%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n018.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 08:28:49 AM UTC 2026
% Result : Unsatisfiable 5.10s 2.40s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 288 ( 42 ~; 42 |; 0 &; 204 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(as_decl,type,
as: $i ).
thf(bs_decl,type,
bs: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(member_of_1_not_of_2_decl,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i] : ( A @ ( A @ equal_sets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_set_equal) ).
thf(50,plain,
! [A: $i] : ( A @ ( A @ equal_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equal_sets ) )
| ~ ( C @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_set_equal) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equal_sets ) )
| ~ ( C @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( as @ ( bs @ intersection ) @ ( bs @ ( as @ intersection ) @ equal_sets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
thf(20,plain,
~ ( as @ ( bs @ intersection ) @ ( bs @ ( as @ intersection ) @ equal_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ union ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ union ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_for_set_equal) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ member ) )
| ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_or_complement) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ member ) )
| ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(30,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(230,plain,
$false,
inference(e,[status(thm)],[53,48,50,42,24,20,46,28,38,32,34,22,44,40,26,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % 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
% 0.16/0.52 % Computer : n018.cluster.edu
% 0.16/0.52 % Model : x86_64 x86_64
% 0.16/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.52 % Memory : 8046.5625MB
% 0.16/0.52 % OS : Linux 6.8.0-71-generic
% 0.16/0.52 % CPULimit : 300
% 0.16/0.52 % WCLimit : 300
% 0.16/0.52 % DateTime : Sat Sep 26 06:51:53 UTC 2026
% 0.16/0.53 % CPUTime :
% 0.16/0.53 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
% 0.68/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.93 % [INFO] Parsing done (104ms).
% 0.91/0.94 % [INFO] Running in sequential loop mode.
% 1.25/1.13 % [INFO] eprover registered as external prover.
% 1.50/1.13 % [INFO] Scanning for conjecture ...
% 1.50/1.17 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 1.65/1.21 % [INFO] Axiom selection finished. Selected 18 axioms (removed 3 axioms).
% 1.65/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.65/1.24 % [INFO] Type checking passed.
% 1.65/1.25 % [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 ...
% 4.23/2.39 % External prover 'e' found a proof!
% 4.23/2.40 % [INFO] Killing All external provers ...
% 4.23/2.40 % Time passed: 1778ms (effective reasoning time: 1454ms)
% 5.10/2.40 % Axioms used in derivation (18): member_of_intersection_is_member_of_set2, reflexivity_for_set_equal, set_equal_sets_are_subsets2, subsets_are_set_equal_sets, member_of_intersection_is_member_of_set1, set_equal_sets_are_subsets1, transitivity_for_set_equal, member_of_set_or_complement, symmetry_for_set_equal, member_of_set1_is_member_of_union, member_of_union_is_member_of_one_set, not_member_of_set_and_complement, subsets_axiom2, empty_set, member_of_set2_is_member_of_union, member_of_both_is_member_of_intersection, membership_in_subsets, subsets_axiom1
% 5.10/2.40 % No. of inferences in proof: 39
% 5.10/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1778 ms resp. 1454 ms w/o parsing
% 5.10/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.10/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------