%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n019.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 08:59:18 AM UTC 2026
% Result : Theorem 6.94s 8.80s
% Output : Refutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 449 ( 15 ~; 11 |; 31 &; 364 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 130 ( 0 ^; 123 !; 7 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(contains_slb_decl,type,
contains_slb: $i > $i > $o ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(pair_in_list_decl,type,
pair_in_list: $i > $i > $i > $o ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(isnonempty_slb_decl,type,
isnonempty_slb: $i > $o ).
thf(insert_slb_decl,type,
insert_slb: $i > $i > $i ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(create_slb_decl,type,
create_slb: $i ).
thf(bottom_decl,type,
bottom: $i ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ strictly_less_than ) )
& ( B @ ( A @ contains_slb ) ) )
=> ( ? [D: $i] :
( ( D @ ( C @ less_than ) )
& ( D @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) )
| ( C @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ strictly_less_than ) )
& ( B @ ( A @ contains_slb ) ) )
=> ( ? [D: $i] :
( ( D @ ( C @ less_than ) )
& ( D @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) )
| ( C @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ strictly_less_than ) )
& ( B @ ( A @ contains_slb ) ) )
=> ( ? [D: $i] :
( ( D @ ( C @ less_than ) )
& ( D @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) )
| ( C @ ( B @ ( C @ ( A @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(52,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ strictly_less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( C @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(57,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ strictly_less_than ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ update_slb ) )
= ( C @ ( B @ pair ) @ ( C @ ( A @ update_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(84,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) )
<=> ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(89,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) )
=> ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
& ( ( E @ ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) )
=> ( ( ( D = E )
& ( B = C ) )
| ( E @ ( C @ ( A @ pair_in_list ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ remove_slb ) @ insert_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= ( D @ ( B @ pair ) @ ( C @ ( A @ remove_slb ) @ insert_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ strictly_less_than ) )
<=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( B @ ( A @ strictly_less_than ) ) )
& ( ( B @ ( A @ strictly_less_than ) )
=> ( ~ ( A @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(50,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(82,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ contains_slb ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ pair_in_list ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ contains_slb ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ pair_in_list ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
~ ( create_slb @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(38,plain,
~ ( create_slb @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(70,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ less_than ) )
& ( D @ ( B @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ? [E: $i] :
( ( E @ ( D @ less_than ) )
& ( E @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).
thf(64,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ less_than ) )
& ( D @ ( B @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ? [E: $i] :
( ( E @ ( D @ less_than ) )
& ( E @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( D @ ( B @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).
thf(80,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( D @ ( B @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ remove_slb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= ( C @ ( A @ lookup_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ contains_slb ) )
& ( B != C ) )
=> ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ lookup_slb ) )
= ( C @ ( A @ lookup_slb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
<=> ( ( B = C )
| ( C @ ( A @ contains_slb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(40,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = C )
| ( C @ ( A @ contains_slb ) ) )
=> ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) ) )
& ( ( C @ ( D @ ( B @ pair ) @ ( A @ insert_slb ) @ contains_slb ) )
=> ( ( B = C )
| ( C @ ( A @ contains_slb ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ less_than ) )
& ( B @ ( A @ less_than ) ) )
=> ( C @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(108,plain,
$false,
inference(e,[status(thm)],[101,24,52,57,84,89,60,73,50,82,30,68,38,70,32,64,80,35,87,104,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.11/5.50 % Computer : n019.cluster.edu
% 0.11/5.50 % Model : x86_64 x86_64
% 0.11/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.50 % Memory : 8046.5625MB
% 0.11/5.50 % OS : Linux 6.8.0-71-generic
% 0.11/5.50 % CPULimit : 300
% 0.11/5.50 % WCLimit : 300
% 0.11/5.50 % DateTime : Sat Sep 26 13:41:54 UTC 2026
% 0.11/5.50 % CPUTime :
% 0.11/5.50 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
% 1.43/6.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.01/6.63 % [INFO] Parsing done (302ms).
% 2.01/6.65 % [INFO] Running in sequential loop mode.
% 3.22/7.23 % [INFO] eprover registered as external prover.
% 3.22/7.24 % [INFO] Scanning for conjecture ...
% 3.42/7.40 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 3.60/7.50 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.81/7.57 % [INFO] Problem is first-order (TPTP FOF).
% 3.81/7.58 % [INFO] Type checking passed.
% 3.81/7.59 % [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 ...
% 6.94/8.79 % External prover 'e' found a proof!
% 6.94/8.79 % [INFO] Killing All external provers ...
% 6.94/8.79 % Time passed: 3083ms (effective reasoning time: 2129ms)
% 6.94/8.79 % 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)>
% 6.94/8.79 % Axioms used in derivation (21): ax20, ax24, stricly_smaller_definition, ax28, ax27, ax21, l45_l49, l45_li4647, ax22, ax19, totality, ax23, ax25, reflexivity, l45_l48, ax26, bottom_smallest, transitivity, ax30, ax18, ax29
% 6.94/8.79 % No. of inferences in proof: 46
% 6.94/8.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3083 ms resp. 2129 ms w/o parsing
% 7.24/8.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.24/8.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------