%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP021+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 : Tue May 5 05:56:36 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 6 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 36 ( 1 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kelley_5_19a,conjecture,
! [X4,X3] :
( a_locally_compact_top_space(the_product_top_space_over(X4,X3))
=> ! [X1] : a_locally_compact_top_space(apply(X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_5_19a) ).
fof(kelley_3_2,axiom,
! [X1,X2,X3,X4] : an_open_function_from_onto(the_projection_function(X1,X2,X3),the_product_top_space_over(X4,X3),apply(X4,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_3_2) ).
fof(kelley_p90a,axiom,
! [X1,X2,X3] : a_continuous_function_from_onto(the_projection_function(X1,X2,X3),the_product_top_space_over(X2,X3),apply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p90a) ).
fof(kelley_p_147e,axiom,
! [X5,X1,X6] :
( ( an_open_function_from_onto(X5,X1,X6)
& a_continuous_function_from_onto(X5,X1,X6)
& a_locally_compact_top_space(X1) )
=> a_locally_compact_top_space(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p_147e) ).
fof(i_0_4,negated_conjecture,
~ ! [X4,X3] :
( a_locally_compact_top_space(the_product_top_space_over(X4,X3))
=> ! [X1] : a_locally_compact_top_space(apply(X4,X1)) ),
inference(assume_negation,[status(cth)],[kelley_5_19a]) ).
fof(i_0_5,plain,
! [X23,X24,X25,X26] : an_open_function_from_onto(the_projection_function(X23,X24,X25),the_product_top_space_over(X26,X25),apply(X26,X23)),
inference(variable_rename,[status(thm)],[kelley_3_2]) ).
fof(i_0_6,plain,
! [X20,X21,X22] : a_continuous_function_from_onto(the_projection_function(X20,X21,X22),the_product_top_space_over(X21,X22),apply(X21,X20)),
inference(variable_rename,[status(thm)],[kelley_p90a]) ).
fof(i_0_7,plain,
! [X27,X28,X29] :
( ~ an_open_function_from_onto(X27,X28,X29)
| ~ a_continuous_function_from_onto(X27,X28,X29)
| ~ a_locally_compact_top_space(X28)
| a_locally_compact_top_space(X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kelley_p_147e])]) ).
fof(i_0_8,negated_conjecture,
( a_locally_compact_top_space(the_product_top_space_over(esk1_0,esk2_0))
& ~ a_locally_compact_top_space(apply(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])])]) ).
cnf(i_0_9,plain,
an_open_function_from_onto(the_projection_function(X1,X2,X3),the_product_top_space_over(X4,X3),apply(X4,X1)),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_10,plain,
a_continuous_function_from_onto(the_projection_function(X1,X2,X3),the_product_top_space_over(X2,X3),apply(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_11,plain,
( a_locally_compact_top_space(X3)
| ~ an_open_function_from_onto(X1,X2,X3)
| ~ a_continuous_function_from_onto(X1,X2,X3)
| ~ a_locally_compact_top_space(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_12,negated_conjecture,
~ a_locally_compact_top_space(apply(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_13,negated_conjecture,
a_locally_compact_top_space(the_product_top_space_over(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_14,plain,
$false,
inference(scs_inference,[],[i_0_12,i_0_9,i_0_10,i_0_13,i_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : TOP021+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 09:54:22 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.62 % Total time : 1.271s
%------------------------------------------------------------------------------