%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU319+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 : n008.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 08:38:26 AM UTC 2026
% Result : Theorem 3.96s 3.11s
% Output : Refutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 270 ( 2 ~; 0 |; 7 &; 225 @)
% ( 4 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 0-3 aty)
% Number of variables : 53 ( 0 ^; 47 !; 6 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
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(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(open_subset_decl,type,
open_subset: $i > $i > $o ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(3,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(24,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,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(52,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)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(57,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subset ) )
<=> ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(41,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(45,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(12,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(49,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subset ) )
<=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subset ) )
<=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(47,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
? [A: $i] : ( A @ top_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(28,plain,
? [A: $i] : ( A @ top_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(26,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(55,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(30,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(59,plain,
$false,
inference(e,[status(thm)],[24,52,57,41,45,49,16,47,28,38,26,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.16/0.95 % Computer : n008.cluster.edu
% 0.16/0.95 % Model : x86_64 x86_64
% 0.16/0.95 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.95 % Memory : 8046.5625MB
% 0.16/0.95 % OS : Linux 6.8.0-71-generic
% 0.16/0.95 % CPULimit : 300
% 0.16/0.95 % WCLimit : 300
% 0.16/0.95 % DateTime : Sat Sep 26 09:11:55 UTC 2026
% 0.16/0.95 % CPUTime :
% 0.16/0.95 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
% 0.95/1.55 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.74 % [INFO] Parsing done (190ms).
% 1.27/1.76 % [INFO] Running in sequential loop mode.
% 2.01/2.17 % [INFO] eprover registered as external prover.
% 2.01/2.18 % [INFO] Scanning for conjecture ...
% 2.14/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.32/2.35 % [INFO] Axiom selection finished. Selected 13 axioms (removed 5 axioms).
% 2.32/2.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/2.39 % [INFO] Type checking passed.
% 2.32/2.40 % [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 ...
% 3.96/3.10 % External prover 'e' found a proof!
% 3.96/3.11 % [INFO] Killing All external provers ...
% 3.96/3.11 % Time passed: 2001ms (effective reasoning time: 1343ms)
% 3.96/3.11 % 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)>
% 3.96/3.11 % Axioms used in derivation (13): d6_pre_topc, involutiveness_k3_subset_1, t17_pre_topc, dt_l1_pre_topc, dt_k6_subset_1, t3_subset, existence_m1_subset_1, existence_l1_pre_topc, reflexivity_r1_tarski, existence_l1_struct_0, redefinition_k6_subset_1, dt_k3_subset_1, dt_k2_pre_topc
% 3.96/3.11 % No. of inferences in proof: 30
% 3.96/3.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2001 ms resp. 1343 ms w/o parsing
% 4.28/3.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.28/3.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------