%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n019.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 08:30:33 AM UTC 2026
% Result : Theorem 4.19s 2.18s
% Output : Refutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 6 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 124 ( 10 ~; 0 |; 10 &; 81 @)
% ( 7 <=>; 16 =>; 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 : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 29 !; 3 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersect_decl,type,
intersect: $i > $i > $o ).
thf(not_equal_decl,type,
not_equal: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
=> ( A @ ( B @ intersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
=> ( A @ ( B @ intersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ( A @ intersect ) )
<=> ( empty_set @ ( A @ not_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ( A @ intersect ) )
<=> ( empty_set @ ( A @ not_equal ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i] :
( ( ( empty_set @ ( A @ not_equal ) )
=> ( A @ ( A @ intersect ) ) )
& ( ( A @ ( A @ intersect ) )
=> ( empty_set @ ( A @ not_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
<=> ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersect ) ) )
& ( ( B @ ( A @ intersect ) )
=> ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ empty )
<=> ! [B: $i] :
~ ( A @ ( B @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
thf(58,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ member ) )
=> ( A @ empty ) )
& ( ( A @ empty )
=> ! [B: $i] :
~ ( A @ ( B @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ not_equal ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( B @ ( A @ not_equal ) ) )
& ( ( B @ ( A @ not_equal ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(23,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[56,9,16,58,47,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.22/0.49 % Computer : n019.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 08:01:48 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
% 0.98/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.12 % [INFO] Parsing done (154ms).
% 1.33/1.13 % [INFO] Running in sequential loop mode.
% 2.00/1.46 % [INFO] eprover registered as external prover.
% 2.00/1.47 % [INFO] Scanning for conjecture ...
% 2.27/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.27/1.57 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.27/1.59 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.59 % [INFO] Type checking passed.
% 2.27/1.59 % [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 ...
% 4.19/2.18 % External prover 'e' found a proof!
% 4.19/2.18 % [INFO] Killing All external provers ...
% 4.19/2.18 % Time passed: 1563ms (effective reasoning time: 1043ms)
% 4.19/2.18 % 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)>
% 4.19/2.18 % Axioms used in derivation (6): equal_member_defn, empty_defn, not_equal_defn, symmetry_of_intersect, empty_set_defn, intersect_defn
% 4.19/2.18 % No. of inferences in proof: 16
% 4.19/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1563 ms resp. 1043 ms w/o parsing
% 4.48/2.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.48/2.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------