%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV403+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 : n005.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 08:59:17 AM UTC 2026
% Result : Theorem 6.84s 3.62s
% Output : Refutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 410 ( 15 ~; 8 |; 21 &; 338 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 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 : 121 ( 0 ^; 121 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(pair_in_list_decl,type,
pair_in_list: $i > $i > $i > $o ).
thf(strictly_less_than_decl,type,
strictly_less_than: $i > $i > $o ).
thf(update_slb_decl,type,
update_slb: $i > $i > $i ).
thf(insert_slb_decl,type,
insert_slb: $i > $i > $i ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(contains_slb_decl,type,
contains_slb: $i > $i > $o ).
thf(create_slb_decl,type,
create_slb: $i ).
thf(less_than_decl,type,
less_than: $i > $i > $o ).
thf(bottom_decl,type,
bottom: $i ).
thf(isnonempty_slb_decl,type,
isnonempty_slb: $i > $o ).
thf(remove_slb_decl,type,
remove_slb: $i > $i > $i ).
thf(lookup_slb_decl,type,
lookup_slb: $i > $i > $i ).
thf(15,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(69,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)],[15]) ).
thf(10,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(42,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)],[10]) ).
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(52,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(20,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(93,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)],[20]) ).
thf(14,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(66,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)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( create_slb @ pair_in_list ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,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(87,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)],[18]) ).
thf(17,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(75,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)],[17]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( create_slb @ update_slb ) )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,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)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ update_slb ) @ pair_in_list ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_co) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( A @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( A @ update_slb ) @ pair_in_list ) ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ strictly_less_than ) )
& ( C @ ( B @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ pair_in_list ) ) ) )
=> ( D @ ( B @ ( D @ ( F @ ( E @ pair ) @ ( A @ insert_slb ) @ update_slb ) @ pair_in_list ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(34,plain,
! [A: $i] : ( A @ ( bottom @ less_than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,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(59,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)],[13]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(27,plain,
! [A: $i] :
~ ( A @ ( create_slb @ contains_slb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ pair ) @ ( A @ insert_slb ) @ isnonempty_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(55,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(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ less_than ) )
| ( B @ ( A @ less_than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,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(30,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)],[4]) ).
thf(97,plain,
$false,
inference(e,[status(thm)],[69,42,52,93,66,72,87,75,90,38,21,32,34,59,27,40,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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 : n005.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
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 13:41:02 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.27/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.49 % [INFO] Parsing done (294ms).
% 1.92/1.51 % [INFO] Running in sequential loop mode.
% 2.94/2.10 % [INFO] eprover registered as external prover.
% 2.94/2.11 % [INFO] Scanning for conjecture ...
% 3.27/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.44/2.35 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.67/2.40 % [INFO] Problem is first-order (TPTP FOF).
% 3.67/2.42 % [INFO] Type checking passed.
% 3.67/2.42 % [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 ...
% 6.84/3.61 % External prover 'e' found a proof!
% 6.84/3.61 % [INFO] Killing All external provers ...
% 6.84/3.61 % Time passed: 3044ms (effective reasoning time: 2091ms)
% 6.84/3.61 % 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)>
% 6.84/3.62 % Axioms used in derivation (18): ax20, ax24, stricly_smaller_definition, ax28, ax27, ax21, reflexivity, ax22, ax19, totality, ax23, ax25, ax26, bottom_smallest, transitivity, ax30, ax18, ax29
% 6.84/3.62 % No. of inferences in proof: 40
% 6.84/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3044 ms resp. 2091 ms w/o parsing
% 7.05/3.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.05/3.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------