%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET804+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 : n014.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 08:30:56 AM UTC 2026
% Result : Theorem 6.74s 8.94s
% Output : Refutation 6.74s
% 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 : 184 ( 12 equ; 0 cnn)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 609 ( 8 ~; 3 |; 79 &; 441 @)
% ( 10 <=>; 68 =>; 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 : 123 ( 0 ^; 120 !; 3 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(order_decl,type,
order: $i > $i > $o ).
thf(min_decl,type,
min: $i > $i > $i > $o ).
thf(least_decl,type,
least: $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(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(101,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(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(174,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(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( C != D )
& ( B @ ( A @ ( D @ min ) ) )
& ( B @ ( A @ ( C @ min ) ) ) )
=> ~ ? [E: $i] : ( B @ ( A @ ( E @ least ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( C != D )
& ( B @ ( A @ ( D @ min ) ) )
& ( B @ ( A @ ( C @ min ) ) ) )
=> ~ ? [E: $i] : ( B @ ( A @ ( E @ least ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ order ) )
=> ! [C: $i,D: $i] :
( ( ( C != D )
& ( B @ ( A @ ( D @ min ) ) )
& ( B @ ( A @ ( C @ min ) ) ) )
=> ~ ? [E: $i] : ( B @ ( A @ ( E @ least ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(22,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(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(130,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(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(122,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(148,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(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(161,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(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(186,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(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(114,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(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(139,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(198,plain,
$false,
inference(e,[status(thm)],[101,174,13,22,130,122,148,161,186,114,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.14/6.02 % Computer : n014.cluster.edu
% 0.14/6.02 % Model : x86_64 x86_64
% 0.14/6.02 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/6.02 % Memory : 8046.5625MB
% 0.14/6.02 % OS : Linux 6.8.0-71-generic
% 0.14/6.02 % CPULimit : 300
% 0.14/6.02 % WCLimit : 300
% 0.14/6.02 % DateTime : Sat Sep 26 08:17:09 UTC 2026
% 0.14/6.02 % CPUTime :
% 0.14/6.02 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
% 0.92/6.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/6.79 % [INFO] Parsing done (291ms).
% 1.65/6.81 % [INFO] Running in sequential loop mode.
% 2.47/7.32 % [INFO] eprover registered as external prover.
% 2.47/7.32 % [INFO] Scanning for conjecture ...
% 2.63/7.43 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.63/7.46 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.92/7.50 % [INFO] Problem is first-order (TPTP FOF).
% 2.92/7.51 % [INFO] Type checking passed.
% 2.92/7.51 % [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 ...
% 6.74/8.94 % External prover 'e' found a proof!
% 6.74/8.94 % [INFO] Killing All external provers ...
% 6.74/8.94 % Time passed: 2793ms (effective reasoning time: 2116ms)
% 6.74/8.94 % 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)>
% 6.74/8.94 % Axioms used in derivation (10): upper_bound, min, least, max, greatest, order, total_order, lower_bound, least_upper_bound, greatest_lower_bound
% 6.74/8.94 % No. of inferences in proof: 24
% 6.74/8.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2793 ms resp. 2116 ms w/o parsing
% 6.74/9.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.74/9.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------