%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% 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 : n008.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 08:30:55 AM UTC 2026
% Result : Theorem 5.81s 2.68s
% Output : Refutation 6.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 18 equ; 0 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 892 ( 7 ~; 9 |; 104 &; 655 @)
% ( 20 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 2 con; 0-4 aty)
% Number of variables : 185 ( 0 ^; 182 !; 3 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
thf(order_decl,type,
order: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(member_decl,type,
member: $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(union_decl,type,
union: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(total_order_decl,type,
total_order: $i > $i > $o ).
thf(least_decl,type,
least: $i > $i > $i > $o ).
thf(min_decl,type,
min: $i > $i > $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i > $i > $o ).
thf(upper_bound_decl,type,
upper_bound: $i > $i > $i > $o ).
thf(lower_bound_decl,type,
lower_bound: $i > $i > $i > $o ).
thf(greatest_decl,type,
greatest: $i > $i > $i > $o ).
thf(max_decl,type,
max: $i > $i > $i > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ max ) ) )
<=> ( ! [D: $i] :
( ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) )
=> ( B @ ( A @ ( C @ max ) ) ) )
& ( ( B @ ( A @ ( C @ max ) ) )
=> ( ! [D: $i] :
( ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ subset ) )
& ( B @ ( C @ subset ) ) )
=> ! [E: $i,F: $i] :
( ( ( B @ ( A @ ( D @ ( F @ greatest_lower_bound ) ) ) )
& ( B @ ( A @ ( C @ ( E @ greatest_lower_bound ) ) ) ) )
=> ( E @ ( F @ ( A @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ subset ) )
& ( B @ ( C @ subset ) ) )
=> ! [E: $i,F: $i] :
( ( ( B @ ( A @ ( D @ ( F @ greatest_lower_bound ) ) ) )
& ( B @ ( A @ ( C @ ( E @ greatest_lower_bound ) ) ) ) )
=> ( E @ ( F @ ( A @ apply ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ subset ) )
& ( B @ ( C @ subset ) ) )
=> ! [E: $i,F: $i] :
( ( ( B @ ( A @ ( D @ ( F @ greatest_lower_bound ) ) ) )
& ( B @ ( A @ ( C @ ( E @ greatest_lower_bound ) ) ) ) )
=> ( E @ ( F @ ( A @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ least ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) )
=> ( B @ ( A @ ( C @ least ) ) ) )
& ( ( B @ ( A @ ( C @ least ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,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(261,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)],[21]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(84,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)],[10]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(206,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)],[15]) ).
thf(3,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(33,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)],[3]) ).
thf(4,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(41,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ lower_bound ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).
thf(244,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) )
=> ( B @ ( A @ ( C @ lower_bound ) ) ) )
& ( ( B @ ( A @ ( C @ lower_bound ) ) )
=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,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(44,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)],[5]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ upper_bound ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_bound) ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) )
=> ( B @ ( A @ ( C @ upper_bound ) ) ) )
& ( ( B @ ( A @ ( C @ upper_bound ) ) )
=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,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(66,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)],[8]) ).
thf(23,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(282,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)],[23]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ total_order ) )
<=> ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( C @ ( D @ ( A @ apply ) ) )
| ( D @ ( C @ ( A @ apply ) ) ) ) )
& ( B @ ( A @ order ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_order) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( C @ ( D @ ( A @ apply ) ) )
| ( D @ ( C @ ( A @ apply ) ) ) ) )
& ( B @ ( A @ order ) ) )
=> ( B @ ( A @ total_order ) ) )
& ( ( B @ ( A @ total_order ) )
=> ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( C @ ( D @ ( A @ apply ) ) )
| ( D @ ( C @ ( A @ apply ) ) ) ) )
& ( B @ ( A @ order ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,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(58,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)],[7]) ).
thf(6,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(51,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)],[6]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ 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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(92,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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) )
=> ( B @ ( A @ order ) ) )
& ( ( B @ ( A @ 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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ greatest ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest) ).
thf(252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) )
=> ( B @ ( A @ ( C @ greatest ) ) ) )
& ( ( B @ ( A @ ( C @ greatest ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ greatest_lower_bound ) ) ) )
<=> ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ lower_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( A @ ( E @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ lower_bound ) ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest_lower_bound) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ lower_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( A @ ( E @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ lower_bound ) ) )
& ( B @ ( A @ member ) ) )
=> ( D @ ( C @ ( B @ ( A @ greatest_lower_bound ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ greatest_lower_bound ) ) ) )
=> ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ lower_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( A @ ( E @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ lower_bound ) ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,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(77,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)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ min ) ) )
<=> ( ! [D: $i] :
( ( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',min) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) )
=> ( B @ ( A @ ( C @ min ) ) ) )
& ( ( B @ ( A @ ( C @ min ) ) )
=> ( ! [D: $i] :
( ( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( C = D ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ least_upper_bound ) ) ) )
<=> ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ upper_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( E @ ( A @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ upper_bound ) ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least_upper_bound) ).
thf(212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ upper_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( E @ ( A @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ upper_bound ) ) )
& ( B @ ( A @ member ) ) )
=> ( D @ ( C @ ( B @ ( A @ least_upper_bound ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ least_upper_bound ) ) ) )
=> ( ! [E: $i] :
( ( ( B @ ( C @ ( E @ upper_bound ) ) )
& ( D @ ( E @ member ) ) )
=> ( E @ ( A @ ( C @ apply ) ) ) )
& ( B @ ( C @ ( A @ upper_bound ) ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(289,plain,
$false,
inference(e,[status(thm)],[269,24,184,261,84,206,33,41,244,44,236,66,282,171,58,51,92,252,224,77,193,212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.14/0.40 % Computer : n008.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 08:17:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.18 % [INFO] Parsing done (207ms).
% 1.31/1.19 % [INFO] Running in sequential loop mode.
% 2.30/1.60 % [INFO] eprover registered as external prover.
% 2.30/1.60 % [INFO] Scanning for conjecture ...
% 2.30/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.55/1.72 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 2.55/1.76 % [INFO] Problem is first-order (TPTP FOF).
% 2.55/1.77 % [INFO] Type checking passed.
% 2.55/1.77 % [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 ...
% 5.81/2.67 % External prover 'e' found a proof!
% 5.81/2.67 % [INFO] Killing All external provers ...
% 5.81/2.67 % Time passed: 2130ms (effective reasoning time: 1471ms)
% 5.81/2.67 % 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)>
% 5.81/2.67 % Axioms used in derivation (21): power_set, unordered_pair, union, intersection, empty_set, upper_bound, min, least, max, total_order, singleton, difference, product, least_upper_bound, greatest_lower_bound, greatest, subset, order, equal_set, lower_bound, sum
% 5.81/2.67 % No. of inferences in proof: 46
% 5.81/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2130 ms resp. 1471 ms w/o parsing
% 6.58/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.58/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------