%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP232^1 : 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 : n011.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 22.78s 6.94s
% Output : Refutation 22.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 362 ( 12 ~; 0 |; 0 &; 312 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 79 ( 78 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 95 ( 14 ^; 74 !; 7 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc4471711990508489141at_nat_type,type,
produc4471711990508489141at_nat: $tType ).
thf(set_fi4554929511873752355omplex_type,type,
set_fi4554929511873752355omplex: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(list_P5578671422887162913nteger_type,type,
list_P5578671422887162913nteger: $tType ).
thf(set_Pr4811707699266497531nteger_type,type,
set_Pr4811707699266497531nteger: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(set_fi7789364187291644575l_real_type,type,
set_fi7789364187291644575l_real: $tType ).
thf(filter6041513312241820739omplex_type,type,
filter6041513312241820739omplex: $tType ).
thf(list_P7037539587688870467BT_nat_type,type,
list_P7037539587688870467BT_nat: $tType ).
thf(list_P4547456442757143711BT_int_type,type,
list_P4547456442757143711BT_int: $tType ).
thf(list_P5647936690300460905T_VEBT_type,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(produc8243902056947475879T_VEBT_type,type,
produc8243902056947475879T_VEBT: $tType ).
thf(set_Pr7556676689462069481BT_nat_type,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(set_Pr5085853215250843933omplex_type,type,
set_Pr5085853215250843933omplex: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(filter2146258269922977983l_real_type,type,
filter2146258269922977983l_real: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(set_Pr448751882837621926eger_o_type,type,
set_Pr448751882837621926eger_o: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(filter1242075044329608583at_nat_type,type,
filter1242075044329608583at_nat: $tType ).
thf(set_Pr6218003697084177305l_real_type,type,
set_Pr6218003697084177305l_real: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(produc4411394909380815293omplex_type,type,
produc4411394909380815293omplex: $tType ).
thf(list_P7333126701944960589_nat_o_type,type,
list_P7333126701944960589_nat_o: $tType ).
thf(list_P6285523579766656935_o_nat_type,type,
list_P6285523579766656935_o_nat: $tType ).
thf(list_P3795440434834930179_o_int_type,type,
list_P3795440434834930179_o_int: $tType ).
thf(set_list_VEBT_VEBT_type,type,
set_list_VEBT_VEBT: $tType ).
thf(produc334124729049499915VEBT_o_type,type,
produc334124729049499915VEBT_o: $tType ).
thf(produc2504756804600209347T_VEBT_type,type,
produc2504756804600209347T_VEBT: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(produc2422161461964618553l_real_type,type,
produc2422161461964618553l_real: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(list_P4002435161011370285od_o_o_type,type,
list_P4002435161011370285od_o_o: $tType ).
thf(set_list_complex_type,type,
set_list_complex: $tType ).
thf(set_set_complex_type,type,
set_set_complex: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(set_list_int_type,type,
set_list_int: $tType ).
thf(product_prod_o_nat_type,type,
product_prod_o_nat: $tType ).
thf(product_prod_o_int_type,type,
product_prod_o_int: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(list_Code_integer_type,type,
list_Code_integer: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(list_complex_type,type,
list_complex: $tType ).
thf(set_list_o_type,type,
set_list_o: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(set_complex_type,type,
set_complex: $tType ).
thf(filter_real_type,type,
filter_real: $tType ).
thf(option_num_type,type,
option_num: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(set_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(set_o_type,type,
set_o: $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(if_VEBT_VEBT_decl,type,
if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(set_VEBT_VEBT2_decl,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(list_u1324408373059187874T_VEBT_decl,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(nth_VEBT_VEBT_decl,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ord_le4337996190870823476T_VEBT_decl,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
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_VEBT_VEBT_decl,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $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(14,axiom,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C0_C) ).
thf(56,plain,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(24,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(13,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B @ E )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__update__swap) ).
thf(52,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B @ E )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
thf(78,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
( ord_le4337996190870823476T_VEBT
= ( ^ [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1262_subset__iff) ).
thf(38,plain,
( ord_le4337996190870823476T_VEBT
= ( ^ [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: list_VEBT_VEBT,B: nat] :
( ( list_u1324408373059187874T_VEBT @ A @ B @ ( nth_VEBT_VEBT @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list__update__id) ).
thf(73,plain,
! [A: list_VEBT_VEBT,B: nat] :
( ( list_u1324408373059187874T_VEBT @ A @ B @ ( nth_VEBT_VEBT @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,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(59,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)],[16]) ).
thf(22,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(76,plain,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ A @ B )
=> ( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1277_subsetD) ).
thf(35,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ A @ B )
=> ( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
vEBT_invar_vebt @ summary @ m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__C1_C) ).
thf(48,plain,
vEBT_invar_vebt @ summary @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_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 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_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)],[9]) ).
thf(15,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(58,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)],[15]) ).
thf(4,axiom,
( ord_le4337996190870823476T_VEBT
= ( ^ [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1270_subset__eq) ).
thf(30,plain,
( ord_le4337996190870823476T_VEBT
= ( ^ [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
= ( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ ( set_VEBT_VEBT2 @ A ) )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_subset__code_I1_J) ).
thf(32,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
= ( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ ( set_VEBT_VEBT2 @ A ) )
=> ( member_VEBT_VEBT @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ B @ D )
= ( list_u1324408373059187874T_VEBT @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list__update__overwrite) ).
thf(45,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ B @ D )
= ( list_u1324408373059187874T_VEBT @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B )
= ( nth_VEBT_VEBT @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_nth__list__update__neq) ).
thf(64,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B )
= ( nth_VEBT_VEBT @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
na = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C8_C) ).
thf(71,plain,
na = m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
=> ( ( member_VEBT_VEBT @ C @ B )
=> ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ A @ D @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_set__update__subsetI) ).
thf(49,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
=> ( ( member_VEBT_VEBT @ C @ B )
=> ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ A @ D @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ A @ B )
=> ( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1282_in__mono) ).
thf(40,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ A @ B )
=> ( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) )
=> ( ord_le4337996190870823476T_VEBT @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_subsetI) ).
thf(26,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT @ C @ A )
=> ( member_VEBT_VEBT @ C @ B ) )
=> ( ord_le4337996190870823476T_VEBT @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ~ ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__C5_C) ).
thf(68,plain,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ~ ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,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(62,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)],[17]) ).
thf(82,plain,
$false,
inference(e,[status(thm)],[56,24,52,78,38,73,59,76,35,48,43,58,30,32,45,64,71,49,40,26,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232^1 : 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
% 0.21/0.31 % Computer : n011.cluster.edu
% 0.21/0.31 % Model : x86_64 x86_64
% 0.21/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.31 % Memory : 8046.5625MB
% 0.21/0.31 % OS : Linux 6.8.0-71-generic
% 0.21/0.31 % CPULimit : 300
% 0.21/0.31 % WCLimit : 300
% 0.21/0.31 % DateTime : Tue Sep 29 20:24:31 UTC 2026
% 0.21/0.31 % CPUTime :
% 0.21/0.31 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
% 1.45/1.14 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 10.72/3.51 % [INFO] Parsing done (2366ms).
% 10.72/3.54 % [INFO] Running in sequential loop mode.
% 11.51/3.97 % [INFO] eprover registered as external prover.
% 11.51/3.98 % [INFO] Scanning for conjecture ...
% 14.39/4.78 % [INFO] Found a conjecture (or negated_conjecture) and 9602 axioms. Running axiom selection ...
% 15.54/5.12 % [INFO] Axiom selection finished. Selected 21 axioms (removed 9581 axioms).
% 15.98/5.18 % [INFO] Problem is higher-order (TPTP THF).
% 15.98/5.19 % [INFO] Type checking passed.
% 15.98/5.20 % [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 ...
% 22.78/6.93 % External prover 'e' found a proof!
% 22.78/6.93 % [INFO] Killing All external provers ...
% 22.78/6.93 % Time passed: 6415ms (effective reasoning time: 3382ms)
% 22.78/6.93 % 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)>
% 22.78/6.94 % Axioms used in derivation (21): fact_8__C0_C, fact_1_False, fact_6_in__children__def, fact_3__C8_C, fact_1270_subset__eq, fact_58_subset__code_I1_J, 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_139_list__update__swap, fact_0_not__min__Null__member, fact_1282_in__mono, fact_10__C11_C, fact_1277_subsetD, fact_64_set__update__subsetI, fact_54_list__update__overwrite, fact_18_nth__list__update__neq, fact_4__C12_C, fact_15__C1_C, fact_5__C5_C, fact_21_list__update__id, fact_1262_subset__iff, fact_1100_subsetI
% 22.78/6.94 % No. of inferences in proof: 46
% 22.78/6.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6415 ms resp. 3382 ms w/o parsing
% 22.78/7.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.78/7.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------