%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 08:30:52 AM UTC 2026
% Result : Theorem 9.09s 4.47s
% Output : Refutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 12 equ; 0 cnn)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 665 ( 10 ~; 6 |; 78 &; 481 @)
% ( 15 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 2 con; 0-3 aty)
% Number of variables : 143 ( 0 ^; 131 !; 12 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(equivalence_decl,type,
equivalence: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(equivalence_class_decl,type,
equivalence_class: $i > $i > $i > $i ).
thf(pre_order_decl,type,
pre_order: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(product_decl,type,
product: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(partition_decl,type,
partition: $i > $i > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pre_order ) )
<=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pre_order) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) )
=> ( B @ ( A @ pre_order ) ) )
& ( ( B @ ( A @ pre_order ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ partition ) )
<=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) )
=> ( B @ ( A @ partition ) ) )
& ( ( B @ ( A @ partition ) )
=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(95,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( C @ ( B @ intersection ) @ ( A @ member ) ) )
& ( ( C @ ( B @ intersection ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ sum @ ( A @ member ) )
<=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) )
=> ( B @ sum @ ( A @ member ) ) )
& ( ( B @ sum @ ( A @ member ) )
=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
<=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ power_set @ ( A @ member ) ) )
& ( ( B @ power_set @ ( A @ member ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(85,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
<=> ( ( A = C )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) )
=> ( C @ ( B @ union ) @ ( A @ member ) ) )
& ( ( C @ ( B @ union ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ equivalence ) )
<=> ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) )
=> ( A @ ( B @ equivalence ) ) )
& ( ( A @ ( B @ equivalence ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) )
<=> ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
thf(219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) ) )
& ( ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) )
=> ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ equivalence ) )
=> ( A @ ( B @ ( A @ ( C @ equivalence_class ) ) @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ equivalence ) )
=> ( A @ ( B @ ( A @ ( C @ equivalence_class ) ) @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ equivalence ) )
=> ( A @ ( B @ ( A @ ( C @ equivalence_class ) ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(243,plain,
$false,
inference(e,[status(thm)],[24,121,77,226,95,62,69,88,233,85,102,54,159,113,219,151,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.23/0.48 % Computer : n018.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 08:16:06 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.42/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.68 % [INFO] Parsing done (319ms).
% 2.26/1.70 % [INFO] Running in sequential loop mode.
% 3.28/2.30 % [INFO] eprover registered as external prover.
% 3.28/2.31 % [INFO] Scanning for conjecture ...
% 3.48/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 3.66/2.56 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 3.88/2.65 % [INFO] Problem is first-order (TPTP FOF).
% 3.88/2.67 % [INFO] Type checking passed.
% 3.88/2.67 % [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 ...
% 9.09/4.46 % External prover 'e' found a proof!
% 9.09/4.46 % [INFO] Killing All external provers ...
% 9.09/4.46 % Time passed: 3763ms (effective reasoning time: 2751ms)
% 9.09/4.46 % Solved by 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)>
% 9.09/4.46 % Axioms used in derivation (16): power_set, unordered_pair, pre_order, intersection, empty_set, subset, equal_set, singleton, disjoint, difference, sum, product, equivalence, union, partition, equivalence_class
% 9.09/4.46 % No. of inferences in proof: 36
% 9.09/4.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3763 ms resp. 2751 ms w/o parsing
% 9.42/4.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.42/4.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------