%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n007.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 09:52:25 AM UTC 2026
% Result : Unsatisfiable 4.71s 3.29s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 4 ~; 2 |; 0 &; 24 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_of_collection_decl,type,
element_of_collection: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(top_of_basis_decl,type,
top_of_basis: $i > $i ).
thf(f_decl,type,
f: $i ).
thf(element_of_set_decl,type,
element_of_set: $i > $i > $o ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(1,negated_conjecture,
~ ( f @ top_of_basis @ ( empty_set @ element_of_collection ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1b_2) ).
thf(4,plain,
~ ( f @ top_of_basis @ ( empty_set @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ element_of_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_6) ).
thf(8,plain,
! [A: $i] :
~ ( empty_set @ ( A @ element_of_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
$false,
inference(e,[status(thm)],[4,6,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.22/0.48 % Computer : n007.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 20:27:54 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.55/1.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.69 % [INFO] Parsing done (278ms).
% 2.08/1.71 % [INFO] Running in sequential loop mode.
% 2.95/2.37 % [INFO] eprover registered as external prover.
% 2.95/2.38 % [INFO] Scanning for conjecture ...
% 3.29/2.51 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.29/2.55 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.29/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.29/2.57 % [INFO] Type checking passed.
% 3.29/2.57 % [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 ...
% 4.71/3.28 % External prover 'e' found a proof!
% 4.71/3.28 % [INFO] Killing All external provers ...
% 4.71/3.28 % Time passed: 2571ms (effective reasoning time: 1563ms)
% 4.71/3.29 % Axioms used in derivation (2): topology_generated_40, set_theory_6
% 4.71/3.29 % No. of inferences in proof: 7
% 4.71/3.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2571 ms resp. 1563 ms w/o parsing
% 5.10/3.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.10/3.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------