%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET581+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 : 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 08:30:19 AM UTC 2026
% Result : Theorem 6.10s 3.53s
% Output : Refutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 8 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 137 ( 10 ~; 0 |; 12 &; 95 @)
% ( 5 <=>; 15 =>; 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 : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(not_equal_decl,type,
not_equal: $i > $i > $o ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(empty_decl,type,
empty: $i > $o ).
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(24,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(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ( ( B @ ( A @ intersection ) @ ( C @ member ) )
=> ( ( 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(57,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(4,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(21,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( empty_set @ ( C @ ( B @ intersection ) @ not_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th24) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( empty_set @ ( C @ ( B @ intersection ) @ not_equal ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( empty_set @ ( C @ ( B @ intersection ) @ not_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ not_equal ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
thf(45,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(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(71,plain,
$false,
inference(e,[status(thm)],[24,14,57,21,9,45,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.14/0.39 % Computer : n008.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 07:58:09 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 1.27/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.54 % [INFO] Parsing done (274ms).
% 1.80/1.56 % [INFO] Running in sequential loop mode.
% 2.92/2.19 % [INFO] eprover registered as external prover.
% 3.01/2.21 % [INFO] Scanning for conjecture ...
% 3.22/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 3.38/2.41 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 3.38/2.43 % [INFO] Problem is first-order (TPTP FOF).
% 3.38/2.44 % [INFO] Type checking passed.
% 3.38/2.44 % [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 ...
% 6.10/3.52 % External prover 'e' found a proof!
% 6.10/3.52 % [INFO] Killing All external provers ...
% 6.10/3.52 % Time passed: 2912ms (effective reasoning time: 1950ms)
% 6.10/3.52 % 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)>
% 6.10/3.52 % Axioms used in derivation (6): equal_member_defn, empty_set_defn, empty_defn, commutativity_of_intersection, not_equal_defn, intersection_defn
% 6.10/3.52 % No. of inferences in proof: 16
% 6.10/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2912 ms resp. 1950 ms w/o parsing
% 6.37/3.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.37/3.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------