%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 08:30:35 AM UTC 2026
% Result : Theorem 6.50s 3.68s
% Output : Refutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 22 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 278 ( 10 ~; 0 |; 18 &; 221 @)
% ( 8 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 78 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ intersection ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
thf(110,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ intersection ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
thf(89,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(41,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( empty_set @ ( A @ union ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
thf(73,plain,
! [A: $i] :
( ( empty_set @ ( A @ union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ empty )
<=> ! [B: $i] :
~ ( A @ ( B @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(44,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)],[6]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(71,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
<=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ difference ) @ ( C @ member ) ) )
& ( ( B @ ( A @ difference ) @ ( C @ member ) )
=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( A @ intersection ) @ ( B @ ( A @ intersection ) @ difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( A @ intersection ) @ ( B @ ( A @ intersection ) @ difference ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( A @ intersection ) @ ( B @ ( A @ intersection ) @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(50,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)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(82,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)],[12]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ difference ) )
= ( C @ ( A @ difference ) @ ( B @ ( A @ difference ) @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ difference ) )
= ( C @ ( A @ difference ) @ ( B @ ( A @ difference ) @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(118,plain,
$false,
inference(e,[status(thm)],[110,89,92,41,73,44,71,76,103,18,50,82,79,100,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.53 % Computer : n014.cluster.edu
% 0.12/0.53 % Model : x86_64 x86_64
% 0.12/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.53 % Memory : 8046.5625MB
% 0.12/0.53 % OS : Linux 6.8.0-71-generic
% 0.12/0.53 % CPULimit : 300
% 0.12/0.53 % WCLimit : 300
% 0.12/0.53 % DateTime : Sat Sep 26 08:01:47 UTC 2026
% 0.12/0.53 % CPUTime :
% 0.12/0.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.10/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.44 % [INFO] Parsing done (281ms).
% 1.56/1.46 % [INFO] Running in sequential loop mode.
% 2.47/2.05 % [INFO] eprover registered as external prover.
% 2.76/2.06 % [INFO] Scanning for conjecture ...
% 3.04/2.20 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.04/2.28 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.20/2.33 % [INFO] Problem is first-order (TPTP FOF).
% 3.20/2.34 % [INFO] Type checking passed.
% 3.20/2.35 % [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 ...
% 6.50/3.67 % External prover 'e' found a proof!
% 6.50/3.67 % [INFO] Killing All external provers ...
% 6.50/3.68 % Time passed: 3004ms (effective reasoning time: 2206ms)
% 6.50/3.68 % 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)>
% 6.50/3.68 % Axioms used in derivation (15): reflexivity_of_subset, equal_member_defn, empty_defn, difference_and_intersection_and_union, equal_defn, difference_and_intersection, subset_defn, intersection_defn, empty_set_defn, difference_empty_set, commutativity_of_intersection, difference_defn, commutativity_of_union, union_empty_set, intersection_is_subset
% 6.50/3.68 % No. of inferences in proof: 34
% 6.50/3.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3004 ms resp. 2206 ms w/o parsing
% 7.02/3.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.02/3.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------