%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 09:52:27 AM UTC 2026
% Result : Theorem 3.16s 2.82s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 2 ~; 0 |; 4 &; 74 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_locally_compact_top_space_decl,type,
a_locally_compact_top_space: $i > $o ).
thf(the_product_top_space_over_decl,type,
the_product_top_space_over: $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(a_continuous_function_from_onto_decl,type,
a_continuous_function_from_onto: $i > $i > $i > $o ).
thf(the_projection_function_decl,type,
the_projection_function: $i > $i > $i > $i ).
thf(an_open_function_from_onto_decl,type,
an_open_function_from_onto: $i > $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ the_product_top_space_over ) @ a_locally_compact_top_space )
=> ! [C: $i] : ( C @ ( A @ apply ) @ a_locally_compact_top_space ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_5_19a) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ the_product_top_space_over ) @ a_locally_compact_top_space )
=> ! [C: $i] : ( C @ ( A @ apply ) @ a_locally_compact_top_space ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ the_product_top_space_over ) @ a_locally_compact_top_space )
=> ! [C: $i] : ( C @ ( A @ apply ) @ a_locally_compact_top_space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ apply ) @ ( C @ ( B @ the_product_top_space_over ) @ ( C @ ( B @ ( A @ the_projection_function ) ) @ a_continuous_function_from_onto ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_p90a) ).
thf(11,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ apply ) @ ( C @ ( B @ the_product_top_space_over ) @ ( C @ ( B @ ( A @ the_projection_function ) ) @ a_continuous_function_from_onto ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ apply ) @ ( C @ ( D @ the_product_top_space_over ) @ ( C @ ( B @ ( A @ the_projection_function ) ) @ an_open_function_from_onto ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_3_2) ).
thf(13,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ apply ) @ ( C @ ( D @ the_product_top_space_over ) @ ( C @ ( B @ ( A @ the_projection_function ) ) @ an_open_function_from_onto ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ a_locally_compact_top_space )
& ( C @ ( B @ ( A @ a_continuous_function_from_onto ) ) )
& ( C @ ( B @ ( A @ an_open_function_from_onto ) ) ) )
=> ( C @ a_locally_compact_top_space ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_p_147e) ).
thf(15,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ a_locally_compact_top_space )
& ( C @ ( B @ ( A @ a_continuous_function_from_onto ) ) )
& ( C @ ( B @ ( A @ an_open_function_from_onto ) ) ) )
=> ( C @ a_locally_compact_top_space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[6,11,13,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.14 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.51 % Computer : n004.cluster.edu
% 0.14/0.51 % Model : x86_64 x86_64
% 0.14/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.51 % Memory : 8046.5625MB
% 0.14/0.51 % OS : Linux 6.8.0-71-generic
% 0.14/0.51 % CPULimit : 300
% 0.14/0.51 % WCLimit : 300
% 0.14/0.51 % DateTime : Sat Sep 26 20:32:36 UTC 2026
% 0.14/0.51 % CPUTime :
% 0.14/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.95/1.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.65 % [INFO] Parsing done (235ms).
% 1.21/1.67 % [INFO] Running in sequential loop mode.
% 1.87/2.15 % [INFO] eprover registered as external prover.
% 1.87/2.16 % [INFO] Scanning for conjecture ...
% 1.97/2.26 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.97/2.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.11/2.30 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/2.30 % [INFO] Type checking passed.
% 2.11/2.31 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.16/2.82 % External prover 'e' found a proof!
% 3.16/2.82 % [INFO] Killing All external provers ...
% 3.16/2.82 % Time passed: 2015ms (effective reasoning time: 1135ms)
% 3.16/2.82 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.16/2.82 % Axioms used in derivation (3): kelley_p90a, kelley_3_2, kelley_p_147e
% 3.16/2.82 % No. of inferences in proof: 10
% 3.16/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2015 ms resp. 1135 ms w/o parsing
% 3.16/2.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/2.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------