenchmark
% 0.13/0.34 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------