%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP232^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n020.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 : Wed Sep 30 08:07:19 AM UTC 2026
% Result : Theorem 13.84s 4.64s
% Output : Refutation 14.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 315 ( 12 ~; 0 |; 0 &; 287 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 59 ( 6 ^; 46 !; 7 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(real_type,type,
real: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(size_decl,type,
size:
!>[TA: $tType] : $o ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(set2_decl,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(list_update_decl,type,
list_update:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA > ( list @ TA ) ) ).
thf(nth_decl,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(vEBT_VEBT_high_decl,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(vEBT_V5917875025757280293ildren_decl,type,
vEBT_V5917875025757280293ildren: nat > ( list @ vEBT_VEBT ) > nat > $o ).
thf(vEBT_VEBT_low_decl,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(vEBT_vebt_insert_decl,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(m_decl,type,
m: nat ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(na_decl,type,
na: nat ).
thf(summary_decl,type,
summary: vEBT_VEBT ).
thf(treeList_decl,type,
treeList: list @ vEBT_VEBT ).
thf(17,axiom,
size @ vEBT_VEBT,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_VEBT__Definitions_OVEBT___Nat_Osize_656) ).
thf(52,plain,
size @ vEBT_VEBT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nth__list__update__neq) ).
thf(20,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C0_C) ).
thf(45,plain,
! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA,E: TA] :
( ( A != B )
=> ( ( list_update @ TA @ ( list_update @ TA @ C @ A @ D ) @ B @ E )
= ( list_update @ TA @ ( list_update @ TA @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_list__update__swap) ).
thf(27,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA,E: TA] :
( ( A != B )
=> ( ( list_update @ TA @ ( list_update @ TA @ C @ A @ D ) @ B @ E )
= ( list_update @ TA @ ( list_update @ TA @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
( ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
=> ( ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) )
= summary ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062) ).
thf(35,plain,
( ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
=> ( ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) )
= summary ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__min__Null__member) ).
thf(50,plain,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ ( list_update @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C11_C) ).
thf(43,plain,
! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ ( list_update @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_list__update__overwrite) ).
thf(30,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ treeList ) )
=> ~ ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__C5_C) ).
thf(47,plain,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( member @ vEBT_VEBT @ A @ ( set2 @ vEBT_VEBT @ treeList ) )
=> ~ ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
vEBT_invar_vebt @ ( if @ vEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__C12_C) ).
thf(42,plain,
vEBT_invar_vebt @ ( if @ vEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_list__update__id) ).
thf(24,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
na = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C8_C) ).
thf(38,plain,
na = m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
( vEBT_V5917875025757280293ildren
= ( ^ [A: nat,B: list @ vEBT_VEBT,C: nat] : ( vEBT_V8194947554948674370ptions @ ( nth @ vEBT_VEBT @ B @ ( vEBT_VEBT_high @ C @ A ) ) @ ( vEBT_VEBT_low @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_in__children__def) ).
thf(33,plain,
( vEBT_V5917875025757280293ildren
= ( ^ [A: nat,B: list @ vEBT_VEBT,C: nat] : ( vEBT_V8194947554948674370ptions @ ( nth @ vEBT_VEBT @ B @ ( vEBT_VEBT_high @ C @ A ) ) @ ( vEBT_VEBT_low @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
~ ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
thf(40,plain,
~ ( vEBT_VEBT_minNull @ ( nth @ vEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
vEBT_invar_vebt @ summary @ m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__C1_C) ).
thf(23,plain,
vEBT_invar_vebt @ summary @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[52,20,45,27,35,18,50,43,30,47,42,24,38,33,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.09 % 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
% 0.07/0.22 % Computer : n020.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Sep 29 20:26:04 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 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
% 0.96/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 6.65/2.46 % [INFO] Parsing done (1651ms).
% 6.65/2.48 % [INFO] Running in sequential loop mode.
% 7.63/2.87 % [INFO] eprover registered as external prover.
% 7.63/2.88 % [INFO] Scanning for conjecture ...
% 9.69/3.46 % [INFO] Found a conjecture (or negated_conjecture) and 9015 axioms. Running axiom selection ...
% 10.76/3.76 % [INFO] Axiom selection finished. Selected 15 axioms (removed 9000 axioms).
% 10.76/3.79 % [INFO] Problem is higher-order (TPTP THF).
% 11.04/3.80 % [INFO] Type checking passed.
% 11.04/3.80 % [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 ...
% 13.84/4.64 % External prover 'e' found a proof!
% 13.84/4.64 % [INFO] Killing All external provers ...
% 13.84/4.64 % Time passed: 4275ms (effective reasoning time: 2155ms)
% 13.84/4.64 % 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)>
% 13.84/4.64 % Axioms used in derivation (15): fact_68_list__update__swap, fact_8__C0_C, fact_4__C12_C, fact_1_False, fact_17_list__update__id, fact_6_in__children__def, fact_3__C8_C, fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062, fact_10__C11_C, fact_15__C1_C, fact_5__C5_C, fact_0_not__min__Null__member, fact_16_nth__list__update__neq, tcon_VEBT__Definitions_OVEBT___Nat_Osize_656, fact_32_list__update__overwrite
% 13.84/4.64 % No. of inferences in proof: 34
% 13.84/4.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4275 ms resp. 2155 ms w/o parsing
% 14.28/4.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.28/4.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------