%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 08:38:27 AM UTC 2026
% Result : Theorem 6.24s 3.54s
% Output : Refutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 336 ( 2 ~; 0 |; 32 &; 269 @)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 53 !; 10 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(topological_space_decl,type,
topological_space: $i > $o ).
thf(top_str_decl,type,
top_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(open_subset_decl,type,
open_subset: $i > $i > $o ).
thf(interior_decl,type,
interior: $i > $i > $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(topstr_closure_decl,type,
topstr_closure: $i > $i > $i ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ closed_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ closed_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(65,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ interior ) )
= ( B @ ( A @ the_carrier @ subset_complement ) @ ( A @ topstr_closure ) @ ( A @ the_carrier @ subset_complement ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(43,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ interior ) )
= ( B @ ( A @ the_carrier @ subset_complement ) @ ( A @ topstr_closure ) @ ( A @ the_carrier @ subset_complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(37,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(25,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
? [A: $i] : ( A @ top_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(29,plain,
? [A: $i] : ( A @ top_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(27,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ open_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ open_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(63,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ interior ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ interior ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(67,plain,
$false,
inference(e,[status(thm)],[52,65,41,54,43,19,37,25,46,57,29,59,27,48,63,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.13 % 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
% 0.23/0.51 % Computer : n011.cluster.edu
% 0.23/0.51 % Model : x86_64 x86_64
% 0.23/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.51 % Memory : 8046.5625MB
% 0.23/0.51 % OS : Linux 6.8.0-71-generic
% 0.23/0.51 % CPULimit : 300
% 0.23/0.51 % WCLimit : 300
% 0.23/0.51 % DateTime : Sat Sep 26 09:12:14 UTC 2026
% 0.23/0.51 % CPUTime :
% 0.23/0.51 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
% 1.42/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.62 % [INFO] Parsing done (290ms).
% 1.99/1.64 % [INFO] Running in sequential loop mode.
% 3.10/2.23 % [INFO] eprover registered as external prover.
% 3.10/2.25 % [INFO] Scanning for conjecture ...
% 3.50/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.70/2.50 % [INFO] Axiom selection finished. Selected 16 axioms (removed 4 axioms).
% 3.70/2.56 % [INFO] Problem is first-order (TPTP FOF).
% 3.70/2.57 % [INFO] Type checking passed.
% 3.70/2.58 % [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 ...
% 6.24/3.54 % External prover 'e' found a proof!
% 6.24/3.54 % [INFO] Killing All external provers ...
% 6.24/3.54 % Time passed: 2834ms (effective reasoning time: 1883ms)
% 6.24/3.54 % 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)>
% 6.24/3.54 % Axioms used in derivation (16): rc1_tops_1, dt_l1_pre_topc, fc2_tops_1, fc3_tops_1, dt_k6_pre_topc, dt_k3_subset_1, dt_k1_tops_1, fc4_tops_1, involutiveness_k3_subset_1, rc6_pre_topc, t3_subset, existence_m1_subset_1, existence_l1_pre_topc, reflexivity_r1_tarski, existence_l1_struct_0, d1_tops_1
% 6.24/3.54 % No. of inferences in proof: 36
% 6.24/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2834 ms resp. 1883 ms w/o parsing
% 6.51/3.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.51/3.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------