%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET002-1 : 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 : n015.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 08:28:45 AM UTC 2026
% Result : Unsatisfiable 3.48s 7.32s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 288 ( 36 ~; 44 |; 0 &; 208 @)
% ( 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 : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(aUa_decl,type,
aUa: $i ).
thf(a_decl,type,
a: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(member_of_1_not_of_2_decl,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(union_decl,type,
union: $i > $i > $i > $o ).
thf(g_decl,type,
g: $i > $i > $i > $i ).
thf(8,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(29,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)],[8]) ).
thf(14,axiom,
aUa @ ( a @ ( a @ union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).
thf(41,plain,
aUa @ ( a @ ( a @ union ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,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(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,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(27,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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(39,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)],[13]) ).
thf(11,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(35,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)],[11]) ).
thf(9,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(31,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)],[9]) ).
thf(5,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(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,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(19,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)],[3]) ).
thf(1,negated_conjecture,
~ ( a @ ( aUa @ equal_sets ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_aUa) ).
thf(15,plain,
~ ( a @ ( aUa @ equal_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,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(37,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)],[12]) ).
thf(6,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(25,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(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)],[4]) ).
thf(10,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(33,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)],[10]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[29,41,17,27,39,35,31,23,19,15,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002-1 : 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
% 0.15/5.43 % Computer : n015.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 06:50:34 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 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
% 0.19/6.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/6.22 % [INFO] Parsing done (193ms).
% 1.32/6.24 % [INFO] Running in sequential loop mode.
% 1.98/6.64 % [INFO] eprover registered as external prover.
% 1.98/6.64 % [INFO] Scanning for conjecture ...
% 2.16/6.73 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.16/6.76 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.16/6.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/6.79 % [INFO] Type checking passed.
% 2.16/6.79 % [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 ...
% 3.48/7.31 % External prover 'e' found a proof!
% 3.48/7.31 % [INFO] Killing All external provers ...
% 3.48/7.31 % Time passed: 1733ms (effective reasoning time: 1066ms)
% 3.48/7.32 % Axioms used in derivation (13): set_equal_sets_are_subsets2, union_axiom3, subsets_are_set_equal_sets, subsets_axiom2, member_of_set2_is_member_of_union, a_union_a_is_aUa, union_axiom1, member_of_set1_is_member_of_union, member_of_union_is_member_of_one_set, union_axiom2, set_equal_sets_are_subsets1, membership_in_subsets, subsets_axiom1
% 3.48/7.32 % No. of inferences in proof: 29
% 3.48/7.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1733 ms resp. 1066 ms w/o parsing
% 3.48/7.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.48/7.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------