%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:52:57 AM UTC 2026
% Result : Theorem 0.03s 0.38s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 6 |; 4 &)
% ( 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 : 36 ( 4 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kelley_p90a,axiom,
! [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('theBenchmark.p',kelley_p90a) ).
fof(kelley_3_2,axiom,
! [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('theBenchmark.p',kelley_3_2) ).
fof(kelley_p_147e,axiom,
! [F,A,B] :
( ( a_locally_compact_top_space(A)
& a_continuous_function_from_onto(F,A,B)
& an_open_function_from_onto(F,A,B) )
=> a_locally_compact_top_space(B) ),
file('theBenchmark.p',kelley_p_147e) ).
fof(kelley_5_19a,conjecture,
! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
file('theBenchmark.p',kelley_5_19a) ).
fof(kelley_5_19a_neg,negated_conjecture,
~ ! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
inference(assume_negation,[status(cth)],[kelley_5_19a]) ).
cnf(c_5,plain,
( a_locally_compact_top_space(C)
| ~ a_locally_compact_top_space(B)
| ~ a_continuous_function_from_onto(A,B,C)
| ~ an_open_function_from_onto(A,B,C) ),
inference(clausify,[status(thm)],[kelley_p_147e]) ).
cnf(c_6,plain,
a_continuous_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(B,C),apply(B,A)),
inference(clausify,[status(thm)],[kelley_p90a]) ).
cnf(c_7,plain,
an_open_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(D,C),apply(D,A)),
inference(clausify,[status(thm)],[kelley_3_2]) ).
cnf(c_8,plain,
( a_locally_compact_top_space(apply(B,A))
| ~ a_locally_compact_top_space(the_product_top_space_over(B,C))
| ~ an_open_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(B,C),apply(B,A)) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,plain,
( a_locally_compact_top_space(apply(A,C))
| ~ a_locally_compact_top_space(the_product_top_space_over(A,B)) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(nnf_4,plain,
? [X1,A1] :
( ? [A] : ~ a_locally_compact_top_space(apply(X1,A))
& a_locally_compact_top_space(the_product_top_space_over(X1,A1)) ),
inference(fof_nnf,[status(thm)],[kelley_5_19a_neg]) ).
fof(sk_kelley_5_19a_neg,plain,
( ~ a_locally_compact_top_space(apply(sK0,sK2))
& a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(A1,sK1),skolemize(A,sK2)],[nnf_4]) ).
cnf(c_10,negated_conjecture,
a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_kelley_5_19a_neg]) ).
cnf(c_11,negated_conjecture,
~ a_locally_compact_top_space(apply(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_kelley_5_19a_neg]) ).
cnf(c_12,negated_conjecture,
a_locally_compact_top_space(apply(sK0,A)),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:32:45 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 1054092 was started by sandbox2 on n009,
% 0.03/0.36 % Sat Sep 26 20:32:45 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.37
% 0.03/0.37 % From the command line: assign(max_seconds, 300).
% 0.03/0.38
% 0.03/0.38 % SZS status Theorem for theBenchmark
% 0.03/0.38
% 0.03/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.38 % Length of proof is 13.
% 0.03/0.38 % Level of proof is 5.
% 0.03/0.38 % Maximum clause weight is 8.000.
% 0.03/0.38 % Given clauses 2.
% 0.03/0.38
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------