%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n011.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 08:28:47 AM UTC 2026
% Result : Unsatisfiable 5.87s 3.49s
% Output : Refutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 298 ( 36 ~; 44 |; 0 &; 218 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(bDa_decl,type,
bDa: $i ).
thf(bDd_decl,type,
bDd: $i ).
thf(difference_decl,type,
difference: $i > $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(k_decl,type,
k: $i > $i > $i > $i ).
thf(d_decl,type,
d: $i ).
thf(a_decl,type,
a: $i ).
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(member_of_1_not_of_2_decl,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) ) )
| ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ k ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom1) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) ) )
| ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ k ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) ) )
| ( B @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( A @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom3) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) ) )
| ( B @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( A @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(41,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)],[14]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
a @ ( d @ subset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_a_subset_of_a) ).
thf(31,plain,
a @ ( d @ subset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
bDd @ ( d @ ( b @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_d) ).
thf(43,plain,
bDd @ ( d @ ( b @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( D @ ( A @ member ) )
| ~ ( D @ ( C @ ( B @ difference ) ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( D @ ( A @ member ) )
| ~ ( D @ ( C @ ( B @ difference ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ( A @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ( C @ ( B @ ( A @ difference ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom2) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ( A @ ( C @ ( B @ ( A @ k ) ) @ member ) )
| ( C @ ( B @ ( A @ difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(37,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)],[12]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ difference ) ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_difference) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ difference ) ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
~ ( bDd @ ( bDa @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).
thf(17,plain,
~ ( bDd @ ( bDa @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
bDa @ ( a @ ( b @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_a) ).
thf(34,plain,
bDa @ ( a @ ( b @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ difference ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[29,21,41,39,35,31,43,23,19,37,25,17,32,34,44,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.13 % 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
% 0.25/0.50 % Computer : n011.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 06:48:59 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 1.39/1.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.62 % [INFO] Parsing done (300ms).
% 1.92/1.64 % [INFO] Running in sequential loop mode.
% 2.99/2.29 % [INFO] eprover registered as external prover.
% 3.21/2.31 % [INFO] Scanning for conjecture ...
% 3.44/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.60/2.53 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.60/2.57 % [INFO] Problem is propositional (TPTP CNF).
% 3.60/2.58 % [INFO] Type checking passed.
% 3.60/2.58 % [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 ...
% 5.87/3.48 % External prover 'e' found a proof!
% 5.87/3.48 % [INFO] Killing All external provers ...
% 5.87/3.48 % Time passed: 2779ms (effective reasoning time: 1829ms)
% 5.87/3.49 % Axioms used in derivation (15): d_is_a_subset_of_a, difference_axiom3, subsets_are_set_equal_sets, subsets_axiom2, difference_axiom2, set_equal_sets_are_subsets1, difference_axiom1, b_minus_a, not_member_of_difference, member_of_difference, b_minus_d, member_of_difference_or_set2, set_equal_sets_are_subsets2, membership_in_subsets, subsets_axiom1
% 5.87/3.49 % No. of inferences in proof: 33
% 5.87/3.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2779 ms resp. 1829 ms w/o parsing
% 6.09/3.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.09/3.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------