%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET010-1 : 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 : n013.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 08:28:48 AM UTC 2026
% Result : Unsatisfiable 6.10s 3.00s
% Output : Refutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 53 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 145 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 628 ( 68 ~; 92 |; 0 &; 468 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: $i > $i > $i > $o ).
thf(cDa_decl,type,
cDa: $i ).
thf(cDb_decl,type,
cDb: $i ).
thf(cD_aIb_decl,type,
cD_aIb: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(k_decl,type,
k: $i > $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i > $o ).
thf(intersection_decl,type,
intersection: $i > $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(h_decl,type,
h: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(aIb_decl,type,
aIb: $i ).
thf(g_decl,type,
g: $i > $i > $i > $i ).
thf(c_decl,type,
c: $i ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,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(52,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)],[14]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( A @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( C @ ( B @ ( A @ union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom1) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( B @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( A @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ( C @ ( B @ ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
aIb @ ( b @ ( a @ intersection ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
thf(39,plain,
aIb @ ( b @ ( a @ intersection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
cDb @ ( b @ ( c @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_b) ).
thf(66,plain,
cDb @ ( b @ ( c @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,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(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,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(48,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)],[12]) ).
thf(8,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(40,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)],[8]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,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(42,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)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,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(29,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)],[2]) ).
thf(24,axiom,
cD_aIb @ ( aIb @ ( c @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_aIb) ).
thf(70,plain,
cD_aIb @ ( aIb @ ( c @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,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(33,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)],[4]) ).
thf(10,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(44,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)],[10]) ).
thf(1,negated_conjecture,
~ ( cD_aIb @ ( cDb @ ( cDa @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
thf(27,plain,
~ ( cD_aIb @ ( cDb @ ( cDa @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,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(54,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)],[15]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) ) )
| ~ ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) ) )
| ~ ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
cDa @ ( a @ ( c @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_a) ).
thf(67,plain,
cDa @ ( a @ ( c @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ~ ( A @ ( C @ ( B @ ( A @ g ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom2) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ~ ( A @ ( C @ ( B @ ( A @ g ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ g ) ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom3) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ g ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ g ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(372,plain,
$false,
inference(e,[status(thm)],[56,52,60,73,64,39,66,35,48,40,58,42,37,46,29,70,33,44,27,71,54,50,67,31,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 06:48:21 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.84/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.17 % [INFO] Parsing done (214ms).
% 1.23/1.19 % [INFO] Running in sequential loop mode.
% 1.98/1.57 % [INFO] eprover registered as external prover.
% 1.98/1.58 % [INFO] Scanning for conjecture ...
% 2.18/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.33/1.72 % [INFO] Axiom selection finished. Selected 25 axioms (removed 3 axioms).
% 2.33/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.33/1.77 % [INFO] Type checking passed.
% 2.33/1.77 % [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 ...
% 6.10/3.00 % External prover 'e' found a proof!
% 6.10/3.00 % [INFO] Killing All external provers ...
% 6.10/3.00 % Time passed: 2467ms (effective reasoning time: 1809ms)
% 6.10/3.00 % Axioms used in derivation (25): member_of_intersection_is_member_of_set2, member_of_difference_or_set2, subsets_axiom2, member_of_intersection_is_member_of_set1, union_axiom2, difference_axiom1, intersection_axiom1, not_member_of_difference, member_of_difference, member_of_union_is_member_of_one_set, union_axiom3, difference_axiom3, member_of_both_is_member_of_intersection, member_of_set2_is_member_of_union, c_minus_a, difference_axiom2, c_minus_aIb, intersection_axiom3, intersection_axiom2, union_axiom1, c_minus_b, a_intersection_b, member_of_set1_is_member_of_union, membership_in_subsets, subsets_axiom1
% 6.10/3.00 % No. of inferences in proof: 53
% 6.10/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2467 ms resp. 1809 ms w/o parsing
% 6.54/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------