TSTP Solution File: ITP242_1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : ITP242_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:20:17 EDT 2024
% Result : Theorem 128.14s 18.18s
% Output : CNFRefutation 128.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 64
% Syntax : Number of formulae : 94 ( 26 unt; 53 typ; 0 def)
% Number of atoms : 87 ( 19 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 77 ( 31 ~; 28 |; 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 : 27 ( 15 >; 12 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 22 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 31 :)
% 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_949,type,
one_one_nat: nat ).
tff(decl_956,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_969,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(decl_1101,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
tff(decl_1129,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(decl_1155,type,
suc: fun_nat_nat ).
tff(decl_1224,type,
bit0: fun_num_num ).
tff(decl_1226,type,
one: num ).
tff(decl_1234,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1270,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1292,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1329,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1401,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1548,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1550,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1557,type,
vEBT_invar_vebt: fun_VE3763956218935105199t_bool ).
tff(decl_1566,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
tff(decl_1567,type,
vEBT_vebt_member: fun_VE3763956218935105199t_bool ).
tff(decl_1584,type,
vEBT_is_succ_in_set: set_nat > fun_nat_fun_nat_bool ).
tff(decl_1668,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(decl_1670,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(decl_1695,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(decl_1697,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(decl_1725,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(decl_1726,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(decl_1800,type,
aa_set8260762808118238015T_bool: ( fun_se448528567104302406T_bool * set_VEBT_VEBT ) > bool ).
tff(decl_1816,type,
aa_VEB4832260192069861672t_bool: ( fun_VE3763956218935105199t_bool * vEBT_VEBT ) > fun_nat_bool ).
tff(decl_1820,type,
aa_VEB289770264548726718T_bool: ( fun_VE7346385682144900493T_bool * vEBT_VEBT ) > fun_se448528567104302406T_bool ).
tff(decl_2068,type,
member_VEBT_VEBT: fun_VE7346385682144900493T_bool ).
tff(decl_2069,type,
pp: bool > $o ).
tff(decl_2070,type,
deg: nat ).
tff(decl_2071,type,
m: nat ).
tff(decl_2075,type,
na: nat ).
tff(decl_2076,type,
succy: nat ).
tff(decl_2078,type,
treeList: list_VEBT_VEBT ).
tff(decl_2079,type,
xa: nat ).
tff(decl_2371,type,
esk285_3: ( vEBT_VEBT * nat * nat ) > nat ).
tff(conj_0,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_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,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))))))
& ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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/sandbox/benchmark/theBenchmark.p',fact_953_member__bound) ).
tff(fact_979__C01_C,axiom,
( 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))
& 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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979__C01_C) ).
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/sandbox/benchmark/theBenchmark.p',fact_1313_Suc__1) ).
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/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).
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/sandbox/benchmark/theBenchmark.p',fact_207__C04_C) ).
tff(fact_149_mult__2__right,axiom,
! [X220: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X220),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X220),X220) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_mult__2__right) ).
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))
<=> ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X867),X868))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X3),X868))
& ! [X869: nat] :
( ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X867),X869))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X3),X869)) )
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X868),X869)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_succ__member) ).
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/sandbox/benchmark/theBenchmark.p',fact_38__C4_Ohyps_C_I6_J) ).
tff(fact_29__C4_Ohyps_C_I5_J,axiom,
m = na,
file('/export/starexec/sandbox/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_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)))
& 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))) ),
file('/export/starexec/sandbox/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_11,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_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,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))))))
& ( 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 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_12,plain,
! [X19449: vEBT_VEBT,X19450: nat,X19451: nat] :
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X19449),X19450))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X19449),X19451))
| 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))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_953_member__bound])])]) ).
tcf(c_0_13,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_14,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]) ).
tcf(c_0_15,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_16,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_17,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_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,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))))))
| ( 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 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
tff(c_0_18,plain,
! [X18133: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X18133),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X18133),X18133) ),
inference(variable_rename,[status(thm)],[fact_149_mult__2__right]) ).
tcf(c_0_19,plain,
! [X1: nat,X162: vEBT_VEBT,X2: nat] :
( 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)))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X162),X1))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X162),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_20,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_nat_nat(suc,one_one_nat))))),na)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
tcf(c_0_21,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_15,c_0_14]) ).
tff(c_0_22,plain,
! [X22038: vEBT_VEBT,X22039: nat,X22040: nat,X22041: nat,X22042: vEBT_VEBT,X22043: nat,X22044: nat] :
( ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X22038),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_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),X22041))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X22039),X22041))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X22040),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_VEB4832260192069861672t_bool(vEBT_vebt_member,X22042),esk285_3(X22042,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),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),esk285_3(X22042,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),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_eq_nat,X22044),esk285_3(X22042,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),X22044))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X22042)),X22043),X22044)) ) ),
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_23,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_nat_nat(suc,one_one_nat)))))),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_nat_nat(suc,one_one_nat)))),succy)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_14]) ).
tcf(c_0_24,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_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,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))))))
| ( 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 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_25,plain,
! [X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X1),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_26,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_27,plain,
m = na,
inference(split_conjunct,[status(thm)],[fact_29__C4_Ohyps_C_I5_J]) ).
tcf(c_0_28,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_29,plain,
! [X162: vEBT_VEBT,X2: nat,X1: nat] :
( 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)))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_invar_vebt,X162),X2))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_vebt_member,X162),X1)) ),
inference(rw,[status(thm)],[c_0_19,c_0_14]) ).
tcf(c_0_30,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)],[c_0_20,c_0_21]) ).
tcf(c_0_31,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_nat_fun_nat_bool(vEBT_is_succ_in_set(vEBT_VEBT_set_vebt(X162)),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_32,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)],[c_0_23,c_0_21]),c_0_21]) ).
tcf(c_0_33,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_nat_nat(suc,one_one_nat))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat))) != 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_nat_nat(suc,one_one_nat)))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)))))
| ~ 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)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat))))) ),
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_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
tcf(c_0_34,plain,
! [X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X1),aa_nat_nat(suc,one_one_nat)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X1),X1),
inference(rw,[status(thm)],[c_0_25,c_0_14]) ).
tcf(c_0_35,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),na) = deg,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
tcf(c_0_36,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_28,c_0_14]) ).
tcf(c_0_37,plain,
! [X1: nat] :
( 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)))
| ~ 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)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
tcf(c_0_38,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_31,c_0_32]) ).
tcf(c_0_39,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)],[c_0_33,c_0_34]),c_0_21]),c_0_34]),c_0_35]),c_0_21]),c_0_21]),c_0_36]),c_0_21])]) ).
cnf(c_0_40,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_37,c_0_38,c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP242_1 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 16:21:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.20/0.48 Running first-order model finding
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 128.14/18.18 # Version: 3.1.0
% 128.14/18.18 # Preprocessing class: FMLLSMLLSSSNFFN.
% 128.14/18.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 128.14/18.18 # Starting new_bool_3 with 900s (3) cores
% 128.14/18.18 # Starting new_bool_1 with 900s (3) cores
% 128.14/18.18 # Starting sh5l with 300s (1) cores
% 128.14/18.18 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 128.14/18.18 # new_bool_3 with pid 6615 completed with status 0
% 128.14/18.18 # Result found by new_bool_3
% 128.14/18.18 # Preprocessing class: FMLLSMLLSSSNFFN.
% 128.14/18.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 128.14/18.18 # Starting new_bool_3 with 900s (3) cores
% 128.14/18.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 128.14/18.18 # Search class: FGHSM-SMLM32-DFFFFFNN
% 128.14/18.18 # Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 128.14/18.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 128.14/18.18 # Starting new_bool_3 with 90s (1) cores
% 128.14/18.18 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 128.14/18.18 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 6619 completed with status 0
% 128.14/18.18 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 128.14/18.18 # Preprocessing class: FMLLSMLLSSSNFFN.
% 128.14/18.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 128.14/18.18 # Starting new_bool_3 with 900s (3) cores
% 128.14/18.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 128.14/18.18 # Search class: FGHSM-SMLM32-DFFFFFNN
% 128.14/18.18 # Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 128.14/18.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 128.14/18.18 # Preprocessing time : 0.210 s
% 128.14/18.18 # Presaturation interreduction done
% 128.14/18.18 # SatCheck found unsatisfiable ground set
% 128.14/18.18
% 128.14/18.18 # Proof found!
% 128.14/18.18 # SZS status Theorem
% 128.14/18.18 # SZS output start CNFRefutation
% See solution above
% 128.14/18.18 # Parsed axioms : 13177
% 128.14/18.18 # Removed by relevancy pruning/SinE : 9436
% 128.14/18.18 # Initial clauses : 9932
% 128.14/18.18 # Removed in clause preprocessing : 1996
% 128.14/18.18 # Initial clauses in saturation : 7936
% 128.14/18.18 # Processed clauses : 12094
% 128.14/18.18 # ...of these trivial : 409
% 128.14/18.18 # ...subsumed : 1685
% 128.14/18.18 # ...remaining for further processing : 10000
% 128.14/18.18 # Other redundant clauses eliminated : 3122
% 128.14/18.18 # Clauses deleted for lack of memory : 0
% 128.14/18.18 # Backward-subsumed : 66
% 128.14/18.18 # Backward-rewritten : 114
% 128.14/18.18 # Generated clauses : 73066
% 128.14/18.18 # ...of the previous two non-redundant : 62081
% 128.14/18.18 # ...aggressively subsumed : 0
% 128.14/18.18 # Contextual simplify-reflections : 93
% 128.14/18.18 # Paramodulations : 70529
% 128.14/18.18 # Factorizations : 16
% 128.14/18.18 # NegExts : 0
% 128.14/18.18 # Equation resolutions : 3205
% 128.14/18.18 # Disequality decompositions : 0
% 128.14/18.18 # Total rewrite steps : 36607
% 128.14/18.18 # ...of those cached : 31095
% 128.14/18.18 # Propositional unsat checks : 3
% 128.14/18.18 # Propositional check models : 2
% 128.14/18.18 # Propositional check unsatisfiable : 1
% 128.14/18.18 # Propositional clauses : 66092
% 128.14/18.18 # Propositional clauses after purity: 26547
% 128.14/18.18 # Propositional unsat core size : 3
% 128.14/18.18 # Propositional preprocessing time : 0.000
% 128.14/18.18 # Propositional encoding time : 0.251
% 128.14/18.18 # Propositional solver time : 0.025
% 128.14/18.18 # Success case prop preproc time : 0.000
% 128.14/18.18 # Success case prop encoding time : 0.167
% 128.14/18.18 # Success case prop solver time : 0.015
% 128.14/18.18 # Current number of processed clauses : 2809
% 128.14/18.18 # Positive orientable unit clauses : 590
% 128.14/18.18 # Positive unorientable unit clauses: 35
% 128.14/18.18 # Negative unit clauses : 176
% 128.14/18.18 # Non-unit-clauses : 2008
% 128.14/18.18 # Current number of unprocessed clauses: 63283
% 128.14/18.18 # ...number of literals in the above : 182942
% 128.14/18.18 # Current number of archived formulas : 0
% 128.14/18.18 # Current number of archived clauses : 5540
% 128.14/18.18 # Clause-clause subsumption calls (NU) : 26488716
% 128.14/18.18 # Rec. Clause-clause subsumption calls : 1851644
% 128.14/18.18 # Non-unit clause-clause subsumptions : 1602
% 128.14/18.18 # Unit Clause-clause subsumption calls : 102824
% 128.14/18.18 # Rewrite failures with RHS unbound : 0
% 128.14/18.18 # BW rewrite match attempts : 13305
% 128.14/18.18 # BW rewrite match successes : 647
% 128.14/18.18 # Condensation attempts : 0
% 128.14/18.18 # Condensation successes : 0
% 128.14/18.18 # Termbank termtop insertions : 4150602
% 128.14/18.18 # Search garbage collected termcells : 192356
% 128.14/18.18
% 128.14/18.18 # -------------------------------------------------
% 128.14/18.18 # User time : 16.331 s
% 128.14/18.18 # System time : 0.186 s
% 128.14/18.18 # Total time : 16.517 s
% 128.14/18.18 # Maximum resident set size: 52020 pages
% 128.14/18.18
% 128.14/18.18 # -------------------------------------------------
% 128.14/18.18 # User time : 47.472 s
% 128.14/18.18 # System time : 0.479 s
% 128.14/18.18 # Total time : 47.951 s
% 128.14/18.18 # Maximum resident set size: 28376 pages
% 128.14/18.18 % E---3.1 exiting
%------------------------------------------------------------------------------