%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:30:54 AM UTC 2026
% Result : Theorem 2.76s 1.68s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 9 equ; 0 cnn)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 588 ( 2 ~; 3 |; 76 &; 432 @)
% ( 10 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-4 aty)
% Number of variables : 117 ( 0 ^; 117 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(order_decl,type,
order: $i > $i > $o ).
thf(least_decl,type,
least: $i > $i > $i > $o ).
thf(min_decl,type,
min: $i > $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(total_order_decl,type,
total_order: $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(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i > $i > $o ).
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i > $i > $o ).
thf(11,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/sandbox/benchmark/theBenchmark.p',least_upper_bound) ).
thf(170,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)],[11]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',total_order) ).
thf(97,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)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ least ) ) )
& ( B @ ( A @ order ) ) )
=> ( B @ ( A @ ( C @ min ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV4) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ least ) ) )
& ( B @ ( A @ order ) ) )
=> ( B @ ( A @ ( C @ min ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ least ) ) )
& ( B @ ( A @ order ) ) )
=> ( B @ ( A @ ( C @ min ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ lower_bound ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( D @ ( C @ ( A @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
thf(118,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)],[6]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',max) ).
thf(144,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)],[9]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',least) ).
thf(135,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)],[8]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',order) ).
thf(18,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)],[3]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',greatest_lower_bound) ).
thf(182,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)],[12]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',greatest) ).
thf(126,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)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ upper_bound ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( C @ ( D @ ( A @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).
thf(110,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)],[5]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',min) ).
thf(157,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)],[10]) ).
thf(194,plain,
$false,
inference(e,[status(thm)],[170,97,13,118,144,135,18,182,126,110,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Sat Sep 26 08:16:04 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.51/0.63 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.73 % [INFO] Parsing done (106ms).
% 0.65/0.74 % [INFO] Running in sequential loop mode.
% 1.04/0.95 % [INFO] eprover registered as external prover.
% 1.04/0.95 % [INFO] Scanning for conjecture ...
% 1.04/1.00 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.26/1.02 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.26/1.05 % [INFO] Problem is first-order (TPTP FOF).
% 1.26/1.05 % [INFO] Type checking passed.
% 1.26/1.06 % [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 ...
% 2.76/1.67 % External prover 'e' found a proof!
% 2.76/1.67 % [INFO] Killing All external provers ...
% 2.76/1.67 % Time passed: 1271ms (effective reasoning time: 928ms)
% 2.76/1.67 % 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)>
% 2.76/1.67 % Axioms used in derivation (10): upper_bound, min, least, max, greatest, order, total_order, lower_bound, least_upper_bound, greatest_lower_bound
% 2.76/1.67 % No. of inferences in proof: 24
% 2.76/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1271 ms resp. 928 ms w/o parsing
% 3.09/1.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.09/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------