%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP269_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 : n014.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 12:55:08 PM UTC 2026
% Result : Theorem 134.67s 22.33s
% Output : CNFRefutation 134.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 22 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_sort3,type,
num: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort5,type,
fun_nat_nat: $tType ).
tff(decl_sort6,type,
fun_nat_bool: $tType ).
tff(decl_sort7,type,
vEBT_VEBT: $tType ).
tff(decl_sort8,type,
bool: $tType ).
tff(decl_sort9,type,
option_nat: $tType ).
tff(decl_sort10,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort11,type,
fun_num_nat: $tType ).
tff(decl_sort12,type,
fun_num_num: $tType ).
tff(decl_767,type,
bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).
tff(decl_914,type,
one_one_nat: nat ).
tff(decl_920,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_930,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(decl_1009,type,
if_nat: bool > fun_nat_fun_nat_nat ).
tff(decl_1069,type,
list_u1324408373059187874T_VEBT: ( vEBT_VEBT * ( nat * list_VEBT_VEBT ) ) > list_VEBT_VEBT ).
tff(decl_1088,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1116,type,
suc: fun_nat_nat ).
tff(decl_1184,type,
bit0: fun_num_num ).
tff(decl_1186,type,
one: num ).
tff(decl_1194,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1213,type,
the_nat: option_nat > nat ).
tff(decl_1233,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1249,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1296,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1378,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1388,type,
modulo_modulo_nat: fun_nat_fun_nat_nat ).
tff(decl_1534,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1536,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1547,type,
vEBT_vebt_delete: ( nat * vEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1568,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
tff(decl_1665,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1667,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1695,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_1697,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1720,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1721,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_1934,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(decl_1953,type,
pp: bool > $o ).
tff(decl_1954,type,
deg: nat ).
tff(decl_1955,type,
lx: nat ).
tff(decl_1957,type,
ma: nat ).
tff(decl_1959,type,
na: nat ).
tff(decl_1961,type,
summin: nat ).
tff(decl_1962,type,
treeList: list_VEBT_VEBT ).
tff(fact_3387_low__def,axiom,
! [X1: nat,X5: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X5) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3387_low__def) ).
tff(conj_0,conjecture,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_5266_take__bit__eq__mod,axiom,
! [X5: nat,X3: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X5),X3) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X3),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5266_take__bit__eq__mod) ).
tff(fact_561_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_561_Suc__1) ).
tff(fact_1125_add_Ocommute,axiom,
! [X3: nat,X4: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X3),X4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_add_Ocommute) ).
tff(fact_6__C9_C,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_6__C9_C) ).
tff(fact_1101_mult_Ocommute,axiom,
! [X3: nat,X4: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X3),X4) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_mult_Ocommute) ).
tff(fact_16_hprolist,axiom,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_hprolist) ).
tff(fact_21__C114_C,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__C114_C) ).
tff(c_0_9,plain,
! [X20261: nat,X20262: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X20261),X20262) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X20261),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X20262)) ),
inference(variable_rename,[status(thm)],[fact_3387_low__def]) ).
tff(c_0_10,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_11,plain,
! [X27585: nat,X27586: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X27585),X27586) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X27586),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X27585)) ),
inference(variable_rename,[status(thm)],[fact_5266_take__bit__eq__mod]) ).
tcf(c_0_12,plain,
! [X1: nat,X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_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_9]) ).
tcf(c_0_13,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_561_Suc__1]) ).
tff(c_0_14,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
tff(c_0_15,plain,
! [X19958: nat,X19959: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X19958),X19959) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X19959),X19958) ),
inference(variable_rename,[status(thm)],[fact_1125_add_Ocommute]) ).
tcf(c_0_16,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_17,plain,
! [X1: nat,X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),X2)) = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
tff(c_0_18,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
tcf(c_0_19,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_6__C9_C]) ).
tff(c_0_20,plain,
! [X19604: nat,X19605: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X19604),X19605) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X19605),X19604) ),
inference(variable_rename,[status(thm)],[fact_1101_mult_Ocommute]) ).
tcf(c_0_21,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),
inference(split_conjunct,[status(thm)],[fact_16_hprolist]) ).
tcf(c_0_22,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_23,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
tcf(c_0_24,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_25,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_19,c_0_13]) ).
tcf(c_0_26,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_27,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[fact_21__C114_C]) ).
tcf(c_0_28,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))))),
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_21,c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_23]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_23]) ).
tcf(c_0_29,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_13]),c_0_25]),c_0_26]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_23]),c_0_13]),c_0_22]),c_0_13]) ).
tcf(c_0_30,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))))))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
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)],[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_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_13]),c_0_25]),c_0_26]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_13]),c_0_22]),c_0_23]),c_0_13]),c_0_22]),c_0_28]),c_0_13]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP269_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:24:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 134.67/22.33 % Version: 3.5.1
% 134.67/22.33 % Preprocessing class: FMLLSMLLSSSNFFN.
% 134.67/22.33 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 134.67/22.33 % Starting new_bool_3 with 897s (3) cores
% 134.67/22.33 % Starting new_bool_1 with 897s (3) cores
% 134.67/22.33 % Starting sh5l with 299s (1) cores
% 134.67/22.33 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 134.67/22.33 % new_bool_3 with pid 2487814 completed with status 0
% 134.67/22.33 % Result found by new_bool_3
% 134.67/22.33 % Preprocessing class: FMLLSMLLSSSNFFN.
% 134.67/22.33 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 134.67/22.33 % Starting new_bool_3 with 897s (3) cores
% 134.67/22.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 134.67/22.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 134.67/22.33 % Search class: FGHSM-SMLM32-DFFFFFNN
% 134.67/22.33 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 134.67/22.33 % Starting SubtermCWHack with 81s (1) cores
% 134.67/22.33 % Starting new_bool_3 with 90s (1) cores
% 134.67/22.33 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 134.67/22.33 % new_bool_3 with pid 2487819 completed with status 0
% 134.67/22.33 % Result found by new_bool_3
% 134.67/22.33 % Preprocessing class: FMLLSMLLSSSNFFN.
% 134.67/22.33 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 134.67/22.33 % Starting new_bool_3 with 897s (3) cores
% 134.67/22.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 134.67/22.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 134.67/22.33 % Search class: FGHSM-SMLM32-DFFFFFNN
% 134.67/22.33 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 134.67/22.33 % Starting SubtermCWHack with 81s (1) cores
% 134.67/22.33 % Starting new_bool_3 with 90s (1) cores
% 134.67/22.33 % Preprocessing time : 0.269 s
% 134.67/22.33 % Presaturation interreduction done
% 134.67/22.33
% 134.67/22.33 % Proof found!
% 134.67/22.33 % SZS status Theorem
% 134.67/22.33 % SZS output start CNFRefutation
% See solution above
% 134.67/22.33 % Parsed axioms : 13357
% 134.67/22.33 % Removed by relevancy pruning/SinE : 9203
% 134.67/22.33 % Initial clauses : 10232
% 134.67/22.33 % Removed in clause preprocessing : 1965
% 134.67/22.33 % Initial clauses in saturation : 8267
% 134.67/22.33 % Processed clauses : 18486
% 134.67/22.33 % ...of these trivial : 513
% 134.67/22.33 % ...subsumed : 8210
% 134.67/22.33 % ...remaining for further processing : 9762
% 134.67/22.33 % Other redundant clauses eliminated : 2205
% 134.67/22.33 % Clauses deleted for lack of memory : 0
% 134.67/22.33 % Backward-subsumed : 58
% 134.67/22.33 % Backward-rewritten : 464
% 134.67/22.33 % Generated clauses : 44911
% 134.67/22.33 % ...of the previous two non-redundant : 36953
% 134.67/22.33 % ...aggressively subsumed : 0
% 134.67/22.33 % Contextual simplify-reflections : 89
% 134.67/22.33 % Paramodulations : 43344
% 134.67/22.33 % Factorizations : 42
% 134.67/22.33 % NegExts : 0
% 134.67/22.33 % Equation resolutions : 2230
% 134.67/22.33 % Disequality decompositions : 0
% 134.67/22.33 % Total rewrite steps : 36189
% 134.67/22.33 % ...of those cached : 29141
% 134.67/22.33 % Propositional unsat checks : 2
% 134.67/22.33 % Propositional check models : 2
% 134.67/22.33 % Propositional check unsatisfiable : 0
% 134.67/22.33 % Propositional clauses : 0
% 134.67/22.33 % Propositional clauses after purity: 0
% 134.67/22.33 % Propositional unsat core size : 0
% 134.67/22.33 % Propositional preprocessing time : 0.000
% 134.67/22.33 % Propositional encoding time : 0.088
% 134.67/22.33 % Propositional solver time : 0.019
% 134.67/22.33 % Success case prop preproc time : 0.000
% 134.67/22.33 % Success case prop encoding time : 0.000
% 134.67/22.33 % Success case prop solver time : 0.000
% 134.67/22.33 % Current number of processed clauses : 2270
% 134.67/22.33 % Positive orientable unit clauses : 1154
% 134.67/22.33 % Positive unorientable unit clauses: 59
% 134.67/22.33 % Negative unit clauses : 658
% 134.67/22.33 % Non-unit-clauses : 399
% 134.67/22.33 % Current number of unprocessed clauses: 31677
% 134.67/22.33 % ...number of literals in the above : 67452
% 134.67/22.33 % Current number of archived formulas : 0
% 134.67/22.33 % Current number of archived clauses : 6072
% 134.67/22.33 % Clause-clause subsumption calls (NU) : 23485529
% 134.67/22.33 % Rec. Clause-clause subsumption calls : 1091293
% 134.67/22.33 % Non-unit clause-clause subsumptions : 3169
% 134.67/22.33 % Unit Clause-clause subsumption calls : 106802
% 134.67/22.33 % Rewrite failures with RHS unbound : 0
% 134.67/22.33 % BW rewrite match attempts : 18304
% 134.67/22.33 % BW rewrite match successes : 1924
% 134.67/22.33 % Condensation attempts : 0
% 134.67/22.33 % Condensation successes : 0
% 134.67/22.33 % Termbank termtop insertions : 2397238
% 134.67/22.33 % Search garbage collected termcells : 203006
% 134.67/22.33
% 134.67/22.33 % -------------------------------------------------
% 134.67/22.33 % User time : 19.584 s
% 134.67/22.33 % System time : 0.181 s
% 134.67/22.33 % Total time : 19.765 s
% 134.67/22.33 % Maximum resident set size: 56564 pages
% 134.67/22.33
% 134.67/22.33 % -------------------------------------------------
% 134.67/22.33 % User time : 58.099 s
% 134.67/22.33 % System time : 0.987 s
% 134.67/22.33 % Total time : 59.086 s
% 134.67/22.33 % Maximum resident set size: 33280 pages
% 134.67/22.33 % E exiting
%------------------------------------------------------------------------------