TSTP Solution File: ITP229_1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP229_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 22:17:11 EDT 2024
% Result : Theorem 80.27s 11.71s
% Output : CNFRefutation 80.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 82
% Syntax : Number of formulae : 168 ( 58 unt; 57 typ; 0 def)
% Number of atoms : 254 ( 147 equ)
% Maximal formula atoms : 43 ( 2 avg)
% Number of connectives : 252 ( 109 ~; 82 |; 29 &)
% ( 8 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 31 ( 19 >; 12 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 24 con; 0-4 aty)
% Number of variables : 131 ( 0 sgn 128 !; 3 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
nat: $tType ).
tff(decl_sort2,type,
fun_nat_bool: $tType ).
tff(decl_sort3,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort5,type,
fun_nat_nat: $tType ).
tff(decl_sort6,type,
num: $tType ).
tff(decl_sort7,type,
bool: $tType ).
tff(decl_sort8,type,
fun_na1476630412504255114at_nat: $tType ).
tff(decl_sort9,type,
product_prod_nat_nat: $tType ).
tff(decl_sort10,type,
fun_num_num: $tType ).
tff(decl_sort11,type,
vEBT_VEBT: $tType ).
tff(decl_sort12,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort13,type,
fun_num_nat: $tType ).
tff(decl_sort14,type,
option4927543243414619207at_nat: $tType ).
tff(decl_896,type,
one_one_nat: nat ).
tff(decl_902,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_913,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(decl_929,type,
zero_zero_nat: nat ).
tff(decl_1094,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(decl_1121,type,
suc: fun_nat_nat ).
tff(decl_1155,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
tff(decl_1173,type,
bit0: fun_num_num ).
tff(decl_1175,type,
one: num ).
tff(decl_1181,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1188,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
tff(decl_1225,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1247,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1273,type,
ord_max_nat: fun_nat_fun_nat_nat ).
tff(decl_1296,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1305,type,
product_Pair_nat_nat: nat > fun_na1476630412504255114at_nat ).
tff(decl_1369,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1502,type,
vEBT_Node: ( option4927543243414619207at_nat * nat * list_VEBT_VEBT * vEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1505,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1507,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1523,type,
vEBT_vebt_member: vEBT_VEBT > fun_nat_bool ).
tff(decl_1609,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(decl_1611,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(decl_1613,type,
aa_nat7603221163087113075at_nat: ( fun_na1476630412504255114at_nat * nat ) > product_prod_nat_nat ).
tff(decl_1639,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(decl_1641,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(decl_1670,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(decl_1671,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(decl_1984,type,
pp: bool > $o ).
tff(decl_1985,type,
deg: nat ).
tff(decl_1986,type,
m: nat ).
tff(decl_1987,type,
ma: nat ).
tff(decl_1988,type,
mi: nat ).
tff(decl_1989,type,
na: nat ).
tff(decl_1990,type,
summary: vEBT_VEBT ).
tff(decl_1991,type,
treeList: list_VEBT_VEBT ).
tff(decl_1992,type,
xa: nat ).
tff(decl_1993,type,
ya: nat ).
tff(decl_2217,type,
esk219_1: nat > nat ).
tff(decl_2218,type,
esk220_1: nat > nat ).
tff(decl_2219,type,
esk221_1: nat > nat ).
tff(decl_2226,type,
esk228_1: nat > nat ).
tff(decl_2227,type,
esk229_2: ( nat * nat ) > nat ).
tff(fact_1500_not0__implies__Suc,axiom,
! [X92: nat] :
( ( X92 != zero_zero_nat )
=> ? [X57: nat] : ( X92 = aa_nat_nat(suc,X57) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1500_not0__implies__Suc) ).
tff(fact_1489_nat_Odistinct_I1_J,axiom,
! [X3498: nat] : ( zero_zero_nat != aa_nat_nat(suc,X3498) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1489_nat_Odistinct_I1_J) ).
tff(fact_1852_numeral__2__eq__2,axiom,
aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) = aa_nat_nat(suc,aa_nat_nat(suc,zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1852_numeral__2__eq__2) ).
tff(fact_2436_One__nat__def,axiom,
one_one_nat = aa_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2436_One__nat__def) ).
tff(fact_1475_old_Onat_Oinject,axiom,
! [X3492: nat,X3493: nat] :
( ( aa_nat_nat(suc,X3492) = aa_nat_nat(suc,X3493) )
<=> ( X3492 = X3493 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1475_old_Onat_Oinject) ).
tff(fact_1521_Suc__le__D,axiom,
! [X92: nat,X3515: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X92)),X3515))
=> ? [X57: nat] : ( X3515 = aa_nat_nat(suc,X57) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1521_Suc__le__D) ).
tff(fact_1815__C00_C,axiom,
( ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) )
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,zero_zero_nat),na))
& ( na = m )
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))
& ( size_s6755466524823107622T_VEBT(treeList) = 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_1815__C00_C) ).
tff(fact_1493_old_Onat_Oexhaust,axiom,
! [X3500: nat] :
( ( X3500 != zero_zero_nat )
=> ~ ! [X3501: nat] : ( X3500 != aa_nat_nat(suc,X3501) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1493_old_Onat_Oexhaust) ).
tff(fact_364_order_Oasym,axiom,
! [X957: nat,X958: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X957),X958))
=> ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X958),X957)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_order_Oasym) ).
tff(fact_1557_Suc__le__eq,axiom,
! [X489: nat,X92: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X489)),X92))
<=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X489),X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1557_Suc__le__eq) ).
tff(fact_1488_list__decode_Ocases,axiom,
! [X2: nat] :
( ( X2 != zero_zero_nat )
=> ~ ! [X2414: nat] : ( X2 != aa_nat_nat(suc,X2414) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1488_list__decode_Ocases) ).
tff(fact_2364_zero__neq__one,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2364_zero__neq__one) ).
tff(fact_2519_Euclidean__Division_Odiv__eq__0__iff,axiom,
! [X489: nat,X92: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X489),X92) = zero_zero_nat )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X489),X92))
| ( X92 = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2519_Euclidean__Division_Odiv__eq__0__iff) ).
tff(fact_2227_div__by__1,axiom,
! [X4857: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X4857),one_one_nat) = X4857 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2227_div__by__1) ).
tff(fact_3225_mult__2__right,axiom,
! [X6659: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X6659),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X6659),X6659) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3225_mult__2__right) ).
tff(fact_1485_n__not__Suc__n,axiom,
! [X92: nat] : ( X92 != aa_nat_nat(suc,X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1485_n__not__Suc__n) ).
tff(fact_1487_vebt__buildup_Ocases,axiom,
! [X2: nat] :
( ( X2 != zero_zero_nat )
=> ( ( X2 != aa_nat_nat(suc,zero_zero_nat) )
=> ~ ! [X3497: nat] : ( X2 != aa_nat_nat(suc,aa_nat_nat(suc,X3497)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1487_vebt__buildup_Ocases) ).
tff(fact_2593_nat__1__eq__mult__iff,axiom,
! [X489: nat,X92: nat] :
( ( one_one_nat = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X489),X92) )
<=> ( ( X489 = one_one_nat )
& ( X92 = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2593_nat__1__eq__mult__iff) ).
tff(fact_0_False,axiom,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,mi),ma)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
tff(fact_544_nless__le,axiom,
! [X1496: nat,X1497: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1496),X1497))
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X1496),X1497))
| ( X1496 = X1497 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_nless__le) ).
tff(fact_3926_vebt__member_Osimps_I5_J,axiom,
! [X94: nat,X95: nat,X196: nat,X90: list_VEBT_VEBT,X91: vEBT_VEBT,X2: nat] :
( pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X94),X95)),aa_nat_nat(suc,aa_nat_nat(suc,X196)),X90,X91)),X2))
<=> ( ( X2 != X94 )
=> ( ( X2 != X95 )
=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X94))
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X94))
=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X95),X2))
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X95),X2))
=> ( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X90)))
=> pp(aa_nat_bool(vEBT_vebt_member(nth_VEBT_VEBT(X90,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),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,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X90))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3926_vebt__member_Osimps_I5_J) ).
tff(conj_0,conjecture,
( pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList,summary)),ya))
| ( xa = ya ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_73_max_Oabsorb2,axiom,
! [X179: nat,X180: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X179),X180))
=> ( aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,X179),X180) = X180 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_max_Oabsorb2) ).
tff(fact_2__C4_Ohyps_C_I7_J,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,mi),ma)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C4_Ohyps_C_I7_J) ).
tff(fact_5__092_060open_062y_A_061_Amax_Ami_Ama_092_060close_062,axiom,
ya = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,mi),ma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062y_A_061_Amax_Ami_Ama_092_060close_062) ).
tff(c_0_25,plain,
! [X92: nat] :
( ( X92 != zero_zero_nat )
=> ? [X57: nat] : ( X92 = aa_nat_nat(suc,X57) ) ),
inference(fof_simplification,[status(thm)],[fact_1500_not0__implies__Suc]) ).
tff(c_0_26,plain,
! [X3498: nat] : ( zero_zero_nat != aa_nat_nat(suc,X3498) ),
inference(fof_simplification,[status(thm)],[fact_1489_nat_Odistinct_I1_J]) ).
tcf(c_0_27,plain,
aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) = aa_nat_nat(suc,aa_nat_nat(suc,zero_zero_nat)),
inference(split_conjunct,[status(thm)],[fact_1852_numeral__2__eq__2]) ).
tcf(c_0_28,plain,
one_one_nat = aa_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_2436_One__nat__def]) ).
tff(c_0_29,plain,
! [X20527: nat,X20528: nat] :
( ( ( aa_nat_nat(suc,X20527) != aa_nat_nat(suc,X20528) )
| ( X20527 = X20528 ) )
& ( ( X20527 != X20528 )
| ( aa_nat_nat(suc,X20527) = aa_nat_nat(suc,X20528) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1475_old_Onat_Oinject])])]) ).
tff(c_0_30,plain,
! [X20565: nat] :
( ( X20565 = zero_zero_nat )
| ( X20565 = aa_nat_nat(suc,esk228_1(X20565)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
tff(c_0_31,plain,
! [X20542: nat] : ( zero_zero_nat != aa_nat_nat(suc,X20542) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
tff(c_0_32,plain,
! [X20573: nat,X20574: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X20573)),X20574))
| ( X20574 = aa_nat_nat(suc,esk229_2(X20573,X20574)) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1521_Suc__le__D])])])]) ).
tcf(c_0_33,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)),
inference(split_conjunct,[status(thm)],[fact_1815__C00_C]) ).
tcf(c_0_34,plain,
aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) = aa_nat_nat(suc,one_one_nat),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
tff(c_0_35,plain,
! [X3500: nat] :
( ( X3500 != zero_zero_nat )
=> ~ ! [X3501: nat] : ( X3500 != aa_nat_nat(suc,X3501) ) ),
inference(fof_simplification,[status(thm)],[fact_1493_old_Onat_Oexhaust]) ).
tcf(c_0_36,plain,
! [X2: nat,X4: nat] :
( ( X2 = X4 )
| ( aa_nat_nat(suc,X2) != aa_nat_nat(suc,X4) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_37,plain,
! [X2: nat] :
( ( X2 = zero_zero_nat )
| ( X2 = aa_nat_nat(suc,esk228_1(X2)) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
tcf(c_0_38,plain,
! [X2: nat] : zero_zero_nat != aa_nat_nat(suc,X2),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
tcf(c_0_39,plain,
! [X2: nat,X4: nat] :
( ( X4 = aa_nat_nat(suc,esk229_2(X2,X4)) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X2)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tcf(c_0_40,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,one_one_nat)),deg)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
tff(c_0_41,plain,
! [X957: nat,X958: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X957),X958))
=> ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X958),X957)) ),
inference(fof_simplification,[status(thm)],[fact_364_order_Oasym]) ).
tff(c_0_42,plain,
! [X20131: nat,X20132: nat] :
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X20131)),X20132))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20131),X20132)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20131),X20132))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X20131)),X20132)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1557_Suc__le__eq])])]) ).
tff(c_0_43,plain,
! [X2: nat] :
( ( X2 != zero_zero_nat )
=> ~ ! [X2414: nat] : ( X2 != aa_nat_nat(suc,X2414) ) ),
inference(fof_simplification,[status(thm)],[fact_1488_list__decode_Ocases]) ).
tff(c_0_44,plain,
! [X20547: nat] :
( ( X20547 = zero_zero_nat )
| ( X20547 = aa_nat_nat(suc,esk221_1(X20547)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
tcf(c_0_45,plain,
! [X2: nat] : esk228_1(aa_nat_nat(suc,X2)) = X2,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37])]),c_0_38]) ).
tcf(c_0_46,plain,
aa_nat_nat(suc,esk229_2(one_one_nat,deg)) = deg,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
tff(c_0_47,plain,
! [X19806: nat,X19807: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19806),X19807))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19807),X19806)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
tcf(c_0_48,plain,
! [X2: nat,X4: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X4))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X2)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
tff(c_0_49,plain,
zero_zero_nat != one_one_nat,
inference(fof_simplification,[status(thm)],[fact_2364_zero__neq__one]) ).
tff(c_0_50,plain,
! [X20540: nat] :
( ( X20540 = zero_zero_nat )
| ( X20540 = aa_nat_nat(suc,esk220_1(X20540)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
tcf(c_0_51,plain,
! [X2: nat] :
( ( X2 = zero_zero_nat )
| ( X2 = aa_nat_nat(suc,esk221_1(X2)) ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
tcf(c_0_52,plain,
esk229_2(one_one_nat,deg) = esk228_1(deg),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
tcf(c_0_53,plain,
! [X4: nat,X2: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X4))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
tcf(c_0_54,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,one_one_nat),deg)),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
tff(c_0_55,plain,
! [X20688: nat,X20689: nat] :
( ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X20688),X20689) != zero_zero_nat )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20688),X20689))
| ( X20689 = zero_zero_nat ) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20688),X20689))
| ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X20688),X20689) = zero_zero_nat ) )
& ( ( X20689 != zero_zero_nat )
| ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X20688),X20689) = zero_zero_nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2519_Euclidean__Division_Odiv__eq__0__iff])])])]) ).
tff(c_0_56,plain,
! [X20673: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X20673),one_one_nat) = X20673 ),
inference(variable_rename,[status(thm)],[fact_2227_div__by__1]) ).
tff(c_0_57,plain,
zero_zero_nat != one_one_nat,
inference(fof_nnf,[status(thm)],[c_0_49]) ).
tcf(c_0_58,plain,
! [X2: nat] :
( ( X2 = zero_zero_nat )
| ( X2 = aa_nat_nat(suc,esk220_1(X2)) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
tcf(c_0_59,plain,
! [X2: nat] : esk221_1(aa_nat_nat(suc,X2)) = X2,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_51])]),c_0_38]) ).
tcf(c_0_60,plain,
aa_nat_nat(suc,esk228_1(deg)) = deg,
inference(rw,[status(thm)],[c_0_46,c_0_52]) ).
tcf(c_0_61,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,deg),one_one_nat)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
tcf(c_0_62,plain,
! [X2: nat,X4: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X4))
| ( X4 = zero_zero_nat )
| ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),X4) != zero_zero_nat ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
tcf(c_0_63,plain,
! [X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),one_one_nat) = X2,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
tcf(c_0_64,plain,
zero_zero_nat != one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
tff(c_0_65,plain,
! [X19539: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X19539),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X19539),X19539) ),
inference(variable_rename,[status(thm)],[fact_3225_mult__2__right]) ).
tff(c_0_66,plain,
! [X92: nat] : ( X92 != aa_nat_nat(suc,X92) ),
inference(fof_simplification,[status(thm)],[fact_1485_n__not__Suc__n]) ).
tcf(c_0_67,plain,
! [X2: nat] :
( ( esk228_1(X2) = esk220_1(X2) )
| ( X2 = zero_zero_nat ) ),
inference(spm,[status(thm)],[c_0_45,c_0_58]) ).
tcf(c_0_68,plain,
esk228_1(deg) = esk221_1(deg),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
tcf(c_0_69,plain,
deg != zero_zero_nat,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64]) ).
tff(c_0_70,plain,
! [X2: nat] :
( ( X2 != zero_zero_nat )
=> ( ( X2 != aa_nat_nat(suc,zero_zero_nat) )
=> ~ ! [X3497: nat] : ( X2 != aa_nat_nat(suc,aa_nat_nat(suc,X3497)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_1487_vebt__buildup_Ocases]) ).
tff(c_0_71,plain,
! [X21132: nat,X21133: nat] :
( ( ( X21132 = one_one_nat )
| ( one_one_nat != aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X21132),X21133) ) )
& ( ( X21133 = one_one_nat )
| ( one_one_nat != aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X21132),X21133) ) )
& ( ( X21132 != one_one_nat )
| ( X21133 != one_one_nat )
| ( one_one_nat = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X21132),X21133) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2593_nat__1__eq__mult__iff])])])]) ).
tcf(c_0_72,plain,
! [X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
tff(c_0_73,plain,
! [X20535: nat] : ( X20535 != aa_nat_nat(suc,X20535) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_66])]) ).
tff(c_0_74,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,mi),ma)),
inference(fof_simplification,[status(thm)],[fact_0_False]) ).
tff(c_0_75,plain,
! [X1496: nat,X1497: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1496),X1497))
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X1496),X1497))
| ( X1496 = X1497 ) ) ),
inference(fof_simplification,[status(thm)],[fact_544_nless__le]) ).
tff(c_0_76,plain,
! [X94: nat,X95: nat,X196: nat,X90: list_VEBT_VEBT,X91: vEBT_VEBT,X2: nat] :
( pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X94),X95)),aa_nat_nat(suc,aa_nat_nat(suc,X196)),X90,X91)),X2))
<=> ( ( X2 != X94 )
=> ( ( X2 != X95 )
=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X94))
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X94))
=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X95),X2))
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X95),X2))
=> ( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X90)))
=> pp(aa_nat_bool(vEBT_vebt_member(nth_VEBT_VEBT(X90,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),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,X2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X196))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X90))) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_3926_vebt__member_Osimps_I5_J]) ).
tcf(c_0_77,plain,
esk221_1(deg) = esk220_1(deg),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
tff(c_0_78,plain,
! [X20538: nat] :
( ( X20538 = zero_zero_nat )
| ( X20538 = aa_nat_nat(suc,zero_zero_nat) )
| ( X20538 = aa_nat_nat(suc,aa_nat_nat(suc,esk219_1(X20538))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).
tcf(c_0_79,plain,
! [X4: nat,X2: nat] :
( ( X2 = one_one_nat )
| ( one_one_nat != aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X4),X2) ) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
tcf(c_0_80,plain,
! [X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),aa_nat_nat(suc,one_one_nat)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X2),
inference(rw,[status(thm)],[c_0_72,c_0_34]) ).
tcf(c_0_81,plain,
! [X2: nat] : X2 != aa_nat_nat(suc,X2),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
tcf(c_0_82,plain,
deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),
inference(split_conjunct,[status(thm)],[fact_1815__C00_C]) ).
tcf(c_0_83,plain,
na = m,
inference(split_conjunct,[status(thm)],[fact_1815__C00_C]) ).
tff(c_0_84,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,mi),ma)),
inference(fof_nnf,[status(thm)],[c_0_74]) ).
tff(c_0_85,plain,
! [X19882: nat,X19883: nat] :
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19882),X19883))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X19882),X19883))
| ( X19882 = X19883 ) )
& ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X19882),X19883))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19882),X19883)) )
& ( ( X19882 != X19883 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19882),X19883)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).
tff(c_0_86,plain,
! [X19245: nat,X19246: nat,X19247: nat,X19248: list_VEBT_VEBT,X19249: vEBT_VEBT,X19250: nat] :
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| ( X19250 = X19246 )
| ( X19250 = X19245 )
| ~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| ( X19250 = X19246 )
| ( X19250 = X19245 )
| ~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X19248)))
| pp(aa_nat_bool(vEBT_vebt_member(nth_VEBT_VEBT(X19248,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| ( X19250 = X19246 )
| ( X19250 = X19245 )
| ~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X19248)))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| ( X19250 = X19246 )
| ( X19250 = X19245 )
| ~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ( X19250 != X19245 )
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ( X19250 != X19246 )
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X19248)))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X19248)))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) )
& ( ~ pp(aa_nat_bool(vEBT_vebt_member(nth_VEBT_VEBT(X19248,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),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,X19250),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X19247))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),size_s6755466524823107622T_VEBT(X19248)))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19246),X19250))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19250),X19245))
| pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X19245),X19246)),aa_nat_nat(suc,aa_nat_nat(suc,X19247)),X19248,X19249)),X19250)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])]) ).
tcf(c_0_87,plain,
aa_nat_nat(suc,esk220_1(deg)) = deg,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_68]),c_0_77]) ).
tcf(c_0_88,plain,
! [X2: nat] :
( ( X2 = zero_zero_nat )
| ( X2 = aa_nat_nat(suc,zero_zero_nat) )
| ( X2 = aa_nat_nat(suc,aa_nat_nat(suc,esk219_1(X2))) ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
tcf(c_0_89,plain,
! [X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X2) != one_one_nat,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
tcf(c_0_90,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,m),m) = deg,
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
tff(c_0_91,negated_conjecture,
~ ( pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList,summary)),ya))
| ( xa = ya ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_92,plain,
! [X19403: nat,X19404: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X19403),X19404))
| ( aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,X19403),X19404) = X19404 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_max_Oabsorb2])])]) ).
tcf(c_0_93,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,mi),ma)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
tcf(c_0_94,plain,
! [X2: nat,X4: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X2),X4))
| ( X2 = X4 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
tcf(c_0_95,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,mi),ma)),
inference(split_conjunct,[status(thm)],[fact_2__C4_Ohyps_C_I7_J]) ).
tcf(c_0_96,plain,
! [X1: vEBT_VEBT,X2: nat,X25: nat,X8: nat,X5: list_VEBT_VEBT,X4: nat] :
( pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X8),X4)),aa_nat_nat(suc,aa_nat_nat(suc,X25)),X5,X1)),X2))
| ( X2 != X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
tcf(c_0_97,plain,
! [X2: nat] :
( ( esk220_1(deg) = X2 )
| ( aa_nat_nat(suc,X2) != deg ) ),
inference(spm,[status(thm)],[c_0_36,c_0_87]) ).
tcf(c_0_98,plain,
! [X2: nat] :
( ( aa_nat_nat(suc,aa_nat_nat(suc,esk219_1(X2))) = X2 )
| ( X2 = one_one_nat )
| ( X2 = zero_zero_nat ) ),
inference(rw,[status(thm)],[c_0_88,c_0_28]) ).
tcf(c_0_99,plain,
deg != one_one_nat,
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
tff(c_0_100,negated_conjecture,
( ~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList,summary)),ya))
& ( xa != ya ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])]) ).
tcf(c_0_101,plain,
! [X2: nat,X4: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,X2),X4) = X4 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
tcf(c_0_102,plain,
ya = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,mi),ma),
inference(split_conjunct,[status(thm)],[fact_5__092_060open_062y_A_061_Amax_Ami_Ama_092_060close_062]) ).
tcf(c_0_103,plain,
ma = mi,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
tcf(c_0_104,plain,
! [X1: vEBT_VEBT,X2: nat,X8: nat,X5: list_VEBT_VEBT,X4: nat] : pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X2),X4)),aa_nat_nat(suc,aa_nat_nat(suc,X8)),X5,X1)),X4)),
inference(er,[status(thm)],[c_0_96]) ).
tcf(c_0_105,plain,
aa_nat_nat(suc,esk219_1(deg)) = esk220_1(deg),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98])]),c_0_99]),c_0_69]) ).
tcf(c_0_106,negated_conjecture,
~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList,summary)),ya)),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
tcf(c_0_107,plain,
mi = ya,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_95]),c_0_102]),c_0_103]) ).
tcf(c_0_108,plain,
! [X1: vEBT_VEBT,X2: nat,X5: list_VEBT_VEBT,X4: nat] : pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(X2),X4)),deg,X5,X1)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_87]) ).
tcf(c_0_109,negated_conjecture,
~ pp(aa_nat_bool(vEBT_vebt_member(vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(ya),ya)),deg,treeList,summary)),ya)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_103]),c_0_107]) ).
cnf(c_0_110,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_108,c_0_109]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP229_1 : TPTP v8.2.0. Released v8.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 20:47:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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
% 80.27/11.71 # Version: 3.1.0
% 80.27/11.71 # Preprocessing class: FMLLSMLLSSSNFFN.
% 80.27/11.71 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.27/11.71 # Starting new_bool_3 with 900s (3) cores
% 80.27/11.71 # Starting new_bool_1 with 900s (3) cores
% 80.27/11.71 # Starting sh5l with 300s (1) cores
% 80.27/11.71 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 80.27/11.71 # new_bool_1 with pid 11040 completed with status 0
% 80.27/11.71 # Result found by new_bool_1
% 80.27/11.71 # Preprocessing class: FMLLSMLLSSSNFFN.
% 80.27/11.71 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.27/11.71 # Starting new_bool_3 with 900s (3) cores
% 80.27/11.71 # Starting new_bool_1 with 900s (3) cores
% 80.27/11.71 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 80.27/11.71 # Search class: FGHSM-SMLM32-DFFFFFNN
% 80.27/11.71 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 80.27/11.71 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 80.27/11.71 # Starting new_bool_1 with 91s (1) cores
% 80.27/11.71 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 80.27/11.71 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 11182 completed with status 0
% 80.27/11.71 # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 80.27/11.71 # Preprocessing class: FMLLSMLLSSSNFFN.
% 80.27/11.71 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.27/11.71 # Starting new_bool_3 with 900s (3) cores
% 80.27/11.71 # Starting new_bool_1 with 900s (3) cores
% 80.27/11.71 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 80.27/11.71 # Search class: FGHSM-SMLM32-DFFFFFNN
% 80.27/11.71 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 80.27/11.71 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 80.27/11.71 # Starting new_bool_1 with 91s (1) cores
% 80.27/11.71 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 80.27/11.71 # Preprocessing time : 0.096 s
% 80.27/11.71 # SatCheck found unsatisfiable ground set
% 80.27/11.71
% 80.27/11.71 # Proof found!
% 80.27/11.71 # SZS status Theorem
% 80.27/11.71 # SZS output start CNFRefutation
% See solution above
% 80.27/11.71 # Parsed axioms : 11928
% 80.27/11.71 # Removed by relevancy pruning/SinE : 9904
% 80.27/11.71 # Initial clauses : 6644
% 80.27/11.71 # Removed in clause preprocessing : 1815
% 80.27/11.71 # Initial clauses in saturation : 4829
% 80.27/11.71 # Processed clauses : 8685
% 80.27/11.71 # ...of these trivial : 339
% 80.27/11.71 # ...subsumed : 3346
% 80.27/11.71 # ...remaining for further processing : 5000
% 80.27/11.71 # Other redundant clauses eliminated : 3288
% 80.27/11.71 # Clauses deleted for lack of memory : 0
% 80.27/11.71 # Backward-subsumed : 58
% 80.27/11.71 # Backward-rewritten : 135
% 80.27/11.71 # Generated clauses : 125409
% 80.27/11.71 # ...of the previous two non-redundant : 113815
% 80.27/11.71 # ...aggressively subsumed : 0
% 80.27/11.71 # Contextual simplify-reflections : 91
% 80.27/11.71 # Paramodulations : 122726
% 80.27/11.71 # Factorizations : 48
% 80.27/11.71 # NegExts : 0
% 80.27/11.71 # Equation resolutions : 3315
% 80.27/11.71 # Disequality decompositions : 0
% 80.27/11.71 # Total rewrite steps : 62289
% 80.27/11.71 # ...of those cached : 58634
% 80.27/11.71 # Propositional unsat checks : 1
% 80.27/11.71 # Propositional check models : 0
% 80.27/11.71 # Propositional check unsatisfiable : 1
% 80.27/11.71 # Propositional clauses : 113171
% 80.27/11.71 # Propositional clauses after purity: 25642
% 80.27/11.71 # Propositional unsat core size : 2
% 80.27/11.71 # Propositional preprocessing time : 0.000
% 80.27/11.71 # Propositional encoding time : 0.307
% 80.27/11.71 # Propositional solver time : 0.019
% 80.27/11.71 # Success case prop preproc time : 0.000
% 80.27/11.71 # Success case prop encoding time : 0.307
% 80.27/11.71 # Success case prop solver time : 0.019
% 80.27/11.71 # Current number of processed clauses : 3762
% 80.27/11.71 # Positive orientable unit clauses : 464
% 80.27/11.71 # Positive unorientable unit clauses: 23
% 80.27/11.71 # Negative unit clauses : 470
% 80.27/11.71 # Non-unit-clauses : 2805
% 80.27/11.71 # Current number of unprocessed clauses: 109409
% 80.27/11.71 # ...number of literals in the above : 494520
% 80.27/11.71 # Current number of archived formulas : 0
% 80.27/11.71 # Current number of archived clauses : 193
% 80.27/11.71 # Clause-clause subsumption calls (NU) : 7372571
% 80.27/11.71 # Rec. Clause-clause subsumption calls : 366222
% 80.27/11.71 # Non-unit clause-clause subsumptions : 1819
% 80.27/11.71 # Unit Clause-clause subsumption calls : 385933
% 80.27/11.71 # Rewrite failures with RHS unbound : 0
% 80.27/11.71 # BW rewrite match attempts : 5321
% 80.27/11.71 # BW rewrite match successes : 201
% 80.27/11.71 # Condensation attempts : 0
% 80.27/11.71 # Condensation successes : 0
% 80.27/11.71 # Termbank termtop insertions : 7722830
% 80.27/11.71 # Search garbage collected termcells : 178947
% 80.27/11.71
% 80.27/11.71 # -------------------------------------------------
% 80.27/11.71 # User time : 9.970 s
% 80.27/11.71 # System time : 0.204 s
% 80.27/11.71 # Total time : 10.174 s
% 80.27/11.71 # Maximum resident set size: 41120 pages
% 80.27/11.71
% 80.27/11.71 # -------------------------------------------------
% 80.27/11.71 # User time : 29.841 s
% 80.27/11.71 # System time : 0.342 s
% 80.27/11.71 # Total time : 30.183 s
% 80.27/11.71 # Maximum resident set size: 28572 pages
% 80.27/11.71 % E---3.1 exiting
% 80.27/11.71 % E exiting
%------------------------------------------------------------------------------