%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET011-1 : 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 08:28:48 AM UTC 2026
% Result : Unsatisfiable 5.76s 3.43s
% Output : Refutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 434 ( 48 ~; 64 |; 0 &; 322 @)
% ( 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 : 12 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_decl,type,
intersection: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(aD_aDb_decl,type,
aD_aDb: $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(difference_decl,type,
difference: $i > $i > $i > $o ).
thf(k_decl,type,
k: $i > $i > $i > $i ).
thf(aDb_decl,type,
aDb: $i ).
thf(h_decl,type,
h: $i > $i > $i > $i ).
thf(6,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(29,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)],[6]) ).
thf(13,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(41,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)],[13]) ).
thf(15,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(45,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)],[15]) ).
thf(5,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(27,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)],[5]) ).
thf(17,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(49,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)],[17]) ).
thf(11,axiom,
aD_aDb @ ( aDb @ ( a @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_minus_aDb) ).
thf(39,plain,
aD_aDb @ ( aDb @ ( a @ difference ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,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(35,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)],[9]) ).
thf(7,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(31,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)],[7]) ).
thf(14,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(43,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)],[14]) ).
thf(16,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(47,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)],[16]) ).
thf(10,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(37,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)],[10]) ).
thf(4,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(25,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)],[4]) ).
thf(2,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(21,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(8,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(33,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)],[8]) ).
thf(12,axiom,
aDb @ ( b @ ( a @ difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_minus_b) ).
thf(40,plain,
aDb @ ( b @ ( a @ difference ) ),
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/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(23,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(18,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(51,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)],[18]) ).
thf(1,negated_conjecture,
~ ( aD_aDb @ ( b @ ( a @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
thf(19,plain,
~ ( aD_aDb @ ( b @ ( a @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,31,43,47,37,25,21,33,40,23,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % 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
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 06:48:44 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 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
% 1.29/1.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.05/1.60 % [INFO] Parsing done (321ms).
% 2.05/1.63 % [INFO] Running in sequential loop mode.
% 3.01/2.24 % [INFO] eprover registered as external prover.
% 3.01/2.25 % [INFO] Scanning for conjecture ...
% 3.18/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.34/2.48 % [INFO] Axiom selection finished. Selected 17 axioms (removed 3 axioms).
% 3.53/2.54 % [INFO] Problem is propositional (TPTP CNF).
% 3.53/2.55 % [INFO] Type checking passed.
% 3.53/2.56 % [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 ...
% 5.76/3.43 % External prover 'e' found a proof!
% 5.76/3.43 % [INFO] Killing All external provers ...
% 5.76/3.43 % Time passed: 2818ms (effective reasoning time: 1791ms)
% 5.76/3.43 % Axioms used in derivation (17): member_of_intersection_is_member_of_set2, a_minus_aDb, member_of_difference_or_set2, difference_axiom3, subsets_axiom2, member_of_both_is_member_of_intersection, difference_axiom2, a_minus_b, member_of_intersection_is_member_of_set1, difference_axiom1, intersection_axiom1, not_member_of_difference, member_of_difference, intersection_axiom3, intersection_axiom2, membership_in_subsets, subsets_axiom1
% 5.76/3.43 % No. of inferences in proof: 37
% 5.76/3.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2818 ms resp. 1791 ms w/o parsing
% 6.00/3.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.00/3.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------