%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP023^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 : Wed Sep 30 08:06:26 AM UTC 2026
% Result : Theorem 4.11s 2.17s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 72 ( 2 ~; 0 |; 2 &; 66 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $tType ).
thf(c_2Epair_2E_2C_decl,type,
c_2Epair_2E_2C:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( tyop_2Epair_2Eprod @ TB @ TA ) ) ).
thf(c_2Epred__set_2ESUBSET_decl,type,
c_2Epred__set_2ESUBSET:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ereal__topology_2Eball_decl,type,
c_2Ereal__topology_2Eball: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Ebounded__def_decl,type,
c_2Ereal__topology_2Ebounded__def: ( tyop_2Erealax_2Ereal > $o ) > $o ).
thf(c_2Ereal__topology_2Ecball_decl,type,
c_2Ereal__topology_2Ecball: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(1,conjecture,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(8,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Ebounded__def @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) )
=> ( c_2Ereal__topology_2Ebounded__def @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(10,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Ebounded__def @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) )
=> ( c_2Ereal__topology_2Ebounded__def @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(13,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[6,8,10,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:37:41 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (229ms).
% 1.23/1.03 % [INFO] Running in sequential loop mode.
% 2.40/1.43 % [INFO] eprover registered as external prover.
% 2.40/1.44 % [INFO] Scanning for conjecture ...
% 2.60/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.60/1.60 % [INFO] Axiom selection finished. Selected 3 axioms (removed 29 axioms).
% 2.81/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.81/1.61 % [INFO] Type checking passed.
% 2.81/1.62 % [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 ...
% 4.11/2.17 % External prover 'e' found a proof!
% 4.11/2.17 % [INFO] Killing All external provers ...
% 4.11/2.17 % Time passed: 1818ms (effective reasoning time: 1128ms)
% 4.11/2.17 % 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)>
% 4.11/2.17 % Axioms used in derivation (3): thm_2Ereal__topology_2EBALL__SUBSET__CBALL, thm_2Ereal__topology_2EBOUNDED__SUBSET, thm_2Ereal__topology_2EBOUNDED__CBALL
% 4.11/2.17 % No. of inferences in proof: 10
% 4.11/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1818 ms resp. 1128 ms w/o parsing
% 4.31/2.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------