%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP242_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Thu Sep 24 12:54:53 PM UTC 2026
% Result : Theorem 236.65s 38.01s
% Output : CNFRefutation 236.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 14 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 72 ( 28 ~; 26 |; 14 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 21 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
set_VEBT_VEBT: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_sort3,type,
set_nat: $tType ).
tff(decl_sort4,type,
fun_nat_bool: $tType ).
tff(decl_sort5,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort6,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort7,type,
fun_nat_nat: $tType ).
tff(decl_sort8,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort9,type,
num: $tType ).
tff(decl_sort10,type,
vEBT_VEBT: $tType ).
tff(decl_sort11,type,
fun_VE3763956218935105199t_bool: $tType ).
tff(decl_sort12,type,
fun_VE7346385682144900493T_bool: $tType ).
tff(decl_sort13,type,
bool: $tType ).
tff(decl_sort14,type,
fun_num_nat: $tType ).
tff(decl_sort15,type,
fun_num_num: $tType ).
tff(decl_sort16,type,
fun_se448528567104302406T_bool: $tType ).
tff(decl_950,type,
one_one_nat: nat ).
tff(decl_957,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_1102,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
tff(decl_1130,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1156,type,
suc: fun_nat_nat ).
tff(decl_1225,type,
bit0: fun_num_num ).
tff(decl_1227,type,
one: num ).
tff(decl_1235,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1271,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1293,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1330,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1402,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1549,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1551,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1558,type,
vEBT_invar_vebt: fun_VE3763956218935105199t_bool ).
tff(decl_1567,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
tff(decl_1568,type,
vEBT_vebt_member: fun_VE3763956218935105199t_bool ).
tff(decl_1585,type,
vEBT_is_succ_in_set: set_nat > fun_nat_fun_nat_bool ).
tff(decl_1669,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1671,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1696,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_1698,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1726,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1727,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_1801,type,
aa_set8260762808118238015T_bool: ( set_VEBT_VEBT * fun_se448528567104302406T_bool ) > bool ).
tff(decl_1817,type,
aa_VEB4832260192069861672t_bool: ( vEBT_VEBT * fun_VE3763956218935105199t_bool ) > fun_nat_bool ).
tff(decl_1821,type,
aa_VEB289770264548726718T_bool: ( vEBT_VEBT * fun_VE7346385682144900493T_bool ) > fun_se448528567104302406T_bool ).
tff(decl_2069,type,
member_VEBT_VEBT: fun_VE7346385682144900493T_bool ).
tff(decl_2070,type,
pp: bool > $o ).
tff(decl_2071,type,
deg: nat ).
tff(decl_2072,type,
m: nat ).
tff(decl_2076,type,
na: nat ).
tff(decl_2077,type,
succy: nat ).
tff(decl_2079,type,
treeList: list_VEBT_VEBT ).
tff(decl_2080,type,
xa: nat ).
tff(decl_2372,type,
esk285_3: ( nat * ( nat * vEBT_VEBT ) ) > nat ).
tff(fact_953_member__bound,axiom,
! [X1841: vEBT_VEBT,X3: nat,X4: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X1841),X3))
=> ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X1841),X4))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X3),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_member__bound) ).
tff(fact_14__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).
tff(fact_1313_Suc__1,axiom,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1313_Suc__1) ).
tff(conj_0,conjecture,
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = deg )
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,succy),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_979__C01_C,axiom,
( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),set_VEBT_VEBT2(treeList)))
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979__C01_C) ).
tff(fact_480_succ__member,axiom,
! [X867: vEBT_VEBT,X3: nat,X868: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X867)),X3),X868))
<=> ( ! [X869: nat] :
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X3),X869))
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X867),X869)) )
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X868),X869)) )
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X3),X868))
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X867),X868)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_succ__member) ).
tff(fact_207__C04_C,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),succy)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207__C04_C) ).
tff(fact_38__C4_Ohyps_C_I6_J,axiom,
deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38__C4_Ohyps_C_I6_J) ).
tff(fact_29__C4_Ohyps_C_I5_J,axiom,
m = na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29__C4_Ohyps_C_I5_J) ).
tff(fact_209__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na)))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062) ).
tff(c_0_10,plain,
! [X19449: vEBT_VEBT,X19450: nat,X19451: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19450),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X19451)))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X19449),X19451))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X19449),X19450)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_953_member__bound])])]) ).
tcf(c_0_11,plain,
aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = na,
inference(split_conjunct,[status(thm)],[fact_14__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062]) ).
tcf(c_0_12,plain,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
inference(split_conjunct,[status(thm)],[fact_1313_Suc__1]) ).
tff(c_0_13,negated_conjecture,
~ ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = deg )
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,succy),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tcf(c_0_14,plain,
! [X1: nat,X162: vEBT_VEBT,X2: nat] :
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X162),X2))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X162),X1))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)),
inference(split_conjunct,[status(thm)],[fact_979__C01_C]) ).
tcf(c_0_16,plain,
aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)) = na,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
tff(c_0_17,plain,
! [X22038: vEBT_VEBT,X22039: nat,X22040: nat,X22041: nat,X22042: vEBT_VEBT,X22043: nat,X22044: nat] :
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22042)),X22043),X22044))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22043),X22044))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22042),X22044))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X22044),esk285_3(X22042,X22043,X22044))) )
& ( pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22042)),X22043),X22044))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22043),X22044))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22042),X22044))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22043),esk285_3(X22042,X22043,X22044))) )
& ( pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22042)),X22043),X22044))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22043),X22044))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22042),X22044))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22042),esk285_3(X22042,X22043,X22044))) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22038)),X22039),X22040))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X22040),X22041))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22039),X22041))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22038),X22041)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22038)),X22039),X22040))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22039),X22040)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22038)),X22039),X22040))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22038),X22040)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_succ__member])])])])])])]) ).
tcf(c_0_18,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),succy)),
inference(split_conjunct,[status(thm)],[fact_207__C04_C]) ).
tff(c_0_19,negated_conjecture,
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) != deg )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,succy),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
tcf(c_0_20,plain,
deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),
inference(split_conjunct,[status(thm)],[fact_38__C4_Ohyps_C_I6_J]) ).
tcf(c_0_21,plain,
m = na,
inference(split_conjunct,[status(thm)],[fact_29__C4_Ohyps_C_I5_J]) ).
tcf(c_0_22,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),
inference(split_conjunct,[status(thm)],[fact_209__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062]) ).
tcf(c_0_23,plain,
! [X162: vEBT_VEBT,X2: nat,X1: nat] :
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X162),X1))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X162),X2))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),X2))) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
tcf(c_0_24,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12]),c_0_16]) ).
tcf(c_0_25,plain,
! [X162: vEBT_VEBT,X2: nat,X1: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X162)),X2),X1))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X162),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_26,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)),succy)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_12]),c_0_16]),c_0_12]),c_0_16]) ).
tcf(c_0_27,negated_conjecture,
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) != deg )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,succy),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_28,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),na) = deg,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
tcf(c_0_29,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))),
inference(rw,[status(thm)],[c_0_22,c_0_12]) ).
tcf(c_0_30,plain,
! [X1: nat] :
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),X1))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
tcf(c_0_31,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),succy)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
tcf(c_0_32,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,succy),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_28]),c_0_12]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_12]),c_0_16]),c_0_29])]) ).
cnf(c_0_33,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_30,c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP242_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n018.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 22:18:13 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.54 Running first-order theorem proving
% 0.22/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 236.65/38.01 % Version: 3.5.1
% 236.65/38.01 % Preprocessing class: FMLLSMLLSSSNFFN.
% 236.65/38.01 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 236.65/38.01 % Starting new_bool_3 with 894s (3) cores
% 236.65/38.01 % Starting new_bool_1 with 894s (3) cores
% 236.65/38.01 % Starting sh5l with 298s (1) cores
% 236.65/38.01 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 298s (1) cores
% 236.65/38.01 % new_bool_1 with pid 308839 completed with status 0
% 236.65/38.01 % Result found by new_bool_1
% 236.65/38.01 % Preprocessing class: FMLLSMLLSSSNFFN.
% 236.65/38.01 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 236.65/38.01 % Starting new_bool_3 with 894s (3) cores
% 236.65/38.01 % Starting new_bool_1 with 894s (3) cores
% 236.65/38.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 236.65/38.01 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 236.65/38.01 % Search class: FGHSM-SMLM32-DFFFFFNN
% 236.65/38.01 % Scheduled 13 strats onto 3 cores with 892 seconds (892 total)
% 236.65/38.01 % Starting SubtermCWHack with 81s (1) cores
% 236.65/38.01 % Starting new_bool_1 with 90s (1) cores
% 236.65/38.01 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 67s (1) cores
% 236.65/38.01 % new_bool_1 with pid 308843 completed with status 0
% 236.65/38.01 % Result found by new_bool_1
% 236.65/38.01 % Preprocessing class: FMLLSMLLSSSNFFN.
% 236.65/38.01 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 236.65/38.01 % Starting new_bool_3 with 894s (3) cores
% 236.65/38.01 % Starting new_bool_1 with 894s (3) cores
% 236.65/38.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 236.65/38.01 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 236.65/38.01 % Search class: FGHSM-SMLM32-DFFFFFNN
% 236.65/38.01 % Scheduled 13 strats onto 3 cores with 892 seconds (892 total)
% 236.65/38.01 % Starting SubtermCWHack with 81s (1) cores
% 236.65/38.01 % Starting new_bool_1 with 90s (1) cores
% 236.65/38.01 % Preprocessing time : 0.390 s
% 236.65/38.01 % Presaturation interreduction done
% 236.65/38.01 % SatCheck found unsatisfiable ground set
% 236.65/38.01
% 236.65/38.01 % Proof found!
% 236.65/38.01 % SZS status Theorem
% 236.65/38.01 % SZS output start CNFRefutation
% See solution above
% 236.65/38.01 % Parsed axioms : 13177
% 236.65/38.01 % Removed by relevancy pruning/SinE : 9436
% 236.65/38.01 % Initial clauses : 9932
% 236.65/38.01 % Removed in clause preprocessing : 1996
% 236.65/38.01 % Initial clauses in saturation : 7936
% 236.65/38.01 % Processed clauses : 34289
% 236.65/38.01 % ...of these trivial : 821
% 236.65/38.01 % ...subsumed : 18468
% 236.65/38.01 % ...remaining for further processing : 15000
% 236.65/38.01 % Other redundant clauses eliminated : 3114
% 236.65/38.01 % Clauses deleted for lack of memory : 0
% 236.65/38.01 % Backward-subsumed : 164
% 236.65/38.01 % Backward-rewritten : 1085
% 236.65/38.01 % Generated clauses : 129409
% 236.65/38.01 % ...of the previous two non-redundant : 115237
% 236.65/38.01 % ...aggressively subsumed : 0
% 236.65/38.01 % Contextual simplify-reflections : 95
% 236.65/38.01 % Paramodulations : 126826
% 236.65/38.01 % Factorizations : 18
% 236.65/38.01 % NegExts : 0
% 236.65/38.01 % Equation resolutions : 3222
% 236.65/38.01 % Disequality decompositions : 0
% 236.65/38.01 % Total rewrite steps : 60619
% 236.65/38.01 % ...of those cached : 50415
% 236.65/38.01 % Propositional unsat checks : 4
% 236.65/38.01 % Propositional check models : 2
% 236.65/38.01 % Propositional check unsatisfiable : 1
% 236.65/38.01 % Propositional clauses : 96541
% 236.65/38.01 % Propositional clauses after purity: 12137
% 236.65/38.01 % Propositional unsat core size : 3
% 236.65/38.01 % Propositional preprocessing time : 0.000
% 236.65/38.01 % Propositional encoding time : 0.567
% 236.65/38.01 % Propositional solver time : 0.091
% 236.65/38.01 % Success case prop preproc time : 0.000
% 236.65/38.01 % Success case prop encoding time : 0.340
% 236.65/38.01 % Success case prop solver time : 0.024
% 236.65/38.01 % Current number of processed clauses : 6732
% 236.65/38.01 % Positive orientable unit clauses : 1188
% 236.65/38.01 % Positive unorientable unit clauses: 50
% 236.65/38.01 % Negative unit clauses : 2071
% 236.65/38.01 % Non-unit-clauses : 3423
% 236.65/38.01 % Current number of unprocessed clauses: 89809
% 236.65/38.01 % ...number of literals in the above : 201078
% 236.65/38.01 % Current number of archived formulas : 0
% 236.65/38.01 % Current number of archived clauses : 6619
% 236.65/38.01 % Clause-clause subsumption calls (NU) : 29672025
% 236.65/38.01 % Rec. Clause-clause subsumption calls : 3645633
% 236.65/38.01 % Non-unit clause-clause subsumptions : 8073
% 236.65/38.01 % Unit Clause-clause subsumption calls : 1181465
% 236.65/38.01 % Rewrite failures with RHS unbound : 0
% 236.65/38.01 % BW rewrite match attempts : 39220
% 236.65/38.01 % BW rewrite match successes : 1203
% 236.65/38.01 % Condensation attempts : 0
% 236.65/38.01 % Condensation successes : 0
% 236.65/38.01 % Termbank termtop insertions : 5274126
% 236.65/38.01 % Search garbage collected termcells : 192356
% 236.65/38.01
% 236.65/38.01 % -------------------------------------------------
% 236.65/38.01 % User time : 34.429 s
% 236.65/38.01 % System time : 0.395 s
% 236.65/38.01 % Total time : 34.824 s
% 236.65/38.01 % Maximum resident set size: 53940 pages
% 236.65/38.01
% 236.65/38.01 % -------------------------------------------------
% 236.65/38.01 % User time : 99.920 s
% 236.65/38.01 % System time : 1.433 s
% 236.65/38.01 % Total time : 101.353 s
% 236.65/38.01 % Maximum resident set size: 31232 pages
% 236.65/38.01 % E exiting
%------------------------------------------------------------------------------