%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:07 AM UTC 2026
% Result : Theorem 21.36s 4.16s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 144
% Syntax : Number of formulae : 1979 ( 767 unt; 0 typ; 0 def)
% Number of atoms : 12776 (5750 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 13752 (3211 ~;3307 |; 63 &;7035 @)
% ( 0 <=>; 136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 350 ( 350 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 97 usr; 10 con; 0-3 aty)
% Number of variables : 3159 ( 99 ^;3046 !; 14 ?;3159 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_list_a,type,
list_a: $tType ).
thf(tp_list_l2071841302list_a,type,
list_l2071841302list_a: $tType ).
thf(tp_list_list_a,type,
list_list_a: $tType ).
thf(tp_list_list_list_a,type,
list_list_list_a: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_option_a,type,
option_a: $tType ).
thf(tp_option_list_a,type,
option_list_a: $tType ).
thf(tp_option_list_list_a,type,
option_list_list_a: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_bind_a_a,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(tp_bind_a_list_a,type,
bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
thf(tp_bind_a_list_list_a,type,
bind_a_list_list_a: list_a > ( a > list_list_list_a ) > list_list_list_a ).
thf(tp_bind_l311701255list_a,type,
bind_l311701255list_a: list_list_list_a > ( list_list_a > list_list_list_a ) > list_list_list_a ).
thf(tp_bind_l94945665list_a,type,
bind_l94945665list_a: list_list_list_a > ( list_list_a > list_list_a ) > list_list_a ).
thf(tp_bind_l971853709list_a,type,
bind_l971853709list_a: list_list_a > ( list_a > list_list_list_a ) > list_list_list_a ).
thf(tp_bind_list_a_a,type,
bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
thf(tp_bind_list_a_list_a,type,
bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
thf(tp_bind_list_list_a_a,type,
bind_list_list_a_a: list_list_list_a > ( list_list_a > list_a ) > list_a ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(tp_concat_a,type,
concat_a: list_list_a > list_a ).
thf(tp_concat_list_a,type,
concat_list_a: list_list_list_a > list_list_a ).
thf(tp_concat_list_list_a,type,
concat_list_list_a: list_l2071841302list_a > list_list_list_a ).
thf(tp_count_429956358list_a,type,
count_429956358list_a: list_list_list_a > list_list_a > nat ).
thf(tp_count_list_a,type,
count_list_a: list_a > a > nat ).
thf(tp_count_list_list_a,type,
count_list_list_a: list_list_a > list_a > nat ).
thf(tp_divide_divide_int,type,
divide_divide_int: int > int > int ).
thf(tp_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(tp_divide_divide_real,type,
divide_divide_real: real > real > real ).
thf(tp_gen_le840878749list_a,type,
gen_le840878749list_a: nat > list_list_list_a > nat ).
thf(tp_gen_length_a,type,
gen_length_a: nat > list_a > nat ).
thf(tp_gen_length_list_a,type,
gen_length_list_a: nat > list_list_a > nat ).
thf(tp_if_nat,type,
if_nat: $o > nat > nat > nat ).
thf(tp_inverse_inverse_real,type,
inverse_inverse_real: real > real ).
thf(tp_k,type,
k: nat ).
thf(tp_listSl1495374126_aux_a,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(tp_listSl162220270list_a,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(tp_listSl856612276list_a,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(tp_listSl97544552lice_a,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(tp_list_ex1_a,type,
list_ex1_a: ( a > $o ) > list_a > $o ).
thf(tp_list_ex1_list_a,type,
list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(tp_list_ex1_list_list_a,type,
list_ex1_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
thf(tp_map_fi1090123216list_a,type,
map_fi1090123216list_a: ( list_a > option_list_list_a ) > list_list_a > list_list_list_a ).
thf(tp_map_fi1574988606st_a_a,type,
map_fi1574988606st_a_a: ( list_list_a > option_a ) > list_list_list_a > list_a ).
thf(tp_map_fi2089402454list_a,type,
map_fi2089402454list_a: ( a > option_list_list_a ) > list_a > list_list_list_a ).
thf(tp_map_fi213215172list_a,type,
map_fi213215172list_a: ( list_list_a > option_list_a ) > list_list_list_a > list_list_a ).
thf(tp_map_fi461586634list_a,type,
map_fi461586634list_a: ( list_a > option_list_a ) > list_list_a > list_list_a ).
thf(tp_map_fi824137674list_a,type,
map_fi824137674list_a: ( list_list_a > option_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(tp_map_filter_a_a,type,
map_filter_a_a: ( a > option_a ) > list_a > list_a ).
thf(tp_map_filter_a_list_a,type,
map_filter_a_list_a: ( a > option_list_a ) > list_a > list_list_a ).
thf(tp_map_filter_list_a_a,type,
map_filter_list_a_a: ( list_a > option_a ) > list_list_a > list_a ).
thf(tp_maps_a_a,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(tp_maps_a_list_a,type,
maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
thf(tp_maps_a_list_list_a,type,
maps_a_list_list_a: ( a > list_list_list_a ) > list_a > list_list_list_a ).
thf(tp_maps_l2025957947list_a,type,
maps_l2025957947list_a: ( list_list_a > list_list_a ) > list_list_list_a > list_list_a ).
thf(tp_maps_l57963201list_a,type,
maps_l57963201list_a: ( list_list_a > list_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(tp_maps_l755382343list_a,type,
maps_l755382343list_a: ( list_a > list_list_list_a ) > list_list_a > list_list_list_a ).
thf(tp_maps_list_a_a,type,
maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
thf(tp_maps_list_a_list_a,type,
maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
thf(tp_maps_list_list_a_a,type,
maps_list_list_a_a: ( list_list_a > list_a ) > list_list_list_a > list_a ).
thf(tp_member_a,type,
member_a: list_a > a > $o ).
thf(tp_member_list_a,type,
member_list_a: list_list_a > list_a > $o ).
thf(tp_member_list_list_a,type,
member_list_list_a: list_list_list_a > list_list_a > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_real,type,
member_real: real > set_real > $o ).
thf(tp_nil_a,type,
nil_a: list_a ).
thf(tp_nil_list_a,type,
nil_list_a: list_list_a ).
thf(tp_nil_list_list_a,type,
nil_list_list_a: list_list_list_a ).
thf(tp_nil_list_list_list_a,type,
nil_list_list_list_a: list_l2071841302list_a ).
thf(tp_null_a,type,
null_a: list_a > $o ).
thf(tp_null_list_a,type,
null_list_a: list_list_a > $o ).
thf(tp_null_list_list_a,type,
null_list_list_a: list_list_list_a > $o ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_power_power_int,type,
power_power_int: int > nat > int ).
thf(tp_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(tp_power_power_real,type,
power_power_real: real > nat > real ).
thf(tp_sK10_N2,type,
sK10_N2: ( nat > $o ) > nat ).
thf(tp_sK11_Xs2,type,
sK11_Xs2: nat > list_a ).
thf(tp_sK12_Xs2,type,
sK12_Xs2: ( list_a > $o ) > list_a ).
thf(tp_sK13_SY311,type,
sK13_SY311: nat > nat > nat ).
thf(tp_sK14_SY312,type,
sK14_SY312: nat > nat > nat ).
thf(tp_sK15_SY315,type,
sK15_SY315: nat > nat > nat ).
thf(tp_sK16_SY316,type,
sK16_SY316: nat > nat > nat ).
thf(tp_sK1_K3,type,
sK1_K3: nat > ( nat > $o ) > nat ).
thf(tp_sK2_I3,type,
sK2_I3: ( nat > nat ) > nat ).
thf(tp_sK3_SY210,type,
sK3_SY210: ( nat > nat ) > nat ).
thf(tp_sK4_X3,type,
sK4_X3: ( nat > $o ) > set_nat > nat ).
thf(tp_sK5_X3,type,
sK5_X3: ( nat > $o ) > set_nat > nat > nat ).
thf(tp_sK6_X3,type,
sK6_X3: ( nat > $o ) > set_nat > nat ).
thf(tp_sK7_X3,type,
sK7_X3: ( nat > $o ) > set_nat > nat ).
thf(tp_sK8_N2,type,
sK8_N2: ( nat > $o ) > nat ).
thf(tp_sK9_N2,type,
sK9_N2: ( nat > $o ) > nat ).
thf(tp_semiri1382578993at_nat,type,
semiri1382578993at_nat: nat > nat ).
thf(tp_semiri2019852685at_int,type,
semiri2019852685at_int: nat > int ).
thf(tp_semiri2110766477t_real,type,
semiri2110766477t_real: nat > real ).
thf(tp_size_s1427607542list_a,type,
size_s1427607542list_a: list_list_a > nat ).
thf(tp_size_s575106428list_a,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(tp_size_size_list_a,type,
size_size_list_a: list_a > nat ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Nat__Onat_T) ).
thf(4,axiom,
! [N: nat,M: nat] :
( ( ( divide_divide_nat @ N @ M )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_div__eq__0__conv) ).
thf(34,axiom,
! [M: nat,N: nat] :
( ( ( divide_divide_nat @ M @ N )
= zero_zero_nat )
= ( ( ord_less_nat @ M @ N )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_Euclidean__Division_Odiv__eq__0__iff) ).
thf(89,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( divide_divide_nat @ M @ N )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_div__less) ).
thf(92,axiom,
! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_list__slice__length) ).
thf(93,axiom,
! [Xs: list_a,X: a] : ( ord_less_eq_nat @ ( count_list_a @ Xs @ X ) @ ( size_size_list_a @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_count__le__length) ).
thf(94,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K3: nat] :
( ( ord_less_eq_nat @ K3 @ N )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ K3 )
=> ~ ( P @ I4 ) )
& ( P @ K3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_ex__least__nat__le) ).
thf(99,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( power_power_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_zero__power) ).
thf(104,axiom,
! [I2: nat,M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ I2 )
=> ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_nat__power__less__imp__less) ).
thf(107,axiom,
! [A: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_zero__less__power) ).
thf(108,axiom,
( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_eq_nat @ M3 @ N3 )
& ( M3 != N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_nat__less__le) ).
thf(109,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_less__imp__le__nat) ).
thf(110,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_le__eq__less__or__eq) ).
thf(111,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_less__or__eq__imp__le) ).
thf(112,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_le__neq__implies__less) ).
thf(113,axiom,
! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_less__mono__imp__le__mono) ).
thf(114,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_less__eq__nat_Osimps_I1_J) ).
thf(115,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_le__0__eq) ).
thf(116,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_bot__nat__0_Oextremum__unique) ).
thf(117,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_bot__nat__0_Oextremum__uniqueI) ).
thf(120,axiom,
( ord_less_eq_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_le__greater__neq__conv) ).
thf(123,axiom,
( ord_less_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_greater__le__neq__conv) ).
thf(126,axiom,
( ord_less_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_less__ge__neq__conv) ).
thf(129,axiom,
( ord_less_eq_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ge__less__neq__conv) ).
thf(132,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_le__numeral__extra_I3_J) ).
thf(133,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_zero__le) ).
thf(151,axiom,
! [A: nat,N: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_power__not__zero) ).
thf(177,axiom,
! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_power__eq__0__iff) ).
thf(194,axiom,
! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_nat__zero__less__power__iff) ).
thf(198,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_le__zero__eq) ).
thf(199,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_le0) ).
thf(200,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_bot__nat__0_Oextremum) ).
thf(208,axiom,
( listSl97544552lice_a
= ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_list__slice__def) ).
thf(212,axiom,
! [I: set_nat,P: nat > $o] :
( ? [X4: nat] :
( ( member_nat @ X4 @ I )
& ( P @ X4 ) )
=> ? [X3: nat] :
( ( member_nat @ X3 @ I )
& ( P @ X3 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ I )
=> ( ( ord_less_nat @ Xa @ X3 )
=> ~ ( P @ Xa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Collect__minI__ex) ).
thf(213,axiom,
! [K: nat,I: set_nat,P: nat > $o] :
( ( member_nat @ K @ I )
=> ( ( P @ K )
=> ? [X3: nat] :
( ( member_nat @ X3 @ I )
& ( P @ X3 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ I )
=> ( ( ord_less_nat @ Xa @ X3 )
=> ~ ( P @ Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Collect__minI) ).
thf(216,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
=> ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_of__nat__less__imp__less) ).
thf(219,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_less__imp__of__nat__less) ).
thf(222,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_of__nat__less__0__iff) ).
thf(225,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_of__nat__less__iff) ).
thf(228,axiom,
! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_of__nat__eq__0__iff) ).
thf(231,axiom,
! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_of__nat__0__eq__iff) ).
thf(234,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_of__nat__0) ).
thf(237,axiom,
zero_zero_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_zero__natural_Orsp) ).
thf(238,axiom,
! [I: set_nat,P: nat > $o,A: nat] :
( ! [X3: nat] :
( ! [Y2: nat] :
( ( ( member_nat @ X3 @ I )
& ( member_nat @ Y2 @ I )
& ( ord_less_nat @ Y2 @ X3 ) )
=> ( P @ Y2 ) )
=> ( P @ X3 ) )
=> ( P @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_interval__induct) ).
thf(239,axiom,
! [I: set_nat,P: nat > $o,A: nat] :
( ! [X3: nat] :
( ! [Y2: nat] :
( ( ( member_nat @ X3 @ I )
& ( member_nat @ Y2 @ I )
& ( ord_less_nat @ Y2 @ X3 ) )
=> ( P @ Y2 ) )
=> ( P @ X3 ) )
=> ( P @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_interval__induct__rule) ).
thf(240,axiom,
! [Y: list_list_a] :
( ( count_429956358list_a @ nil_list_list_a @ Y )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_count__list_Osimps_I1_J) ).
thf(241,axiom,
! [Y: list_a] :
( ( count_list_list_a @ nil_list_a @ Y )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_count__list_Osimps_I1_J) ).
thf(242,axiom,
! [Y: a] :
( ( count_list_a @ nil_a @ Y )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_count__list_Osimps_I1_J) ).
thf(245,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_of__nat__0__less__iff) ).
thf(246,axiom,
! [Xs: list_list_a,K: nat] :
( ( listSl856612276list_a @ Xs @ K @ zero_zero_nat )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_list__slice__aux_Osimps_I1_J) ).
thf(247,axiom,
! [Xs: list_a,K: nat] :
( ( listSl1495374126_aux_a @ Xs @ K @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_list__slice__aux_Osimps_I1_J) ).
thf(250,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__numeral__extra_I3_J) ).
thf(252,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_gr__implies__gr0) ).
thf(253,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_infinite__descent0) ).
thf(254,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bot__nat__0_Oextremum__strict) ).
thf(255,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_gr__zeroI) ).
thf(256,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_not__less__zero) ).
thf(257,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_gr__implies__not__zero) ).
thf(262,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__iff__neq__zero) ).
thf(263,axiom,
! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
!= ( size_size_list_a @ Y ) )
=> ( X != Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_size__neq__size__imp__neq) ).
thf(264,axiom,
! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__neq__iff) ).
thf(265,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__not__refl) ).
thf(266,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__not__refl2) ).
thf(267,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__not__refl3) ).
thf(268,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__irrefl__nat) ).
thf(269,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P @ M2 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_nat__less__induct) ).
thf(270,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) )
=> ( P @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_infinite__descent) ).
thf(271,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_linorder__neqE__nat) ).
thf(274,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zero__reorient) ).
thf(275,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_gr__implies__not0) ).
thf(276,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__zeroE) ).
thf(277,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_not__less0) ).
thf(278,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__gr0) ).
thf(279,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_gr0I) ).
thf(280,axiom,
! [N: nat,Xs: list_a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
=> ( Xs != nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_length__greater__imp__not__empty) ).
thf(281,axiom,
! [N: nat,Xs: list_list_list_a] :
( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
=> ( Xs != nil_list_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_length__greater__imp__not__empty) ).
thf(282,axiom,
! [N: nat,Xs: list_list_a] :
( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
=> ( Xs != nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_length__greater__imp__not__empty) ).
thf(283,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_not__gr__zero) ).
thf(284,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_bot__nat__0_Onot__eq__extremum) ).
thf(285,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__nat__zero__code) ).
thf(286,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_neq0__conv) ).
thf(287,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs )
!= ( size_size_list_a @ Ys2 ) )
=> ( Xs != Ys2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_neq__if__length__neq) ).
thf(288,axiom,
! [N: nat] :
? [Xs2: list_a] :
( ( size_size_list_a @ Xs2 )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Ex__list__of__length) ).
thf(289,axiom,
! [P: list_a > $o,Xs: list_a] :
( ! [Xs2: list_a] :
( ! [Ys: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys ) @ ( size_size_list_a @ Xs2 ) )
=> ( P @ Ys ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_length__induct) ).
thf(290,axiom,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_length__code) ).
thf(291,axiom,
( size_s1427607542list_a
= ( gen_length_list_a @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_length__code) ).
thf(292,axiom,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_list_Osize_I3_J) ).
thf(293,axiom,
( ( size_s575106428list_a @ nil_list_list_a )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_list_Osize_I3_J) ).
thf(294,axiom,
( ( size_s1427607542list_a @ nil_list_a )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list_Osize_I3_J) ).
thf(295,axiom,
! [Xs: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
= ( Xs != nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_length__greater__0__conv) ).
thf(296,axiom,
! [Xs: list_list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
= ( Xs != nil_list_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_length__greater__0__conv) ).
thf(297,axiom,
! [Xs: list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
= ( Xs != nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_length__greater__0__conv) ).
thf(298,axiom,
! [Xs: list_a] :
( ( ( size_size_list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_length__0__conv) ).
thf(299,axiom,
! [Xs: list_list_list_a] :
( ( ( size_s575106428list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_length__0__conv) ).
thf(300,axiom,
! [Xs: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_length__0__conv) ).
thf(301,axiom,
! [F: list_list_a > option_list_list_a] :
( ( map_fi824137674list_a @ F @ nil_list_list_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_map__filter__simps_I2_J) ).
thf(302,axiom,
! [F: list_list_a > option_list_a] :
( ( map_fi213215172list_a @ F @ nil_list_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_map__filter__simps_I2_J) ).
thf(303,axiom,
! [F: list_list_a > option_a] :
( ( map_fi1574988606st_a_a @ F @ nil_list_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_map__filter__simps_I2_J) ).
thf(304,axiom,
! [F: list_a > option_list_list_a] :
( ( map_fi1090123216list_a @ F @ nil_list_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_map__filter__simps_I2_J) ).
thf(305,axiom,
! [F: list_a > option_list_a] :
( ( map_fi461586634list_a @ F @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_map__filter__simps_I2_J) ).
thf(306,axiom,
! [F: list_a > option_a] :
( ( map_filter_list_a_a @ F @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_map__filter__simps_I2_J) ).
thf(307,axiom,
! [F: a > option_list_list_a] :
( ( map_fi2089402454list_a @ F @ nil_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_map__filter__simps_I2_J) ).
thf(308,axiom,
! [F: a > option_list_a] :
( ( map_filter_a_list_a @ F @ nil_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_map__filter__simps_I2_J) ).
thf(309,axiom,
! [F: a > option_a] :
( ( map_filter_a_a @ F @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_map__filter__simps_I2_J) ).
thf(310,axiom,
! [Xs: list_list_list_a] :
( ( Xs = nil_list_list_a )
= ( null_list_list_a @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_eq__Nil__null) ).
thf(311,axiom,
! [Xs: list_list_a] :
( ( Xs = nil_list_a )
= ( null_list_a @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_eq__Nil__null) ).
thf(312,axiom,
! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_eq__Nil__null) ).
thf(313,axiom,
null_list_a @ nil_list_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_null__rec_I2_J) ).
thf(314,axiom,
null_a @ nil_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_null__rec_I2_J) ).
thf(315,axiom,
null_list_list_a @ nil_list_list_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_null__rec_I2_J) ).
thf(316,axiom,
! [F: list_a > list_list_a] :
( ( maps_list_a_list_a @ F @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_maps__simps_I2_J) ).
thf(317,axiom,
! [F: list_a > list_a] :
( ( maps_list_a_a @ F @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_maps__simps_I2_J) ).
thf(318,axiom,
! [F: a > list_list_a] :
( ( maps_a_list_a @ F @ nil_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_maps__simps_I2_J) ).
thf(319,axiom,
! [F: a > list_a] :
( ( maps_a_a @ F @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_maps__simps_I2_J) ).
thf(320,axiom,
! [F: list_list_a > list_list_list_a] :
( ( maps_l57963201list_a @ F @ nil_list_list_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_maps__simps_I2_J) ).
thf(321,axiom,
! [F: list_list_a > list_list_a] :
( ( maps_l2025957947list_a @ F @ nil_list_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_maps__simps_I2_J) ).
thf(322,axiom,
! [F: list_list_a > list_a] :
( ( maps_list_list_a_a @ F @ nil_list_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_maps__simps_I2_J) ).
thf(323,axiom,
! [F: list_a > list_list_list_a] :
( ( maps_l755382343list_a @ F @ nil_list_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_maps__simps_I2_J) ).
thf(324,axiom,
! [F: a > list_list_list_a] :
( ( maps_a_list_list_a @ F @ nil_a )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_maps__simps_I2_J) ).
thf(325,axiom,
! [N: nat] :
( ( gen_length_list_a @ N @ nil_list_a )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_gen__length__code_I1_J) ).
thf(326,axiom,
! [N: nat] :
( ( gen_length_a @ N @ nil_a )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_gen__length__code_I1_J) ).
thf(327,axiom,
! [N: nat] :
( ( gen_le840878749list_a @ N @ nil_list_list_a )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_gen__length__code_I1_J) ).
thf(328,axiom,
! [Y: list_a] :
~ ( member_list_a @ nil_list_a @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_member__rec_I2_J) ).
thf(329,axiom,
! [Y: a] :
~ ( member_a @ nil_a @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_member__rec_I2_J) ).
thf(330,axiom,
! [Y: list_list_a] :
~ ( member_list_list_a @ nil_list_list_a @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_member__rec_I2_J) ).
thf(331,axiom,
! [F: list_a > list_list_a] :
( ( bind_list_a_list_a @ nil_list_a @ F )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_bind__simps_I1_J) ).
thf(332,axiom,
! [F: list_a > list_a] :
( ( bind_list_a_a @ nil_list_a @ F )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bind__simps_I1_J) ).
thf(333,axiom,
! [F: a > list_list_a] :
( ( bind_a_list_a @ nil_a @ F )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_bind__simps_I1_J) ).
thf(334,axiom,
! [F: a > list_a] :
( ( bind_a_a @ nil_a @ F )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_bind__simps_I1_J) ).
thf(335,axiom,
! [F: list_list_a > list_list_list_a] :
( ( bind_l311701255list_a @ nil_list_list_a @ F )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bind__simps_I1_J) ).
thf(336,axiom,
! [F: list_list_a > list_list_a] :
( ( bind_l94945665list_a @ nil_list_list_a @ F )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_bind__simps_I1_J) ).
thf(337,axiom,
! [F: list_list_a > list_a] :
( ( bind_list_list_a_a @ nil_list_list_a @ F )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_bind__simps_I1_J) ).
thf(338,axiom,
! [F: list_a > list_list_list_a] :
( ( bind_l971853709list_a @ nil_list_a @ F )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_bind__simps_I1_J) ).
thf(339,axiom,
! [F: a > list_list_list_a] :
( ( bind_a_list_list_a @ nil_a @ F )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_bind__simps_I1_J) ).
thf(340,axiom,
! [Xs: list_a,K: nat] :
( ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
=> ( ( listSl97544552lice_a @ Xs @ K )
= nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list__slice__less) ).
thf(341,axiom,
! [Xs: list_list_a,K: nat] :
( ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
=> ( ( listSl162220270list_a @ Xs @ K )
= nil_list_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list__slice__less) ).
thf(342,axiom,
! [P: list_a > $o] :
~ ( list_ex1_list_a @ P @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list__ex1__simps_I1_J) ).
thf(343,axiom,
! [P: a > $o] :
~ ( list_ex1_a @ P @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list__ex1__simps_I1_J) ).
thf(344,axiom,
! [P: list_list_a > $o] :
~ ( list_ex1_list_list_a @ P @ nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list__ex1__simps_I1_J) ).
thf(345,axiom,
( ( concat_a @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_concat_Osimps_I1_J) ).
thf(346,axiom,
( ( concat_list_a @ nil_list_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_concat_Osimps_I1_J) ).
thf(348,axiom,
! [Xs: list_a] :
( ( listSl97544552lice_a @ Xs @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_list__slice__0) ).
thf(349,axiom,
! [Xs: list_list_a] :
( ( listSl162220270list_a @ Xs @ zero_zero_nat )
= nil_list_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_list__slice__0) ).
thf(350,conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(351,negated_conjecture,
( ( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a )
= $false ),
inference(negate_conjecture,[status(cth)],[350]) ).
thf(352,plain,
( ( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a )
= $false ),
inference(unfold_def,[status(thm)],[351]) ).
thf(353,plain,
( ( ! [N: nat,M: nat] :
( ( ( divide_divide_nat @ N @ M )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(354,plain,
( ( ! [M: nat,N: nat] :
( ( ( divide_divide_nat @ M @ N )
= zero_zero_nat )
= ( ( ord_less_nat @ M @ N )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(355,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( divide_divide_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(356,plain,
( ( ! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(357,plain,
( ( ! [Xs: list_a,X: a] : ( ord_less_eq_nat @ ( count_list_a @ Xs @ X ) @ ( size_size_list_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(358,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K3: nat] :
( ( ord_less_eq_nat @ K3 @ N )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ K3 )
=> ~ ( P @ I4 ) )
& ( P @ K3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(359,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( power_power_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(360,plain,
( ( ! [I2: nat,M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ I2 )
=> ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(361,plain,
( ( ! [A: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(362,plain,
( ( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_eq_nat @ M3 @ N3 )
& ( M3 != N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(363,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(364,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(365,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(366,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(367,plain,
( ( ! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(368,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(369,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(370,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(371,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(372,plain,
( ( ord_less_eq_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(373,plain,
( ( ord_less_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(374,plain,
( ( ord_less_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(375,plain,
( ( ord_less_eq_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(376,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(377,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(378,plain,
( ( ! [A: nat,N: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(379,plain,
( ( ! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(380,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(381,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(382,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(383,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(384,plain,
( ( listSl97544552lice_a
= ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(385,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ? [X4: nat] :
( ( member_nat @ X4 @ I )
& ( P @ X4 ) )
=> ? [X3: nat] :
( ( member_nat @ X3 @ I )
& ( P @ X3 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ I )
=> ( ( ord_less_nat @ Xa @ X3 )
=> ~ ( P @ Xa ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(386,plain,
( ( ! [K: nat,I: set_nat,P: nat > $o] :
( ( member_nat @ K @ I )
=> ( ( P @ K )
=> ? [X3: nat] :
( ( member_nat @ X3 @ I )
& ( P @ X3 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ I )
=> ( ( ord_less_nat @ Xa @ X3 )
=> ~ ( P @ Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(387,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(388,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(389,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(390,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(391,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(392,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(393,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(394,plain,
( ( zero_zero_nat = zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(395,plain,
( ( ! [I: set_nat,P: nat > $o,A: nat] :
( ! [X3: nat] :
( ! [Y2: nat] :
( ( ( member_nat @ X3 @ I )
& ( member_nat @ Y2 @ I )
& ( ord_less_nat @ Y2 @ X3 ) )
=> ( P @ Y2 ) )
=> ( P @ X3 ) )
=> ( P @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(396,plain,
( ( ! [I: set_nat,P: nat > $o,A: nat] :
( ! [X3: nat] :
( ! [Y2: nat] :
( ( ( member_nat @ X3 @ I )
& ( member_nat @ Y2 @ I )
& ( ord_less_nat @ Y2 @ X3 ) )
=> ( P @ Y2 ) )
=> ( P @ X3 ) )
=> ( P @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(397,plain,
( ( ! [Y: list_list_a] :
( ( count_429956358list_a @ nil_list_list_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(398,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(399,plain,
( ( ! [Xs: list_list_a,K: nat] :
( ( listSl856612276list_a @ Xs @ K @ zero_zero_nat )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(400,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(401,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(402,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(403,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(404,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(405,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(406,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(407,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(408,plain,
( ( ! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
!= ( size_size_list_a @ Y ) )
=> ( X != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(409,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(410,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(411,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(412,plain,
( ( ! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(413,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(414,plain,
( ( ! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P @ M2 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(415,plain,
( ( ! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) )
=> ( P @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(416,plain,
( ( ! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(417,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(418,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(419,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(420,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(421,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(422,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(423,plain,
( ( ! [N: nat,Xs: list_list_list_a] :
( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
=> ( Xs != nil_list_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(424,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(425,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(426,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(427,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(428,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs )
!= ( size_size_list_a @ Ys2 ) )
=> ( Xs != Ys2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(429,plain,
( ( ! [N: nat] :
? [Xs2: list_a] :
( ( size_size_list_a @ Xs2 )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(430,plain,
( ( ! [P: list_a > $o,Xs: list_a] :
( ! [Xs2: list_a] :
( ! [Ys: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys ) @ ( size_size_list_a @ Xs2 ) )
=> ( P @ Ys ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(431,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(432,plain,
( ( size_s1427607542list_a
= ( gen_length_list_a @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(433,plain,
( ( ( size_s575106428list_a @ nil_list_list_a )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(434,plain,
( ( ! [Xs: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
= ( Xs != nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(435,plain,
( ( ! [Xs: list_list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
= ( Xs != nil_list_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(436,plain,
( ( ! [Xs: list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
= ( Xs != nil_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(437,plain,
( ( ! [Xs: list_list_list_a] :
( ( ( size_s575106428list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(438,plain,
( ( ! [F: list_list_a > option_list_list_a] :
( ( map_fi824137674list_a @ F @ nil_list_list_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(439,plain,
( ( ! [Xs: list_list_list_a] :
( ( Xs = nil_list_list_a )
= ( null_list_list_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(440,plain,
( ( null_list_list_a @ nil_list_list_a )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(441,plain,
( ( ! [F: list_list_a > list_list_list_a] :
( ( maps_l57963201list_a @ F @ nil_list_list_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(442,plain,
( ( ! [N: nat] :
( ( gen_le840878749list_a @ N @ nil_list_list_a )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(443,plain,
( ( ! [Y: list_list_a] :
~ ( member_list_list_a @ nil_list_list_a @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(444,plain,
( ( ! [F: list_list_a > list_list_list_a] :
( ( bind_l311701255list_a @ nil_list_list_a @ F )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(445,plain,
( ( ! [Xs: list_list_a,K: nat] :
( ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
=> ( ( listSl162220270list_a @ Xs @ K )
= nil_list_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(446,plain,
( ( ! [P: list_list_a > $o] :
~ ( list_ex1_list_list_a @ P @ nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(447,plain,
( ( ! [Xs: list_list_a] :
( ( listSl162220270list_a @ Xs @ zero_zero_nat )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(448,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(449,plain,
( ( ! [Y: list_a] :
( ( count_list_list_a @ nil_list_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(450,plain,
( ( ! [Y: a] :
( ( count_list_a @ nil_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(451,plain,
( ( ! [Xs: list_a,K: nat] :
( ( listSl1495374126_aux_a @ Xs @ K @ zero_zero_nat )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(452,plain,
( ( ! [N: nat,Xs: list_a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
=> ( Xs != nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(453,plain,
( ( ! [N: nat,Xs: list_list_a] :
( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
=> ( Xs != nil_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(454,plain,
( ( ( size_size_list_a @ nil_a )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(455,plain,
( ( ( size_s1427607542list_a @ nil_list_a )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(456,plain,
( ( ! [Xs: list_a] :
( ( ( size_size_list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(457,plain,
( ( ! [Xs: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(458,plain,
( ( ! [F: list_list_a > option_list_a] :
( ( map_fi213215172list_a @ F @ nil_list_list_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(459,plain,
( ( ! [F: list_list_a > option_a] :
( ( map_fi1574988606st_a_a @ F @ nil_list_list_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(460,plain,
( ( ! [F: list_a > option_list_list_a] :
( ( map_fi1090123216list_a @ F @ nil_list_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(461,plain,
( ( ! [F: list_a > option_list_a] :
( ( map_fi461586634list_a @ F @ nil_list_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(462,plain,
( ( ! [F: list_a > option_a] :
( ( map_filter_list_a_a @ F @ nil_list_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(463,plain,
( ( ! [F: a > option_list_list_a] :
( ( map_fi2089402454list_a @ F @ nil_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(464,plain,
( ( ! [F: a > option_list_a] :
( ( map_filter_a_list_a @ F @ nil_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(465,plain,
( ( ! [F: a > option_a] :
( ( map_filter_a_a @ F @ nil_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(466,plain,
( ( ! [Xs: list_list_a] :
( ( Xs = nil_list_a )
= ( null_list_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(467,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(468,plain,
( ( null_list_a @ nil_list_a )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(469,plain,
( ( null_a @ nil_a )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(470,plain,
( ( ! [F: list_a > list_list_a] :
( ( maps_list_a_list_a @ F @ nil_list_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(471,plain,
( ( ! [F: list_a > list_a] :
( ( maps_list_a_a @ F @ nil_list_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(472,plain,
( ( ! [F: a > list_list_a] :
( ( maps_a_list_a @ F @ nil_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(473,plain,
( ( ! [F: a > list_a] :
( ( maps_a_a @ F @ nil_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(474,plain,
( ( ! [F: list_list_a > list_list_a] :
( ( maps_l2025957947list_a @ F @ nil_list_list_a )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(475,plain,
( ( ! [F: list_list_a > list_a] :
( ( maps_list_list_a_a @ F @ nil_list_list_a )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(476,plain,
( ( ! [F: list_a > list_list_list_a] :
( ( maps_l755382343list_a @ F @ nil_list_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(477,plain,
( ( ! [F: a > list_list_list_a] :
( ( maps_a_list_list_a @ F @ nil_a )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(478,plain,
( ( ! [N: nat] :
( ( gen_length_list_a @ N @ nil_list_a )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(479,plain,
( ( ! [N: nat] :
( ( gen_length_a @ N @ nil_a )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(480,plain,
( ( ! [Y: list_a] :
~ ( member_list_a @ nil_list_a @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(481,plain,
( ( ! [Y: a] :
~ ( member_a @ nil_a @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(482,plain,
( ( ! [F: list_a > list_list_a] :
( ( bind_list_a_list_a @ nil_list_a @ F )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(483,plain,
( ( ! [F: list_a > list_a] :
( ( bind_list_a_a @ nil_list_a @ F )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(484,plain,
( ( ! [F: a > list_list_a] :
( ( bind_a_list_a @ nil_a @ F )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(485,plain,
( ( ! [F: a > list_a] :
( ( bind_a_a @ nil_a @ F )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(486,plain,
( ( ! [F: list_list_a > list_list_a] :
( ( bind_l94945665list_a @ nil_list_list_a @ F )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(487,plain,
( ( ! [F: list_list_a > list_a] :
( ( bind_list_list_a_a @ nil_list_list_a @ F )
= nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(488,plain,
( ( ! [F: list_a > list_list_list_a] :
( ( bind_l971853709list_a @ nil_list_a @ F )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(489,plain,
( ( ! [F: a > list_list_list_a] :
( ( bind_a_list_list_a @ nil_a @ F )
= nil_list_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(490,plain,
( ( ! [Xs: list_a,K: nat] :
( ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
=> ( ( listSl97544552lice_a @ Xs @ K )
= nil_list_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(491,plain,
( ( ! [P: list_a > $o] :
~ ( list_ex1_list_a @ P @ nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(492,plain,
( ( ! [P: a > $o] :
~ ( list_ex1_a @ P @ nil_a ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(493,plain,
( ( ( concat_a @ nil_list_a )
= nil_a )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(494,plain,
( ( ( concat_list_a @ nil_list_list_a )
= nil_list_a )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(495,plain,
( ( ! [Xs: list_a] :
( ( listSl97544552lice_a @ Xs @ zero_zero_nat )
= nil_list_a ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(496,plain,
( ( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a )
= $true ),
inference(polarity_switch,[status(thm)],[352]) ).
thf(497,plain,
( ( ! [M: nat,N: nat] :
( ( ( divide_divide_nat @ M @ N )
= zero_zero_nat )
= ( ( N = zero_zero_nat )
| ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(498,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ( divide_divide_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(499,plain,
( ( ! [P: nat > $o,N: nat] :
( ~ ( P @ N )
| ( P @ zero_zero_nat )
| ( ! [SY209: nat] :
( ~ ( ord_less_nat @ SY209 @ ( sK1_K3 @ N @ P ) )
| ~ ( P @ SY209 ) )
& ( ord_less_eq_nat @ ( sK1_K3 @ N @ P ) @ N )
& ( P @ ( sK1_K3 @ N @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(500,plain,
( ( ! [N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ( ( power_power_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(501,plain,
( ( ! [I2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ I2 )
| ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
| ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(502,plain,
( ( ! [A: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(503,plain,
( ( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( M3 != N3 )
& ( ord_less_eq_nat @ M3 @ N3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(504,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(505,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( M3 = N3 )
| ( ord_less_nat @ M3 @ N3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(506,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
| ( ord_less_eq_nat @ M @ N ) )
& ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(507,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_eq_nat @ M @ N )
| ( M = N )
| ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(508,plain,
( ( ! [F: nat > nat] :
( ( ( ord_less_nat @ ( sK2_I3 @ F ) @ ( sK3_SY210 @ F ) )
& ~ ( ord_less_nat @ ( F @ ( sK2_I3 @ F ) ) @ ( F @ ( sK3_SY210 @ F ) ) ) )
| ! [I2: nat,J: nat] :
( ~ ( ord_less_eq_nat @ I2 @ J )
| ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(509,plain,
( ( ! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
| ( A = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(510,plain,
( ( ord_less_eq_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(511,plain,
( ( ord_less_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(512,plain,
( ( ord_less_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(513,plain,
( ( ord_less_eq_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(514,plain,
( ( ! [A: nat] :
( ( A = zero_zero_nat )
| ! [N: nat] :
( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(515,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(516,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ! [X4: nat] :
( ~ ( P @ X4 )
| ~ ( member_nat @ X4 @ I ) )
| ( ! [SY211: nat] :
( ~ ( member_nat @ SY211 @ I )
| ~ ( ord_less_nat @ SY211 @ ( sK4_X3 @ P @ I ) )
| ~ ( P @ SY211 ) )
& ( P @ ( sK4_X3 @ P @ I ) )
& ( member_nat @ ( sK4_X3 @ P @ I ) @ I ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(517,plain,
( ( ! [K: nat,I: set_nat] :
( ~ ( member_nat @ K @ I )
| ! [P: nat > $o] :
( ~ ( P @ K )
| ( ! [SY212: nat] :
( ~ ( member_nat @ SY212 @ I )
| ~ ( ord_less_nat @ SY212 @ ( sK5_X3 @ P @ I @ K ) )
| ~ ( P @ SY212 ) )
& ( P @ ( sK5_X3 @ P @ I @ K ) )
& ( member_nat @ ( sK5_X3 @ P @ I @ K ) @ I ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(518,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
| ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(519,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(520,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[394]) ).
thf(521,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ( ! [SY213: nat] :
( ~ ( member_nat @ ( sK6_X3 @ P @ I ) @ I )
| ~ ( member_nat @ SY213 @ I )
| ~ ( ord_less_nat @ SY213 @ ( sK6_X3 @ P @ I ) )
| ( P @ SY213 ) )
& ~ ( P @ ( sK6_X3 @ P @ I ) ) )
| ! [A: nat] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(522,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ( ! [SY214: nat] :
( ~ ( member_nat @ ( sK7_X3 @ P @ I ) @ I )
| ~ ( member_nat @ SY214 @ I )
| ~ ( ord_less_nat @ SY214 @ ( sK7_X3 @ P @ I ) )
| ( P @ SY214 ) )
& ~ ( P @ ( sK7_X3 @ P @ I ) ) )
| ! [A: nat] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(523,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(524,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ P ) )
& ~ ( P @ ( sK8_N2 @ P ) )
& ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ ( sK8_N2 @ P ) )
| ( P @ SY215 ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(525,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(526,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(527,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(528,plain,
( ( ! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
= ( size_size_list_a @ Y ) )
| ( X != Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(529,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(530,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
| ( M != N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(531,plain,
( ( ! [S: nat,T: nat] :
( ~ ( ord_less_nat @ S @ T )
| ( S != T ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(532,plain,
( ( ! [P: nat > $o] :
( ( ! [SY216: nat] :
( ~ ( ord_less_nat @ SY216 @ ( sK9_N2 @ P ) )
| ( P @ SY216 ) )
& ~ ( P @ ( sK9_N2 @ P ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(533,plain,
( ( ! [P: nat > $o] :
( ( ~ ( P @ ( sK10_N2 @ P ) )
& ! [SY217: nat] :
( ~ ( ord_less_nat @ SY217 @ ( sK10_N2 @ P ) )
| ( P @ SY217 ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(534,plain,
( ( ! [X: nat,Y: nat] :
( ( X = Y )
| ( ord_less_nat @ X @ Y )
| ( ord_less_nat @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(535,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(536,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[422]) ).
thf(537,plain,
( ( ! [N: nat,Xs: list_list_list_a] :
( ~ ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
| ( Xs != nil_list_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[423]) ).
thf(538,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(539,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(540,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs )
= ( size_size_list_a @ Ys2 ) )
| ( Xs != Ys2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(541,plain,
( ( ! [N: nat] :
( ( size_size_list_a @ ( sK11_Xs2 @ N ) )
= N ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(542,plain,
( ( ! [P: list_a > $o] :
( ( ! [SY218: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY218 ) @ ( size_size_list_a @ ( sK12_Xs2 @ P ) ) )
| ( P @ SY218 ) )
& ~ ( P @ ( sK12_Xs2 @ P ) ) )
| ! [Xs: list_a] : ( P @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[430]) ).
thf(543,plain,
( ( ! [Xs: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
= ( Xs != nil_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[434]) ).
thf(544,plain,
( ( ! [Xs: list_list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
= ( Xs != nil_list_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[435]) ).
thf(545,plain,
( ( ! [Xs: list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
= ( Xs != nil_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[436]) ).
thf(546,plain,
( ( ! [Xs: list_list_a,K: nat] :
( ~ ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
| ( ( listSl162220270list_a @ Xs @ K )
= nil_list_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[445]) ).
thf(547,plain,
( ( ! [N: nat,Xs: list_a] :
( ~ ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
| ( Xs != nil_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[452]) ).
thf(548,plain,
( ( ! [N: nat,Xs: list_list_a] :
( ~ ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
| ( Xs != nil_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[453]) ).
thf(549,plain,
( ( ! [Xs: list_a,K: nat] :
( ~ ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
| ( ( listSl97544552lice_a @ Xs @ K )
= nil_list_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(550,plain,
( ( ! [Xs: list_a] :
( ( listSl97544552lice_a @ Xs @ zero_zero_nat )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(551,plain,
( ( ( concat_list_a @ nil_list_list_a )
= nil_list_a )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(552,plain,
( ( ( concat_a @ nil_list_a )
= nil_a )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(553,plain,
( ( ! [P: a > $o] :
~ ( list_ex1_a @ P @ nil_a ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(554,plain,
( ( ! [P: list_a > $o] :
~ ( list_ex1_list_a @ P @ nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(555,plain,
( ( ! [Xs: list_a,K: nat] :
( ~ ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
| ( ( listSl97544552lice_a @ Xs @ K )
= nil_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(556,plain,
( ( ! [F: a > list_list_list_a] :
( ( bind_a_list_list_a @ nil_a @ F )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(557,plain,
( ( ! [F: list_a > list_list_list_a] :
( ( bind_l971853709list_a @ nil_list_a @ F )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(558,plain,
( ( ! [F: list_list_a > list_a] :
( ( bind_list_list_a_a @ nil_list_list_a @ F )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(559,plain,
( ( ! [F: list_list_a > list_list_a] :
( ( bind_l94945665list_a @ nil_list_list_a @ F )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(560,plain,
( ( ! [F: a > list_a] :
( ( bind_a_a @ nil_a @ F )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(561,plain,
( ( ! [F: a > list_list_a] :
( ( bind_a_list_a @ nil_a @ F )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(562,plain,
( ( ! [F: list_a > list_a] :
( ( bind_list_a_a @ nil_list_a @ F )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(563,plain,
( ( ! [F: list_a > list_list_a] :
( ( bind_list_a_list_a @ nil_list_a @ F )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(564,plain,
( ( ! [Y: a] :
~ ( member_a @ nil_a @ Y ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(565,plain,
( ( ! [Y: list_a] :
~ ( member_list_a @ nil_list_a @ Y ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(566,plain,
( ( ! [N: nat] :
( ( gen_length_a @ N @ nil_a )
= N ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(567,plain,
( ( ! [N: nat] :
( ( gen_length_list_a @ N @ nil_list_a )
= N ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(568,plain,
( ( ! [F: a > list_list_list_a] :
( ( maps_a_list_list_a @ F @ nil_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(569,plain,
( ( ! [F: list_a > list_list_list_a] :
( ( maps_l755382343list_a @ F @ nil_list_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(570,plain,
( ( ! [F: list_list_a > list_a] :
( ( maps_list_list_a_a @ F @ nil_list_list_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(571,plain,
( ( ! [F: list_list_a > list_list_a] :
( ( maps_l2025957947list_a @ F @ nil_list_list_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(572,plain,
( ( ! [F: a > list_a] :
( ( maps_a_a @ F @ nil_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(573,plain,
( ( ! [F: a > list_list_a] :
( ( maps_a_list_a @ F @ nil_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(574,plain,
( ( ! [F: list_a > list_a] :
( ( maps_list_a_a @ F @ nil_list_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(575,plain,
( ( ! [F: list_a > list_list_a] :
( ( maps_list_a_list_a @ F @ nil_list_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(576,plain,
( ( null_a @ nil_a )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(577,plain,
( ( null_list_a @ nil_list_a )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(578,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(579,plain,
( ( ! [Xs: list_list_a] :
( ( Xs = nil_list_a )
= ( null_list_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(580,plain,
( ( ! [F: a > option_a] :
( ( map_filter_a_a @ F @ nil_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(581,plain,
( ( ! [F: a > option_list_a] :
( ( map_filter_a_list_a @ F @ nil_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(582,plain,
( ( ! [F: a > option_list_list_a] :
( ( map_fi2089402454list_a @ F @ nil_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(583,plain,
( ( ! [F: list_a > option_a] :
( ( map_filter_list_a_a @ F @ nil_list_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(584,plain,
( ( ! [F: list_a > option_list_a] :
( ( map_fi461586634list_a @ F @ nil_list_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(585,plain,
( ( ! [F: list_a > option_list_list_a] :
( ( map_fi1090123216list_a @ F @ nil_list_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(586,plain,
( ( ! [F: list_list_a > option_a] :
( ( map_fi1574988606st_a_a @ F @ nil_list_list_a )
= nil_a ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(587,plain,
( ( ! [F: list_list_a > option_list_a] :
( ( map_fi213215172list_a @ F @ nil_list_list_a )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(588,plain,
( ( ! [Xs: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(589,plain,
( ( ! [Xs: list_a] :
( ( ( size_size_list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(590,plain,
( ( ( size_s1427607542list_a @ nil_list_a )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(591,plain,
( ( ( size_size_list_a @ nil_a )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(592,plain,
( ( ! [N: nat,Xs: list_list_a] :
( ~ ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
| ( Xs != nil_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(593,plain,
( ( ! [N: nat,Xs: list_a] :
( ~ ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
| ( Xs != nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(594,plain,
( ( ! [Xs: list_a,K: nat] :
( ( listSl1495374126_aux_a @ Xs @ K @ zero_zero_nat )
= nil_list_a ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(595,plain,
( ( ! [Y: a] :
( ( count_list_a @ nil_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(596,plain,
( ( ! [Y: list_a] :
( ( count_list_list_a @ nil_list_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(597,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(598,plain,
( ( ! [Xs: list_list_a] :
( ( listSl162220270list_a @ Xs @ zero_zero_nat )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(599,plain,
( ( ! [P: list_list_a > $o] :
~ ( list_ex1_list_list_a @ P @ nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(600,plain,
( ( ! [Xs: list_list_a,K: nat] :
( ~ ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
| ( ( listSl162220270list_a @ Xs @ K )
= nil_list_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(601,plain,
( ( ! [F: list_list_a > list_list_list_a] :
( ( bind_l311701255list_a @ nil_list_list_a @ F )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(602,plain,
( ( ! [Y: list_list_a] :
~ ( member_list_list_a @ nil_list_list_a @ Y ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(603,plain,
( ( ! [N: nat] :
( ( gen_le840878749list_a @ N @ nil_list_list_a )
= N ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(604,plain,
( ( ! [F: list_list_a > list_list_list_a] :
( ( maps_l57963201list_a @ F @ nil_list_list_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(605,plain,
( ( null_list_list_a @ nil_list_list_a )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(606,plain,
( ( ! [Xs: list_list_list_a] :
( ( Xs = nil_list_list_a )
= ( null_list_list_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(607,plain,
( ( ! [F: list_list_a > option_list_list_a] :
( ( map_fi824137674list_a @ F @ nil_list_list_a )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(608,plain,
( ( ! [Xs: list_list_list_a] :
( ( ( size_s575106428list_a @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(609,plain,
( ( ! [Xs: list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
= ( Xs != nil_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(610,plain,
( ( ! [Xs: list_list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
= ( Xs != nil_list_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(611,plain,
( ( ! [Xs: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
= ( Xs != nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(612,plain,
( ( ( size_s575106428list_a @ nil_list_list_a )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(613,plain,
( ( size_s1427607542list_a
= ( gen_length_list_a @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(614,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(615,plain,
( ( ! [P: list_a > $o] :
( ( ! [SY218: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY218 ) @ ( size_size_list_a @ ( sK12_Xs2 @ P ) ) )
| ( P @ SY218 ) )
& ~ ( P @ ( sK12_Xs2 @ P ) ) )
| ! [Xs: list_a] : ( P @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(616,plain,
( ( ! [N: nat] :
( ( size_size_list_a @ ( sK11_Xs2 @ N ) )
= N ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(617,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs )
= ( size_size_list_a @ Ys2 ) )
| ( Xs != Ys2 ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(618,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(619,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(620,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(621,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(622,plain,
( ( ! [N: nat,Xs: list_list_list_a] :
( ~ ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
| ( Xs != nil_list_list_a ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(623,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(624,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(625,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(626,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(627,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(628,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(629,plain,
( ( ! [X: nat,Y: nat] :
( ( X = Y )
| ( ord_less_nat @ X @ Y )
| ( ord_less_nat @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(630,plain,
( ( ! [P: nat > $o] :
( ( ~ ( P @ ( sK10_N2 @ P ) )
& ! [SY217: nat] :
( ~ ( ord_less_nat @ SY217 @ ( sK10_N2 @ P ) )
| ( P @ SY217 ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(631,plain,
( ( ! [P: nat > $o] :
( ( ! [SY216: nat] :
( ~ ( ord_less_nat @ SY216 @ ( sK9_N2 @ P ) )
| ( P @ SY216 ) )
& ~ ( P @ ( sK9_N2 @ P ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(632,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(633,plain,
( ( ! [S: nat,T: nat] :
( ~ ( ord_less_nat @ S @ T )
| ( S != T ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(634,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
| ( M != N ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(635,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(636,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(637,plain,
( ( ! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
= ( size_size_list_a @ Y ) )
| ( X != Y ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(638,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(639,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(640,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(641,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(642,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(643,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ P ) )
& ~ ( P @ ( sK8_N2 @ P ) )
& ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ ( sK8_N2 @ P ) )
| ( P @ SY215 ) ) )
| ! [N: nat] : ( P @ N ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(644,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(645,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(646,plain,
( ( ! [Xs: list_list_a,K: nat] :
( ( listSl856612276list_a @ Xs @ K @ zero_zero_nat )
= nil_list_list_a ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(647,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(648,plain,
( ( ! [Y: list_list_a] :
( ( count_429956358list_a @ nil_list_list_a @ Y )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(649,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ( ! [SY214: nat] :
( ~ ( member_nat @ ( sK7_X3 @ P @ I ) @ I )
| ~ ( member_nat @ SY214 @ I )
| ~ ( ord_less_nat @ SY214 @ ( sK7_X3 @ P @ I ) )
| ( P @ SY214 ) )
& ~ ( P @ ( sK7_X3 @ P @ I ) ) )
| ! [A: nat] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(650,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ( ! [SY213: nat] :
( ~ ( member_nat @ ( sK6_X3 @ P @ I ) @ I )
| ~ ( member_nat @ SY213 @ I )
| ~ ( ord_less_nat @ SY213 @ ( sK6_X3 @ P @ I ) )
| ( P @ SY213 ) )
& ~ ( P @ ( sK6_X3 @ P @ I ) ) )
| ! [A: nat] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(651,plain,
$true = $true,
inference(copy,[status(thm)],[520]) ).
thf(652,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(653,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(654,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(655,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(656,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(657,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(658,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
| ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(659,plain,
( ( ! [K: nat,I: set_nat] :
( ~ ( member_nat @ K @ I )
| ! [P: nat > $o] :
( ~ ( P @ K )
| ( ! [SY212: nat] :
( ~ ( member_nat @ SY212 @ I )
| ~ ( ord_less_nat @ SY212 @ ( sK5_X3 @ P @ I @ K ) )
| ~ ( P @ SY212 ) )
& ( P @ ( sK5_X3 @ P @ I @ K ) )
& ( member_nat @ ( sK5_X3 @ P @ I @ K ) @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(660,plain,
( ( ! [I: set_nat,P: nat > $o] :
( ! [X4: nat] :
( ~ ( P @ X4 )
| ~ ( member_nat @ X4 @ I ) )
| ( ! [SY211: nat] :
( ~ ( member_nat @ SY211 @ I )
| ~ ( ord_less_nat @ SY211 @ ( sK4_X3 @ P @ I ) )
| ~ ( P @ SY211 ) )
& ( P @ ( sK4_X3 @ P @ I ) )
& ( member_nat @ ( sK4_X3 @ P @ I ) @ I ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(661,plain,
( ( listSl97544552lice_a
= ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(662,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(663,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(664,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(665,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(666,plain,
( ( ! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(667,plain,
( ( ! [A: nat] :
( ( A = zero_zero_nat )
| ! [N: nat] :
( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(668,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(669,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(670,plain,
( ( ord_less_eq_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(671,plain,
( ( ord_less_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(672,plain,
( ( ord_less_nat
= ( ^ [A3: nat,N3: nat] :
! [X2: nat] :
( ( ord_less_eq_nat @ X2 @ A3 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(673,plain,
( ( ord_less_eq_nat
= ( ^ [N3: nat,A3: nat] :
! [X2: nat] :
( ( ord_less_nat @ A3 @ X2 )
=> ( N3 != X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(674,plain,
( ( ! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
| ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(675,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(676,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(677,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(678,plain,
( ( ! [F: nat > nat] :
( ( ( ord_less_nat @ ( sK2_I3 @ F ) @ ( sK3_SY210 @ F ) )
& ~ ( ord_less_nat @ ( F @ ( sK2_I3 @ F ) ) @ ( F @ ( sK3_SY210 @ F ) ) ) )
| ! [I2: nat,J: nat] :
( ~ ( ord_less_eq_nat @ I2 @ J )
| ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(679,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_eq_nat @ M @ N )
| ( M = N )
| ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(680,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
| ( ord_less_eq_nat @ M @ N ) )
& ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(681,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( M3 = N3 )
| ( ord_less_nat @ M3 @ N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(682,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(683,plain,
( ( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( M3 != N3 )
& ( ord_less_eq_nat @ M3 @ N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(684,plain,
( ( ! [A: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(685,plain,
( ( ! [I2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ I2 )
| ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
| ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(686,plain,
( ( ! [N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ( ( power_power_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(687,plain,
( ( ! [P: nat > $o,N: nat] :
( ~ ( P @ N )
| ( P @ zero_zero_nat )
| ( ! [SY209: nat] :
( ~ ( ord_less_nat @ SY209 @ ( sK1_K3 @ N @ P ) )
| ~ ( P @ SY209 ) )
& ( ord_less_eq_nat @ ( sK1_K3 @ N @ P ) @ N )
& ( P @ ( sK1_K3 @ N @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(688,plain,
( ( ! [Xs: list_a,X: a] : ( ord_less_eq_nat @ ( count_list_a @ Xs @ X ) @ ( size_size_list_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(689,plain,
( ( ! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(690,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( ( divide_divide_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(691,plain,
( ( ! [M: nat,N: nat] :
( ( ( divide_divide_nat @ M @ N )
= zero_zero_nat )
= ( ( N = zero_zero_nat )
| ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(692,plain,
( ( ! [N: nat,M: nat] :
( ( ( divide_divide_nat @ N @ M )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(693,plain,
( ( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(694,plain,
( ( ! [SX0: nat > $o] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SX0 ) )
| ~ ~ ( ~ ~ ( SX0 @ ( sK8_N2 @ SX0 ) )
| ~ ! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( sK8_N2 @ SX0 ) )
| ( SX0 @ SX1 ) ) ) )
| ! [SX1: nat] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(695,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(696,plain,
( ( ! [SX0: nat,SX1: set_nat] :
( ~ ( member_nat @ SX0 @ SX1 )
| ! [SX2: nat > $o] :
( ~ ( SX2 @ SX0 )
| ~ ( ~ ! [SX3: nat] :
( ~ ( member_nat @ SX3 @ SX1 )
| ~ ( ord_less_nat @ SX3 @ ( sK5_X3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( SX2 @ SX3 ) )
| ~ ~ ( ~ ( SX2 @ ( sK5_X3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member_nat @ ( sK5_X3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(697,plain,
( ( ! [SX0: nat > $o] :
( ~ ( ~ ~ ( SX0 @ ( sK10_N2 @ SX0 ) )
| ~ ! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( sK10_N2 @ SX0 ) )
| ( SX0 @ SX1 ) ) )
| ! [SX1: nat] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(698,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(699,plain,
( ( ! [SX0: nat > nat] :
( ~ ( ~ ( ord_less_nat @ ( sK2_I3 @ SX0 ) @ ( sK3_SY210 @ SX0 ) )
| ~ ~ ( ord_less_nat @ ( SX0 @ ( sK2_I3 @ SX0 ) ) @ ( SX0 @ ( sK3_SY210 @ SX0 ) ) ) )
| ! [SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(700,plain,
( ( ! [SX0: nat > $o] :
( ~ ( ~ ! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( sK9_N2 @ SX0 ) )
| ( SX0 @ SX1 ) )
| ~ ~ ( SX0 @ ( sK9_N2 @ SX0 ) ) )
| ! [SX1: nat] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(701,plain,
( ( ! [SX0: set_nat,SX1: nat > $o] :
( ! [SX2: nat] :
( ~ ( SX1 @ SX2 )
| ~ ( member_nat @ SX2 @ SX0 ) )
| ~ ( ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX0 )
| ~ ( ord_less_nat @ SX2 @ ( sK4_X3 @ SX1 @ SX0 ) )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ( ~ ( SX1 @ ( sK4_X3 @ SX1 @ SX0 ) )
| ~ ( member_nat @ ( sK4_X3 @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(702,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ( SX1 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(703,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat )
= ( ~ ( ( SX0 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(704,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( ~ ! [SX1: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SX1 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SX0 ) ) )
| ( SX0 @ SX1 ) )
| ~ ~ ( SX0 @ ( sK12_Xs2 @ SX0 ) ) )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(705,plain,
( ( ! [SX0: set_nat,SX1: nat > $o] :
( ~ ( ~ ! [SX2: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SX1 @ SX0 ) @ SX0 )
| ~ ( member_nat @ SX2 @ SX0 )
| ~ ( ord_less_nat @ SX2 @ ( sK6_X3 @ SX1 @ SX0 ) )
| ( SX1 @ SX2 ) )
| ~ ~ ( SX1 @ ( sK6_X3 @ SX1 @ SX0 ) ) )
| ! [SX2: nat] : ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(706,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ zero_zero_nat )
| ~ ( ~ ~ ( ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( sK1_K3 @ SX1 @ SX0 ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( SX0 @ ( sK1_K3 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(707,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(708,plain,
( ( ! [SX0: set_nat,SX1: nat > $o] :
( ~ ( ~ ! [SX2: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SX1 @ SX0 ) @ SX0 )
| ~ ( member_nat @ SX2 @ SX0 )
| ~ ( ord_less_nat @ SX2 @ ( sK7_X3 @ SX1 @ SX0 ) )
| ( SX1 @ SX2 ) )
| ~ ~ ( SX1 @ ( sK7_X3 @ SX1 @ SX0 ) ) )
| ! [SX2: nat] : ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(709,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( SX0 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(710,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_nat @ SX1 @ SX2 )
| ( SX0 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(711,plain,
! [SV1: list_a] :
( ( ( listSl97544552lice_a @ SV1 @ zero_zero_nat )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(712,plain,
! [SV2: a > $o] :
( ( ~ ( list_ex1_a @ SV2 @ nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(713,plain,
! [SV3: list_a > $o] :
( ( ~ ( list_ex1_list_a @ SV3 @ nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(714,plain,
! [SV4: list_a] :
( ( ! [SY219: nat] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SV4 ) @ SY219 )
| ( ( listSl97544552lice_a @ SV4 @ SY219 )
= nil_list_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(715,plain,
! [SV5: a > list_list_list_a] :
( ( ( bind_a_list_list_a @ nil_a @ SV5 )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(716,plain,
! [SV6: list_a > list_list_list_a] :
( ( ( bind_l971853709list_a @ nil_list_a @ SV6 )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(717,plain,
! [SV7: list_list_a > list_a] :
( ( ( bind_list_list_a_a @ nil_list_list_a @ SV7 )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(718,plain,
! [SV8: list_list_a > list_list_a] :
( ( ( bind_l94945665list_a @ nil_list_list_a @ SV8 )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(719,plain,
! [SV9: a > list_a] :
( ( ( bind_a_a @ nil_a @ SV9 )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(720,plain,
! [SV10: a > list_list_a] :
( ( ( bind_a_list_a @ nil_a @ SV10 )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(721,plain,
! [SV11: list_a > list_a] :
( ( ( bind_list_a_a @ nil_list_a @ SV11 )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(722,plain,
! [SV12: list_a > list_list_a] :
( ( ( bind_list_a_list_a @ nil_list_a @ SV12 )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(723,plain,
! [SV13: a] :
( ( ~ ( member_a @ nil_a @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(724,plain,
! [SV14: list_a] :
( ( ~ ( member_list_a @ nil_list_a @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(725,plain,
! [SV15: nat] :
( ( ( gen_length_a @ SV15 @ nil_a )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(726,plain,
! [SV16: nat] :
( ( ( gen_length_list_a @ SV16 @ nil_list_a )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(727,plain,
! [SV17: a > list_list_list_a] :
( ( ( maps_a_list_list_a @ SV17 @ nil_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(728,plain,
! [SV18: list_a > list_list_list_a] :
( ( ( maps_l755382343list_a @ SV18 @ nil_list_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(729,plain,
! [SV19: list_list_a > list_a] :
( ( ( maps_list_list_a_a @ SV19 @ nil_list_list_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(730,plain,
! [SV20: list_list_a > list_list_a] :
( ( ( maps_l2025957947list_a @ SV20 @ nil_list_list_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(731,plain,
! [SV21: a > list_a] :
( ( ( maps_a_a @ SV21 @ nil_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(732,plain,
! [SV22: a > list_list_a] :
( ( ( maps_a_list_a @ SV22 @ nil_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(733,plain,
! [SV23: list_a > list_a] :
( ( ( maps_list_a_a @ SV23 @ nil_list_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(734,plain,
! [SV24: list_a > list_list_a] :
( ( ( maps_list_a_list_a @ SV24 @ nil_list_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(735,plain,
! [SV25: list_a] :
( ( ( SV25 = nil_a )
= ( null_a @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(736,plain,
! [SV26: list_list_a] :
( ( ( SV26 = nil_list_a )
= ( null_list_a @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(737,plain,
! [SV27: a > option_a] :
( ( ( map_filter_a_a @ SV27 @ nil_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(738,plain,
! [SV28: a > option_list_a] :
( ( ( map_filter_a_list_a @ SV28 @ nil_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(739,plain,
! [SV29: a > option_list_list_a] :
( ( ( map_fi2089402454list_a @ SV29 @ nil_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(740,plain,
! [SV30: list_a > option_a] :
( ( ( map_filter_list_a_a @ SV30 @ nil_list_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(741,plain,
! [SV31: list_a > option_list_a] :
( ( ( map_fi461586634list_a @ SV31 @ nil_list_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(742,plain,
! [SV32: list_a > option_list_list_a] :
( ( ( map_fi1090123216list_a @ SV32 @ nil_list_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(743,plain,
! [SV33: list_list_a > option_a] :
( ( ( map_fi1574988606st_a_a @ SV33 @ nil_list_list_a )
= nil_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(744,plain,
! [SV34: list_list_a > option_list_a] :
( ( ( map_fi213215172list_a @ SV34 @ nil_list_list_a )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(745,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= ( SV35 = nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(746,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= ( SV36 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(747,plain,
! [SV37: nat] :
( ( ! [SY220: list_list_a] :
( ~ ( ord_less_nat @ SV37 @ ( size_s1427607542list_a @ SY220 ) )
| ( SY220 != nil_list_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(748,plain,
! [SV38: nat] :
( ( ! [SY221: list_a] :
( ~ ( ord_less_nat @ SV38 @ ( size_size_list_a @ SY221 ) )
| ( SY221 != nil_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(749,plain,
! [SV39: list_a] :
( ( ! [SY222: nat] :
( ( listSl1495374126_aux_a @ SV39 @ SY222 @ zero_zero_nat )
= nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(750,plain,
! [SV40: a] :
( ( ( count_list_a @ nil_a @ SV40 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(751,plain,
! [SV41: list_a] :
( ( ( count_list_list_a @ nil_list_a @ SV41 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(752,plain,
! [SV42: $o] :
( ( ( SV42 = $true )
| ( SV42 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[597]) ).
thf(753,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[597]) ).
thf(754,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[597]) ).
thf(755,plain,
! [SV43: list_list_a] :
( ( ( listSl162220270list_a @ SV43 @ zero_zero_nat )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(756,plain,
! [SV44: list_list_a > $o] :
( ( ~ ( list_ex1_list_list_a @ SV44 @ nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(757,plain,
! [SV45: list_list_a] :
( ( ! [SY223: nat] :
( ~ ( ord_less_nat @ ( size_s1427607542list_a @ SV45 ) @ SY223 )
| ( ( listSl162220270list_a @ SV45 @ SY223 )
= nil_list_list_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(758,plain,
! [SV46: list_list_a > list_list_list_a] :
( ( ( bind_l311701255list_a @ nil_list_list_a @ SV46 )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(759,plain,
! [SV47: list_list_a] :
( ( ~ ( member_list_list_a @ nil_list_list_a @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(760,plain,
! [SV48: nat] :
( ( ( gen_le840878749list_a @ SV48 @ nil_list_list_a )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(761,plain,
! [SV49: list_list_a > list_list_list_a] :
( ( ( maps_l57963201list_a @ SV49 @ nil_list_list_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(762,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 = nil_list_list_a )
= ( null_list_list_a @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(763,plain,
! [SV51: list_list_a > option_list_list_a] :
( ( ( map_fi824137674list_a @ SV51 @ nil_list_list_a )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(764,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= ( SV52 = nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(765,plain,
! [SV53: list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= ( SV53 != nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(766,plain,
! [SV54: list_list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= ( SV54 != nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(767,plain,
! [SV55: list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= ( SV55 != nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(768,plain,
( ( ! [SV56: list_list_a] :
( ( size_s1427607542list_a @ SV56 )
= ( gen_length_list_a @ zero_zero_nat @ SV56 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[613]) ).
thf(769,plain,
( ( size_s1427607542list_a
= ( gen_length_list_a @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[613]) ).
thf(770,plain,
( ( ! [SV57: list_a] :
( ( size_size_list_a @ SV57 )
= ( gen_length_a @ zero_zero_nat @ SV57 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(771,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(772,plain,
! [SV58: nat] :
( ( ( size_size_list_a @ ( sK11_Xs2 @ SV58 ) )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(773,plain,
! [SV59: list_a] :
( ( ! [SY224: list_a] :
( ( ( size_size_list_a @ SV59 )
= ( size_size_list_a @ SY224 ) )
| ( SV59 != SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(774,plain,
! [SV60: nat] :
( ( ( SV60 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(775,plain,
! [SV61: nat] :
( ( ~ ( ord_less_nat @ SV61 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(776,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(777,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= ( SV63 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(778,plain,
! [SV64: nat] :
( ( ! [SY225: list_list_list_a] :
( ~ ( ord_less_nat @ SV64 @ ( size_s575106428list_a @ SY225 ) )
| ( SY225 != nil_list_list_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(779,plain,
! [SV65: nat] :
( ( ( SV65 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(780,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= ( SV66 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(781,plain,
! [SV67: nat] :
( ( ~ ( ord_less_nat @ SV67 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(782,plain,
! [SV68: nat] :
( ( ~ ( ord_less_nat @ SV68 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(783,plain,
! [SV69: nat] :
( ( ! [SY226: nat] :
( ~ ( ord_less_nat @ SV69 @ SY226 )
| ( SY226 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(784,plain,
! [SV70: nat] :
( ( ( zero_zero_nat = SV70 )
= ( SV70 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(785,plain,
! [SV71: nat] :
( ( ! [SY227: nat] :
( ( SV71 = SY227 )
| ( ord_less_nat @ SV71 @ SY227 )
| ( ord_less_nat @ SY227 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(786,plain,
! [SV72: nat] :
( ( ~ ( ord_less_nat @ SV72 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(787,plain,
! [SV73: nat] :
( ( ! [SY228: nat] :
( ~ ( ord_less_nat @ SV73 @ SY228 )
| ( SV73 != SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(788,plain,
! [SV74: nat] :
( ( ! [SY229: nat] :
( ~ ( ord_less_nat @ SV74 @ SY229 )
| ( SY229 != SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(789,plain,
! [SV75: nat] :
( ( ~ ( ord_less_nat @ SV75 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(790,plain,
! [SV76: nat] :
( ( ! [SY230: nat] :
( ( SV76 != SY230 )
= ( ( ord_less_nat @ SV76 @ SY230 )
| ( ord_less_nat @ SY230 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(791,plain,
! [SV77: list_a] :
( ( ! [SY231: list_a] :
( ( ( size_size_list_a @ SV77 )
= ( size_size_list_a @ SY231 ) )
| ( SV77 != SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(792,plain,
! [SV78: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= ( SV78 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(793,plain,
! [SV79: nat] :
( ( ! [SY232: nat] :
( ~ ( ord_less_nat @ SV79 @ SY232 )
| ( SY232 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(794,plain,
! [SV80: nat] :
( ( ~ ( ord_less_nat @ SV80 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(795,plain,
! [SV81: nat] :
( ( ( SV81 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(796,plain,
! [SV82: nat] :
( ( ~ ( ord_less_nat @ SV82 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(797,plain,
! [SV83: nat] :
( ( ! [SY233: nat] :
( ~ ( ord_less_nat @ SV83 @ SY233 )
| ( ord_less_nat @ zero_zero_nat @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(798,plain,
( ( ord_less_nat @ zero_zero_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(799,plain,
! [SV84: list_list_a] :
( ( ! [SY234: nat] :
( ( listSl856612276list_a @ SV84 @ SY234 @ zero_zero_nat )
= nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(800,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(801,plain,
! [SV86: list_list_a] :
( ( ( count_429956358list_a @ nil_list_list_a @ SV86 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(802,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= ( zero_zero_nat = SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(803,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= ( SV88 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(804,plain,
! [SV89: nat] :
( ( ! [SY235: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SY235 ) )
= ( ord_less_nat @ SV89 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(805,plain,
! [SV90: nat] :
( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV90 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(806,plain,
! [SV91: nat] :
( ( ! [SY236: nat] :
( ~ ( ord_less_nat @ SV91 @ SY236 )
| ( ord_less_nat @ ( semiri1382578993at_nat @ SV91 ) @ ( semiri1382578993at_nat @ SY236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(807,plain,
! [SV92: nat] :
( ( ! [SY237: nat] :
( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV92 ) @ ( semiri1382578993at_nat @ SY237 ) )
| ( ord_less_nat @ SV92 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(808,plain,
( ( ! [SV93: list_a] :
( ( listSl97544552lice_a @ SV93 )
= ( ^ [SY238: nat] : ( listSl1495374126_aux_a @ SV93 @ SY238 @ ( divide_divide_nat @ ( size_size_list_a @ SV93 ) @ SY238 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(809,plain,
( ( listSl97544552lice_a
= ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(810,plain,
! [SV94: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(811,plain,
! [SV95: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(812,plain,
! [SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= ( SV96 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(813,plain,
! [SV97: nat] :
( ( ! [SY239: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SY239 ) )
= ( ( SY239 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(814,plain,
! [SV98: nat] :
( ( ( SV98 = zero_zero_nat )
| ! [SY240: nat] :
( ( power_power_nat @ SV98 @ SY240 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(815,plain,
! [SV99: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV99 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(816,plain,
! [SV100: nat] :
( ( ~ ( ord_less_eq_nat @ SV100 @ zero_zero_nat )
| ( SV100 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(817,plain,
! [SV101: nat] :
( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= ( SV101 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(818,plain,
! [SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= ( SV102 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(819,plain,
! [SV103: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV103 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(820,plain,
! [SV104: nat] :
( ( ! [SY241: nat] :
( ~ ( ord_less_eq_nat @ SV104 @ SY241 )
| ( SV104 = SY241 )
| ( ord_less_nat @ SV104 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(821,plain,
( ( ! [SV105: nat] :
( ( ord_less_eq_nat @ SV105 )
= ( ^ [SY242: nat] :
( ( SV105 = SY242 )
| ( ord_less_nat @ SV105 @ SY242 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[681]) ).
thf(822,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( M3 = N3 )
| ( ord_less_nat @ M3 @ N3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[681]) ).
thf(823,plain,
! [SV106: nat] :
( ( ! [SY243: nat] :
( ~ ( ord_less_nat @ SV106 @ SY243 )
| ( ord_less_eq_nat @ SV106 @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(824,plain,
! [SV107: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV107 )
| ! [SY244: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV107 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(825,plain,
! [SV108: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV108 )
| ! [SY245: nat,SY246: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SY245 ) @ ( power_power_nat @ SV108 @ SY246 ) )
| ( ord_less_nat @ SY245 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(826,plain,
! [SV109: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV109 )
| ( ( power_power_nat @ zero_zero_nat @ SV109 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(827,plain,
! [SV110: list_a] :
( ( ! [SY247: a] : ( ord_less_eq_nat @ ( count_list_a @ SV110 @ SY247 ) @ ( size_size_list_a @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(828,plain,
! [SV111: list_a] :
( ( ! [SY248: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ SV111 @ SY248 ) )
= ( divide_divide_nat @ ( size_size_list_a @ SV111 ) @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(829,plain,
! [SV112: nat] :
( ( ! [SY249: nat] :
( ~ ( ord_less_nat @ SV112 @ SY249 )
| ( ( divide_divide_nat @ SV112 @ SY249 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(830,plain,
! [SV113: nat] :
( ( ! [SY250: nat] :
( ( ( divide_divide_nat @ SV113 @ SY250 )
= zero_zero_nat )
= ( ( SY250 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(831,plain,
! [SV114: nat] :
( ( ! [SY251: nat] :
( ( ( divide_divide_nat @ SV114 @ SY251 )
= zero_zero_nat )
= ( ( SY251 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(832,plain,
( ( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(833,plain,
! [SV115: nat > $o] :
( ( ~ ( SV115 @ zero_zero_nat )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
| ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
| ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(834,plain,
( ( ! [SV116: nat] :
( ( ord_less_eq_nat @ SV116 )
= ( ^ [SY254: nat] :
! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV116 )
| ( SY254 != SY255 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(835,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 != SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(836,plain,
! [SV117: nat] :
( ( ! [SY256: set_nat] :
( ~ ( member_nat @ SV117 @ SY256 )
| ! [SY257: nat > $o] :
( ~ ( SY257 @ SV117 )
| ~ ( ~ ! [SY258: nat] :
( ~ ( member_nat @ SY258 @ SY256 )
| ~ ( ord_less_nat @ SY258 @ ( sK5_X3 @ SY257 @ SY256 @ SV117 ) )
| ~ ( SY257 @ SY258 ) )
| ~ ~ ( ~ ( SY257 @ ( sK5_X3 @ SY257 @ SY256 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SY257 @ SY256 @ SV117 ) @ SY256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(837,plain,
! [SV118: nat > $o] :
( ( ~ ( ~ ~ ( SV118 @ ( sK10_N2 @ SV118 ) )
| ~ ! [SY259: nat] :
( ~ ( ord_less_nat @ SY259 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SY259 ) ) )
| ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(838,plain,
( ( ! [SV119: nat] :
( ( ord_less_nat @ SV119 )
= ( ^ [SY261: nat] :
~ ( ~ ( ( SV119 != SY261 ) )
| ~ ( ord_less_eq_nat @ SV119 @ SY261 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(839,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(840,plain,
! [SV120: nat > nat] :
( ( ~ ( ~ ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
| ~ ~ ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) ) )
| ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(841,plain,
! [SV121: nat > $o] :
( ( ~ ( ~ ! [SY264: nat] :
( ~ ( ord_less_nat @ SY264 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SY264 ) )
| ~ ~ ( SV121 @ ( sK9_N2 @ SV121 ) ) )
| ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(842,plain,
! [SV122: set_nat] :
( ( ! [SY266: nat > $o] :
( ! [SY267: nat] :
( ~ ( SY266 @ SY267 )
| ~ ( member_nat @ SY267 @ SV122 ) )
| ~ ( ~ ! [SY268: nat] :
( ~ ( member_nat @ SY268 @ SV122 )
| ~ ( ord_less_nat @ SY268 @ ( sK4_X3 @ SY266 @ SV122 ) )
| ~ ( SY266 @ SY268 ) )
| ~ ~ ( ~ ( SY266 @ ( sK4_X3 @ SY266 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SY266 @ SV122 ) @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(843,plain,
( ( ! [SV123: nat] :
( ( ord_less_nat @ SV123 )
= ( ^ [SY269: nat] :
! [SY270: nat] :
( ~ ( ord_less_eq_nat @ SY270 @ SV123 )
| ( SY269 != SY270 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[702]) ).
thf(844,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ( SX1 != SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[702]) ).
thf(845,plain,
! [SV124: nat] :
( ( ! [SY271: nat] :
( ( ( power_power_nat @ SV124 @ SY271 )
= zero_zero_nat )
= ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(846,plain,
! [SV125: list_a > $o] :
( ( ~ ( ~ ! [SY272: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY272 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SY272 ) )
| ~ ~ ( SV125 @ ( sK12_Xs2 @ SV125 ) ) )
| ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(847,plain,
! [SV126: set_nat] :
( ( ! [SY274: nat > $o] :
( ~ ( ~ ! [SY275: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SY274 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY275 @ SV126 )
| ~ ( ord_less_nat @ SY275 @ ( sK6_X3 @ SY274 @ SV126 ) )
| ( SY274 @ SY275 ) )
| ~ ~ ( SY274 @ ( sK6_X3 @ SY274 @ SV126 ) ) )
| ! [SX2: nat] : ( SY274 @ SX2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(848,plain,
! [SV127: nat > $o] :
( ( ! [SY277: nat] :
( ~ ( SV127 @ SY277 )
| ( SV127 @ zero_zero_nat )
| ~ ( ~ ~ ( ~ ! [SY278: nat] :
( ~ ( ord_less_nat @ SY278 @ ( sK1_K3 @ SY277 @ SV127 ) )
| ~ ( SV127 @ SY278 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SY277 @ SV127 ) @ SY277 ) )
| ~ ( SV127 @ ( sK1_K3 @ SY277 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(849,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(850,plain,
! [SV128: set_nat] :
( ( ! [SY279: nat > $o] :
( ~ ( ~ ! [SY280: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SY279 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY280 @ SV128 )
| ~ ( ord_less_nat @ SY280 @ ( sK7_X3 @ SY279 @ SV128 ) )
| ( SY279 @ SY280 ) )
| ~ ~ ( SY279 @ ( sK7_X3 @ SY279 @ SV128 ) ) )
| ! [SX2: nat] : ( SY279 @ SX2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(851,plain,
( ( ! [SV129: nat] :
( ( ord_less_nat @ SV129 )
= ( ^ [SY282: nat] :
! [SY283: nat] :
( ~ ( ord_less_eq_nat @ SY282 @ SY283 )
| ( SV129 != SY283 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[709]) ).
thf(852,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( SX0 != SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[709]) ).
thf(853,plain,
( ( ! [SV130: nat] :
( ( ord_less_eq_nat @ SV130 )
= ( ^ [SY284: nat] :
! [SY285: nat] :
( ~ ( ord_less_nat @ SY284 @ SY285 )
| ( SV130 != SY285 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(854,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
! [SX2: nat] :
( ~ ( ord_less_nat @ SX1 @ SX2 )
| ( SX0 != SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(855,plain,
! [SV2: a > $o] :
( ( list_ex1_a @ SV2 @ nil_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(856,plain,
! [SV3: list_a > $o] :
( ( list_ex1_list_a @ SV3 @ nil_list_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(857,plain,
! [SV131: nat,SV4: list_a] :
( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV4 ) @ SV131 )
| ( ( listSl97544552lice_a @ SV4 @ SV131 )
= nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(858,plain,
! [SV13: a] :
( ( member_a @ nil_a @ SV13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(859,plain,
! [SV14: list_a] :
( ( member_list_a @ nil_list_a @ SV14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(860,plain,
! [SV25: list_a] :
( ( ~ ( ( SV25 = nil_a )
| ( null_a @ SV25 ) )
| ~ ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[735]) ).
thf(861,plain,
! [SV25: list_a] :
( ( ( SV25 = nil_a )
= ( null_a @ SV25 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[735]) ).
thf(862,plain,
! [SV26: list_list_a] :
( ( ~ ( ( SV26 = nil_list_a )
| ( null_list_a @ SV26 ) )
| ~ ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[736]) ).
thf(863,plain,
! [SV26: list_list_a] :
( ( ( SV26 = nil_list_a )
= ( null_list_a @ SV26 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[736]) ).
thf(864,plain,
! [SV35: list_list_a] :
( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
| ( SV35 = nil_list_a ) )
| ~ ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[745]) ).
thf(865,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= ( SV35 = nil_list_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[745]) ).
thf(866,plain,
! [SV36: list_a] :
( ( ~ ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
| ( SV36 = nil_a ) )
| ~ ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[746]) ).
thf(867,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= ( SV36 = nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[746]) ).
thf(868,plain,
! [SV132: list_list_a,SV37: nat] :
( ( ~ ( ord_less_nat @ SV37 @ ( size_s1427607542list_a @ SV132 ) )
| ( SV132 != nil_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(869,plain,
! [SV133: list_a,SV38: nat] :
( ( ~ ( ord_less_nat @ SV38 @ ( size_size_list_a @ SV133 ) )
| ( SV133 != nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(870,plain,
! [SV134: nat,SV39: list_a] :
( ( ( listSl1495374126_aux_a @ SV39 @ SV134 @ zero_zero_nat )
= nil_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(871,plain,
! [SV42: $o] :
( ( ( SV42 = $true )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(872,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(873,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(874,plain,
! [SV44: list_list_a > $o] :
( ( list_ex1_list_list_a @ SV44 @ nil_list_list_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(875,plain,
! [SV135: nat,SV45: list_list_a] :
( ( ~ ( ord_less_nat @ ( size_s1427607542list_a @ SV45 ) @ SV135 )
| ( ( listSl162220270list_a @ SV45 @ SV135 )
= nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(876,plain,
! [SV47: list_list_a] :
( ( member_list_list_a @ nil_list_list_a @ SV47 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(877,plain,
! [SV50: list_list_list_a] :
( ( ~ ( ( SV50 = nil_list_list_a )
| ( null_list_list_a @ SV50 ) )
| ~ ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[762]) ).
thf(878,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 = nil_list_list_a )
= ( null_list_list_a @ SV50 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[762]) ).
thf(879,plain,
! [SV52: list_list_list_a] :
( ( ~ ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
| ( SV52 = nil_list_list_a ) )
| ~ ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[764]) ).
thf(880,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= ( SV52 = nil_list_list_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[764]) ).
thf(881,plain,
! [SV53: list_list_a] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ( SV53 != nil_list_a ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(882,plain,
! [SV53: list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= ( SV53 != nil_list_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(883,plain,
! [SV54: list_list_list_a] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ( SV54 != nil_list_list_a ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[766]) ).
thf(884,plain,
! [SV54: list_list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= ( SV54 != nil_list_list_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[766]) ).
thf(885,plain,
! [SV55: list_a] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ( SV55 != nil_a ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[767]) ).
thf(886,plain,
! [SV55: list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= ( SV55 != nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[767]) ).
thf(887,plain,
! [SV136: list_list_a] :
( ( ( size_s1427607542list_a @ SV136 )
= ( gen_length_list_a @ zero_zero_nat @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(888,plain,
! [SV137: list_a] :
( ( ( size_size_list_a @ SV137 )
= ( gen_length_a @ zero_zero_nat @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(889,plain,
! [SV138: list_a,SV59: list_a] :
( ( ( ( size_size_list_a @ SV59 )
= ( size_size_list_a @ SV138 ) )
| ( SV59 != SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(890,plain,
! [SV60: nat] :
( ( ~ ( ( SV60 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV60 ) )
| ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(891,plain,
! [SV60: nat] :
( ( ( SV60 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(892,plain,
! [SV61: nat] :
( ( ord_less_nat @ SV61 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(893,plain,
! [SV62: nat] :
( ( ~ ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) )
| ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[776]) ).
thf(894,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[776]) ).
thf(895,plain,
! [SV63: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[777]) ).
thf(896,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= ( SV63 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[777]) ).
thf(897,plain,
! [SV139: list_list_list_a,SV64: nat] :
( ( ~ ( ord_less_nat @ SV64 @ ( size_s575106428list_a @ SV139 ) )
| ( SV139 != nil_list_list_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(898,plain,
! [SV65: nat] :
( ( ( SV65 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(899,plain,
! [SV66: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[780]) ).
thf(900,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= ( SV66 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[780]) ).
thf(901,plain,
! [SV67: nat] :
( ( ord_less_nat @ SV67 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(902,plain,
! [SV68: nat] :
( ( ord_less_nat @ SV68 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(903,plain,
! [SV140: nat,SV69: nat] :
( ( ~ ( ord_less_nat @ SV69 @ SV140 )
| ( SV140 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(904,plain,
! [SV70: nat] :
( ( ~ ( ( zero_zero_nat = SV70 )
| ( SV70 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(905,plain,
! [SV70: nat] :
( ( ( zero_zero_nat = SV70 )
= ( SV70 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(906,plain,
! [SV141: nat,SV71: nat] :
( ( ( SV71 = SV141 )
| ( ord_less_nat @ SV71 @ SV141 )
| ( ord_less_nat @ SV141 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(907,plain,
! [SV72: nat] :
( ( ord_less_nat @ SV72 @ SV72 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(908,plain,
! [SV142: nat,SV73: nat] :
( ( ~ ( ord_less_nat @ SV73 @ SV142 )
| ( SV73 != SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(909,plain,
! [SV143: nat,SV74: nat] :
( ( ~ ( ord_less_nat @ SV74 @ SV143 )
| ( SV143 != SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(910,plain,
! [SV75: nat] :
( ( ord_less_nat @ SV75 @ SV75 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(911,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(912,plain,
! [SV145: list_a,SV77: list_a] :
( ( ( ( size_size_list_a @ SV77 )
= ( size_size_list_a @ SV145 ) )
| ( SV77 != SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(913,plain,
! [SV78: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV78 )
| ( SV78 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[792]) ).
thf(914,plain,
! [SV78: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= ( SV78 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[792]) ).
thf(915,plain,
! [SV146: nat,SV79: nat] :
( ( ~ ( ord_less_nat @ SV79 @ SV146 )
| ( SV146 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(916,plain,
! [SV80: nat] :
( ( ord_less_nat @ SV80 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(917,plain,
! [SV81: nat] :
( ( ( SV81 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(918,plain,
! [SV82: nat] :
( ( ord_less_nat @ SV82 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(919,plain,
! [SV147: nat,SV83: nat] :
( ( ~ ( ord_less_nat @ SV83 @ SV147 )
| ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(920,plain,
! [SV148: nat,SV84: list_list_a] :
( ( ( listSl856612276list_a @ SV84 @ SV148 @ zero_zero_nat )
= nil_list_list_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(921,plain,
! [SV85: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV85 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(922,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(923,plain,
! [SV87: nat] :
( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat = SV87 ) )
| ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[802]) ).
thf(924,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= ( zero_zero_nat = SV87 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[802]) ).
thf(925,plain,
! [SV88: nat] :
( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
| ( SV88 = zero_zero_nat ) )
| ~ ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[803]) ).
thf(926,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= ( SV88 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[803]) ).
thf(927,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= ( ord_less_nat @ SV89 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(928,plain,
! [SV90: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ SV90 ) @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(929,plain,
! [SV150: nat,SV91: nat] :
( ( ~ ( ord_less_nat @ SV91 @ SV150 )
| ( ord_less_nat @ ( semiri1382578993at_nat @ SV91 ) @ ( semiri1382578993at_nat @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(930,plain,
! [SV151: nat,SV92: nat] :
( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV92 ) @ ( semiri1382578993at_nat @ SV151 ) )
| ( ord_less_nat @ SV92 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(931,plain,
! [SV152: list_a] :
( ( ( listSl97544552lice_a @ SV152 )
= ( ^ [SY286: nat] : ( listSl1495374126_aux_a @ SV152 @ SY286 @ ( divide_divide_nat @ ( size_size_list_a @ SV152 ) @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(932,plain,
! [SV96: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[812]) ).
thf(933,plain,
! [SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= ( SV96 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[812]) ).
thf(934,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(935,plain,
! [SV98: nat] :
( ( ( SV98 = zero_zero_nat )
= $true )
| ( ( ! [SY240: nat] :
( ( power_power_nat @ SV98 @ SY240 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(936,plain,
! [SV100: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV100 @ zero_zero_nat ) )
= $true )
| ( ( SV100 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(937,plain,
! [SV101: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(938,plain,
! [SV101: nat] :
( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= ( SV101 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(939,plain,
! [SV102: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[818]) ).
thf(940,plain,
! [SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= ( SV102 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[818]) ).
thf(941,plain,
! [SV154: nat,SV104: nat] :
( ( ~ ( ord_less_eq_nat @ SV104 @ SV154 )
| ( SV104 = SV154 )
| ( ord_less_nat @ SV104 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(942,plain,
! [SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 )
= ( ^ [SY287: nat] :
( ( SV155 = SY287 )
| ( ord_less_nat @ SV155 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(943,plain,
! [SV156: nat,SV106: nat] :
( ( ~ ( ord_less_nat @ SV106 @ SV156 )
| ( ord_less_eq_nat @ SV106 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(944,plain,
! [SV107: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV107 ) )
= $true )
| ( ( ! [SY244: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV107 @ SY244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(945,plain,
! [SV108: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV108 ) )
= $true )
| ( ( ! [SY245: nat,SY246: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SY245 ) @ ( power_power_nat @ SV108 @ SY246 ) )
| ( ord_less_nat @ SY245 @ SY246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(946,plain,
! [SV109: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV109 ) )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ SV109 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(947,plain,
! [SV157: a,SV110: list_a] :
( ( ord_less_eq_nat @ ( count_list_a @ SV110 @ SV157 ) @ ( size_size_list_a @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(948,plain,
! [SV158: nat,SV111: list_a] :
( ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ SV111 @ SV158 ) )
= ( divide_divide_nat @ ( size_size_list_a @ SV111 ) @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(949,plain,
! [SV159: nat,SV112: nat] :
( ( ~ ( ord_less_nat @ SV112 @ SV159 )
| ( ( divide_divide_nat @ SV112 @ SV159 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(950,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(951,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(952,plain,
! [SV115: nat > $o] :
( ( ( ~ ( SV115 @ zero_zero_nat ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
| ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
| ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(953,plain,
! [SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 )
= ( ^ [SY288: nat] :
! [SY289: nat] :
( ~ ( ord_less_nat @ SY289 @ SV162 )
| ( SY288 != SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(954,plain,
! [SV163: set_nat,SV117: nat] :
( ( ~ ( member_nat @ SV117 @ SV163 )
| ! [SY290: nat > $o] :
( ~ ( SY290 @ SV117 )
| ~ ( ~ ! [SY291: nat] :
( ~ ( member_nat @ SY291 @ SV163 )
| ~ ( ord_less_nat @ SY291 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( SY290 @ SY291 ) )
| ~ ~ ( ~ ( SY290 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) @ SV163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(955,plain,
! [SV118: nat > $o] :
( ( ( ~ ( ~ ~ ( SV118 @ ( sK10_N2 @ SV118 ) )
| ~ ! [SY259: nat] :
( ~ ( ord_less_nat @ SY259 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SY259 ) ) ) )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(956,plain,
! [SV164: nat] :
( ( ( ord_less_nat @ SV164 )
= ( ^ [SY292: nat] :
~ ( ~ ( ( SV164 != SY292 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(957,plain,
! [SV120: nat > nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
| ~ ~ ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) ) ) )
= $true )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(958,plain,
! [SV121: nat > $o] :
( ( ( ~ ( ~ ! [SY264: nat] :
( ~ ( ord_less_nat @ SY264 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SY264 ) )
| ~ ~ ( SV121 @ ( sK9_N2 @ SV121 ) ) ) )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(959,plain,
! [SV122: set_nat,SV165: nat > $o] :
( ( ! [SY293: nat] :
( ~ ( SV165 @ SY293 )
| ~ ( member_nat @ SY293 @ SV122 ) )
| ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(960,plain,
! [SV166: nat] :
( ( ( ord_less_nat @ SV166 )
= ( ^ [SY295: nat] :
! [SY296: nat] :
( ~ ( ord_less_eq_nat @ SY296 @ SV166 )
| ( SY295 != SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(961,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(962,plain,
! [SV125: list_a > $o] :
( ( ( ~ ( ~ ! [SY272: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY272 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SY272 ) )
| ~ ~ ( SV125 @ ( sK12_Xs2 @ SV125 ) ) ) )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(963,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ~ ( ~ ! [SY297: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY297 @ SV126 )
| ~ ( ord_less_nat @ SY297 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SY297 ) )
| ~ ~ ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
| ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(964,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ~ ( SV127 @ SV169 )
| ( SV127 @ zero_zero_nat )
| ~ ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(965,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(966,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(967,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ~ ( ~ ! [SY300: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY300 @ SV128 )
| ~ ( ord_less_nat @ SY300 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SY300 ) )
| ~ ~ ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
| ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(968,plain,
! [SV171: nat] :
( ( ( ord_less_nat @ SV171 )
= ( ^ [SY302: nat] :
! [SY303: nat] :
( ~ ( ord_less_eq_nat @ SY302 @ SY303 )
| ( SV171 != SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(969,plain,
! [SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 )
= ( ^ [SY304: nat] :
! [SY305: nat] :
( ~ ( ord_less_nat @ SY304 @ SY305 )
| ( SV172 != SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(970,plain,
! [SV131: nat,SV4: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV4 ) @ SV131 ) )
= $true )
| ( ( ( listSl97544552lice_a @ SV4 @ SV131 )
= nil_list_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(971,plain,
! [SV25: list_a] :
( ( ( ~ ( ( SV25 = nil_a )
| ( null_a @ SV25 ) ) )
= $true )
| ( ( ~ ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(972,plain,
! [SV26: list_list_a] :
( ( ( ~ ( ( SV26 = nil_list_a )
| ( null_list_a @ SV26 ) ) )
= $true )
| ( ( ~ ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(973,plain,
! [SV35: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
| ( SV35 = nil_list_a ) ) )
= $true )
| ( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(974,plain,
! [SV36: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
| ( SV36 = nil_a ) ) )
= $true )
| ( ( ~ ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(975,plain,
! [SV132: list_list_a,SV37: nat] :
( ( ( ~ ( ord_less_nat @ SV37 @ ( size_s1427607542list_a @ SV132 ) ) )
= $true )
| ( ( SV132 != nil_list_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(976,plain,
! [SV133: list_a,SV38: nat] :
( ( ( ~ ( ord_less_nat @ SV38 @ ( size_size_list_a @ SV133 ) ) )
= $true )
| ( ( SV133 != nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(977,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $true )
| ~ ( ~ SV42
| ~ $true ) )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(978,plain,
! [SV42: $o] :
( ( ( SV42 = $true )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(979,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(980,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(981,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(982,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(983,plain,
! [SV135: nat,SV45: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( size_s1427607542list_a @ SV45 ) @ SV135 ) )
= $true )
| ( ( ( listSl162220270list_a @ SV45 @ SV135 )
= nil_list_list_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(984,plain,
! [SV50: list_list_list_a] :
( ( ( ~ ( ( SV50 = nil_list_list_a )
| ( null_list_list_a @ SV50 ) ) )
= $true )
| ( ( ~ ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(985,plain,
! [SV52: list_list_list_a] :
( ( ( ~ ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
| ( SV52 = nil_list_list_a ) ) )
= $true )
| ( ( ~ ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(986,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ( SV53 != nil_list_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(987,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ( SV54 != nil_list_list_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(988,plain,
! [SV55: list_a] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ( SV55 != nil_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(989,plain,
! [SV138: list_a,SV59: list_a] :
( ( ( ( size_size_list_a @ SV59 )
= ( size_size_list_a @ SV138 ) )
= $true )
| ( ( SV59 != SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(990,plain,
! [SV60: nat] :
( ( ( ~ ( ( SV60 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(991,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(992,plain,
! [SV63: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(993,plain,
! [SV139: list_list_list_a,SV64: nat] :
( ( ( ~ ( ord_less_nat @ SV64 @ ( size_s575106428list_a @ SV139 ) ) )
= $true )
| ( ( SV139 != nil_list_list_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(994,plain,
! [SV66: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(995,plain,
! [SV140: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ SV69 @ SV140 ) )
= $true )
| ( ( SV140 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(996,plain,
! [SV70: nat] :
( ( ( ~ ( ( zero_zero_nat = SV70 )
| ( SV70 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(997,plain,
! [SV141: nat,SV71: nat] :
( ( ( SV71 = SV141 )
= $true )
| ( ( ( ord_less_nat @ SV71 @ SV141 )
| ( ord_less_nat @ SV141 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(998,plain,
! [SV142: nat,SV73: nat] :
( ( ( ~ ( ord_less_nat @ SV73 @ SV142 ) )
= $true )
| ( ( SV73 != SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(999,plain,
! [SV143: nat,SV74: nat] :
( ( ( ~ ( ord_less_nat @ SV74 @ SV143 ) )
= $true )
| ( ( SV143 != SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1000,plain,
! [SV144: nat,SV76: nat] :
( ( ~ ( ( SV76 != SV144 )
| ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
| ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[911]) ).
thf(1001,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[911]) ).
thf(1002,plain,
! [SV145: list_a,SV77: list_a] :
( ( ( ( size_size_list_a @ SV77 )
= ( size_size_list_a @ SV145 ) )
= $true )
| ( ( SV77 != SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1003,plain,
! [SV78: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV78 )
| ( SV78 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1004,plain,
! [SV146: nat,SV79: nat] :
( ( ( ~ ( ord_less_nat @ SV79 @ SV146 ) )
= $true )
| ( ( SV146 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1005,plain,
! [SV147: nat,SV83: nat] :
( ( ( ~ ( ord_less_nat @ SV83 @ SV147 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1006,plain,
! [SV85: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1007,plain,
! [SV87: nat] :
( ( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat = SV87 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1008,plain,
! [SV88: nat] :
( ( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
| ( SV88 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1009,plain,
! [SV149: nat,SV89: nat] :
( ( ~ ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ( ord_less_nat @ SV89 @ SV149 ) )
| ~ ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1010,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= ( ord_less_nat @ SV89 @ SV149 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1011,plain,
! [SV150: nat,SV91: nat] :
( ( ( ~ ( ord_less_nat @ SV91 @ SV150 ) )
= $true )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV91 ) @ ( semiri1382578993at_nat @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1012,plain,
! [SV151: nat,SV92: nat] :
( ( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV92 ) @ ( semiri1382578993at_nat @ SV151 ) ) )
= $true )
| ( ( ord_less_nat @ SV92 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1013,plain,
! [SV152: list_a] :
( ( ! [SV173: nat] :
( ( listSl97544552lice_a @ SV152 @ SV173 )
= ( listSl1495374126_aux_a @ SV152 @ SV173 @ ( divide_divide_nat @ ( size_size_list_a @ SV152 ) @ SV173 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[931]) ).
thf(1014,plain,
! [SV152: list_a] :
( ( ( listSl97544552lice_a @ SV152 )
= ( ^ [SY286: nat] : ( listSl1495374126_aux_a @ SV152 @ SY286 @ ( divide_divide_nat @ ( size_size_list_a @ SV152 ) @ SY286 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[931]) ).
thf(1015,plain,
! [SV96: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1016,plain,
! [SV153: nat,SV97: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[934]) ).
thf(1017,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[934]) ).
thf(1018,plain,
! [SV174: nat,SV98: nat] :
( ( ( ( power_power_nat @ SV98 @ SV174 )
!= zero_zero_nat )
= $true )
| ( ( SV98 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1019,plain,
! [SV100: nat] :
( ( ( ord_less_eq_nat @ SV100 @ zero_zero_nat )
= $false )
| ( ( SV100 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1020,plain,
! [SV101: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1021,plain,
! [SV102: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1022,plain,
! [SV154: nat,SV104: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV104 @ SV154 ) )
= $true )
| ( ( ( SV104 = SV154 )
| ( ord_less_nat @ SV104 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1023,plain,
! [SV155: nat] :
( ( ! [SV175: nat] :
( ( ord_less_eq_nat @ SV155 @ SV175 )
= ( ( SV155 = SV175 )
| ( ord_less_nat @ SV155 @ SV175 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[942]) ).
thf(1024,plain,
! [SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 )
= ( ^ [SY287: nat] :
( ( SV155 = SY287 )
| ( ord_less_nat @ SV155 @ SY287 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[942]) ).
thf(1025,plain,
! [SV156: nat,SV106: nat] :
( ( ( ~ ( ord_less_nat @ SV106 @ SV156 ) )
= $true )
| ( ( ord_less_eq_nat @ SV106 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1026,plain,
! [SV107: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV107 )
= $false )
| ( ( ! [SY244: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV107 @ SY244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1027,plain,
! [SV108: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV108 )
= $false )
| ( ( ! [SY245: nat,SY246: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SY245 ) @ ( power_power_nat @ SV108 @ SY246 ) )
| ( ord_less_nat @ SY245 @ SY246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1028,plain,
! [SV109: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV109 )
= $false )
| ( ( ( power_power_nat @ zero_zero_nat @ SV109 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1029,plain,
! [SV159: nat,SV112: nat] :
( ( ( ~ ( ord_less_nat @ SV112 @ SV159 ) )
= $true )
| ( ( ( divide_divide_nat @ SV112 @ SV159 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1030,plain,
! [SV160: nat,SV113: nat] :
( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
| ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
| ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[950]) ).
thf(1031,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[950]) ).
thf(1032,plain,
! [SV161: nat,SV114: nat] :
( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
| ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
| ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[951]) ).
thf(1033,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[951]) ).
thf(1034,plain,
! [SV115: nat > $o] :
( ( ( SV115 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
| ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
| ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1035,plain,
! [SV162: nat] :
( ( ! [SV176: nat] :
( ( ord_less_eq_nat @ SV162 @ SV176 )
= ( ! [SY306: nat] :
( ~ ( ord_less_nat @ SY306 @ SV162 )
| ( SV176 != SY306 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[953]) ).
thf(1036,plain,
! [SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 )
= ( ^ [SY288: nat] :
! [SY289: nat] :
( ~ ( ord_less_nat @ SY289 @ SV162 )
| ( SY288 != SY289 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[953]) ).
thf(1037,plain,
! [SV163: set_nat,SV117: nat] :
( ( ( ~ ( member_nat @ SV117 @ SV163 ) )
= $true )
| ( ( ! [SY290: nat > $o] :
( ~ ( SY290 @ SV117 )
| ~ ( ~ ! [SY291: nat] :
( ~ ( member_nat @ SY291 @ SV163 )
| ~ ( ord_less_nat @ SY291 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( SY290 @ SY291 ) )
| ~ ~ ( ~ ( SY290 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) @ SV163 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1038,plain,
! [SV118: nat > $o] :
( ( ( ~ ~ ( SV118 @ ( sK10_N2 @ SV118 ) )
| ~ ! [SY259: nat] :
( ~ ( ord_less_nat @ SY259 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SY259 ) ) )
= $false )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1039,plain,
! [SV164: nat] :
( ( ! [SV177: nat] :
( ( ord_less_nat @ SV164 @ SV177 )
= ( ~ ( ~ ( ( SV164 != SV177 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1040,plain,
! [SV164: nat] :
( ( ( ord_less_nat @ SV164 )
= ( ^ [SY292: nat] :
~ ( ~ ( ( SV164 != SY292 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SY292 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1041,plain,
! [SV120: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
| ~ ~ ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) ) )
= $false )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1042,plain,
! [SV121: nat > $o] :
( ( ( ~ ! [SY264: nat] :
( ~ ( ord_less_nat @ SY264 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SY264 ) )
| ~ ~ ( SV121 @ ( sK9_N2 @ SV121 ) ) )
= $false )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1043,plain,
! [SV122: set_nat,SV165: nat > $o] :
( ( ( ! [SY293: nat] :
( ~ ( SV165 @ SY293 )
| ~ ( member_nat @ SY293 @ SV122 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1044,plain,
! [SV166: nat] :
( ( ! [SV178: nat] :
( ( ord_less_nat @ SV166 @ SV178 )
= ( ! [SY307: nat] :
( ~ ( ord_less_eq_nat @ SY307 @ SV166 )
| ( SV178 != SY307 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1045,plain,
! [SV166: nat] :
( ( ( ord_less_nat @ SV166 )
= ( ^ [SY295: nat] :
! [SY296: nat] :
( ~ ( ord_less_eq_nat @ SY296 @ SV166 )
| ( SY295 != SY296 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1046,plain,
! [SV167: nat,SV124: nat] :
( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
| ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
| ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[961]) ).
thf(1047,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[961]) ).
thf(1048,plain,
! [SV125: list_a > $o] :
( ( ( ~ ! [SY272: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY272 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SY272 ) )
| ~ ~ ( SV125 @ ( sK12_Xs2 @ SV125 ) ) )
= $false )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1049,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( ~ ! [SY297: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY297 @ SV126 )
| ~ ( ord_less_nat @ SY297 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SY297 ) )
| ~ ~ ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) ) ) )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1050,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ( ~ ( SV127 @ SV169 ) )
= $true )
| ( ( ( SV127 @ zero_zero_nat )
| ~ ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1051,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1052,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1053,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( ~ ! [SY300: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY300 @ SV128 )
| ~ ( ord_less_nat @ SY300 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SY300 ) )
| ~ ~ ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) ) ) )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1054,plain,
! [SV171: nat] :
( ( ! [SV179: nat] :
( ( ord_less_nat @ SV171 @ SV179 )
= ( ! [SY308: nat] :
( ~ ( ord_less_eq_nat @ SV179 @ SY308 )
| ( SV171 != SY308 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[968]) ).
thf(1055,plain,
! [SV171: nat] :
( ( ( ord_less_nat @ SV171 )
= ( ^ [SY302: nat] :
! [SY303: nat] :
( ~ ( ord_less_eq_nat @ SY302 @ SY303 )
| ( SV171 != SY303 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[968]) ).
thf(1056,plain,
! [SV172: nat] :
( ( ! [SV180: nat] :
( ( ord_less_eq_nat @ SV172 @ SV180 )
= ( ! [SY309: nat] :
( ~ ( ord_less_nat @ SV180 @ SY309 )
| ( SV172 != SY309 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[969]) ).
thf(1057,plain,
! [SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 )
= ( ^ [SY304: nat] :
! [SY305: nat] :
( ~ ( ord_less_nat @ SY304 @ SY305 )
| ( SV172 != SY305 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[969]) ).
thf(1058,plain,
! [SV131: nat,SV4: list_a] :
( ( ( ord_less_nat @ ( size_size_list_a @ SV4 ) @ SV131 )
= $false )
| ( ( ( listSl97544552lice_a @ SV4 @ SV131 )
= nil_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1059,plain,
! [SV25: list_a] :
( ( ( ( SV25 = nil_a )
| ( null_a @ SV25 ) )
= $false )
| ( ( ~ ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1060,plain,
! [SV26: list_list_a] :
( ( ( ( SV26 = nil_list_a )
| ( null_list_a @ SV26 ) )
= $false )
| ( ( ~ ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1061,plain,
! [SV35: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
| ( SV35 = nil_list_a ) )
= $false )
| ( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1062,plain,
! [SV36: list_a] :
( ( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
| ( SV36 = nil_a ) )
= $false )
| ( ( ~ ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1063,plain,
! [SV132: list_list_a,SV37: nat] :
( ( ( ord_less_nat @ SV37 @ ( size_s1427607542list_a @ SV132 ) )
= $false )
| ( ( SV132 != nil_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1064,plain,
! [SV133: list_a,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( size_size_list_a @ SV133 ) )
= $false )
| ( ( SV133 != nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1065,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $true ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $true ) )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1066,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false )
| ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[978]) ).
thf(1067,plain,
! [SV42: $o] :
( ( ( SV42 = $false )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[978]) ).
thf(1068,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1069,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[980]) ).
thf(1070,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[980]) ).
thf(1071,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1072,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[982]) ).
thf(1073,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[982]) ).
thf(1074,plain,
! [SV135: nat,SV45: list_list_a] :
( ( ( ord_less_nat @ ( size_s1427607542list_a @ SV45 ) @ SV135 )
= $false )
| ( ( ( listSl162220270list_a @ SV45 @ SV135 )
= nil_list_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1075,plain,
! [SV50: list_list_list_a] :
( ( ( ( SV50 = nil_list_list_a )
| ( null_list_list_a @ SV50 ) )
= $false )
| ( ( ~ ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1076,plain,
! [SV52: list_list_list_a] :
( ( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
| ( SV52 = nil_list_list_a ) )
= $false )
| ( ( ~ ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1077,plain,
! [SV53: list_list_a] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ( SV53 != nil_list_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1078,plain,
! [SV54: list_list_list_a] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ( SV54 != nil_list_list_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1079,plain,
! [SV55: list_a] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ( SV55 != nil_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1080,plain,
! [SV138: list_a,SV59: list_a] :
( ( ( SV59 = SV138 )
= $false )
| ( ( ( size_size_list_a @ SV59 )
= ( size_size_list_a @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1081,plain,
! [SV60: nat] :
( ( ( ( SV60 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $false )
| ( ( ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1082,plain,
! [SV62: nat] :
( ( ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1083,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1084,plain,
! [SV139: list_list_list_a,SV64: nat] :
( ( ( ord_less_nat @ SV64 @ ( size_s575106428list_a @ SV139 ) )
= $false )
| ( ( SV139 != nil_list_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1085,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1086,plain,
! [SV140: nat,SV69: nat] :
( ( ( ord_less_nat @ SV69 @ SV140 )
= $false )
| ( ( SV140 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1087,plain,
! [SV70: nat] :
( ( ( ( zero_zero_nat = SV70 )
| ( SV70 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1088,plain,
! [SV141: nat,SV71: nat] :
( ( ( ord_less_nat @ SV71 @ SV141 )
= $true )
| ( ( ord_less_nat @ SV141 @ SV71 )
= $true )
| ( ( SV71 = SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1089,plain,
! [SV142: nat,SV73: nat] :
( ( ( ord_less_nat @ SV73 @ SV142 )
= $false )
| ( ( SV73 != SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1090,plain,
! [SV143: nat,SV74: nat] :
( ( ( ord_less_nat @ SV74 @ SV143 )
= $false )
| ( ( SV143 != SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1091,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 )
| ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1092,plain,
! [SV145: list_a,SV77: list_a] :
( ( ( SV77 = SV145 )
= $false )
| ( ( ( size_size_list_a @ SV77 )
= ( size_size_list_a @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1093,plain,
! [SV78: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
| ( SV78 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1094,plain,
! [SV146: nat,SV79: nat] :
( ( ( ord_less_nat @ SV79 @ SV146 )
= $false )
| ( ( SV146 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1095,plain,
! [SV147: nat,SV83: nat] :
( ( ( ord_less_nat @ SV83 @ SV147 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1096,plain,
! [SV85: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1097,plain,
! [SV87: nat] :
( ( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat = SV87 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1098,plain,
! [SV88: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
| ( SV88 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1099,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1100,plain,
! [SV150: nat,SV91: nat] :
( ( ( ord_less_nat @ SV91 @ SV150 )
= $false )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV91 ) @ ( semiri1382578993at_nat @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1101,plain,
! [SV151: nat,SV92: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV92 ) @ ( semiri1382578993at_nat @ SV151 ) )
= $false )
| ( ( ord_less_nat @ SV92 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1102,plain,
! [SV181: nat,SV152: list_a] :
( ( ( listSl97544552lice_a @ SV152 @ SV181 )
= ( listSl1495374126_aux_a @ SV152 @ SV181 @ ( divide_divide_nat @ ( size_size_list_a @ SV152 ) @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1103,plain,
! [SV96: nat] :
( ( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1104,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1105,plain,
! [SV174: nat,SV98: nat] :
( ( ( ( power_power_nat @ SV98 @ SV174 )
= zero_zero_nat )
= $false )
| ( ( SV98 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1106,plain,
! [SV101: nat] :
( ( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1107,plain,
! [SV102: nat] :
( ( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1108,plain,
! [SV154: nat,SV104: nat] :
( ( ( ord_less_eq_nat @ SV104 @ SV154 )
= $false )
| ( ( ( SV104 = SV154 )
| ( ord_less_nat @ SV104 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1109,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1110,plain,
! [SV156: nat,SV106: nat] :
( ( ( ord_less_nat @ SV106 @ SV156 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1111,plain,
! [SV183: nat,SV107: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV107 @ SV183 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1112,plain,
! [SV184: nat,SV108: nat] :
( ( ( ! [SY310: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SV184 ) @ ( power_power_nat @ SV108 @ SY310 ) )
| ( ord_less_nat @ SV184 @ SY310 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1113,plain,
! [SV159: nat,SV112: nat] :
( ( ( ord_less_nat @ SV112 @ SV159 )
= $false )
| ( ( ( divide_divide_nat @ SV112 @ SV159 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1114,plain,
! [SV160: nat,SV113: nat] :
( ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
| ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $true )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1115,plain,
! [SV161: nat,SV114: nat] :
( ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
| ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $true )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1116,plain,
! [SV115: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
| ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1117,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1118,plain,
! [SV163: set_nat,SV117: nat] :
( ( ( member_nat @ SV117 @ SV163 )
= $false )
| ( ( ! [SY290: nat > $o] :
( ~ ( SY290 @ SV117 )
| ~ ( ~ ! [SY291: nat] :
( ~ ( member_nat @ SY291 @ SV163 )
| ~ ( ord_less_nat @ SY291 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( SY290 @ SY291 ) )
| ~ ~ ( ~ ( SY290 @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SY290 @ SV163 @ SV117 ) @ SV163 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1119,plain,
! [SV118: nat > $o] :
( ( ( ~ ~ ( SV118 @ ( sK10_N2 @ SV118 ) ) )
= $false )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1120,plain,
! [SV118: nat > $o] :
( ( ( ~ ! [SY259: nat] :
( ~ ( ord_less_nat @ SY259 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SY259 ) ) )
= $false )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1121,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_nat @ SV164 @ SV186 )
= ( ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1122,plain,
! [SV120: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) ) )
= $false )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1123,plain,
! [SV120: nat > nat] :
( ( ( ~ ~ ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) ) )
= $false )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1124,plain,
! [SV121: nat > $o] :
( ( ( ~ ! [SY264: nat] :
( ~ ( ord_less_nat @ SY264 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SY264 ) ) )
= $false )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1125,plain,
! [SV121: nat > $o] :
( ( ( ~ ~ ( SV121 @ ( sK9_N2 @ SV121 ) ) )
= $false )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1126,plain,
! [SV122: set_nat,SV187: nat,SV165: nat > $o] :
( ( ( ~ ( SV165 @ SV187 )
| ~ ( member_nat @ SV187 @ SV122 ) )
= $true )
| ( ( ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1127,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1128,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
| ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1129,plain,
! [SV125: list_a > $o] :
( ( ( ~ ! [SY272: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY272 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SY272 ) ) )
= $false )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1130,plain,
! [SV125: list_a > $o] :
( ( ( ~ ~ ( SV125 @ ( sK12_Xs2 @ SV125 ) ) )
= $false )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1131,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ! [SY297: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY297 @ SV126 )
| ~ ( ord_less_nat @ SY297 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SY297 ) )
| ~ ~ ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $false )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1132,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ( SV127 @ SV169 )
= $false )
| ( ( ( SV127 @ zero_zero_nat )
| ~ ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1133,plain,
! [SV189: nat] :
( ( ! [SY313: nat] :
( ( SV189 != SY313 )
| ( ord_less_eq_nat @ SV189 @ SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1134,plain,
! [SV190: nat] :
( ( ! [SY314: nat] :
( ~ ( ord_less_nat @ SV190 @ SY314 )
| ( ord_less_eq_nat @ SV190 @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY300 @ SV128 )
| ~ ( ord_less_nat @ SY300 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SY300 ) )
| ~ ~ ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $false )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1136,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1137,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1138,plain,
! [SV25: list_a] :
( ( ( SV25 = nil_a )
= $false )
| ( ( ~ ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1139,plain,
! [SV25: list_a] :
( ( ( null_a @ SV25 )
= $false )
| ( ( ~ ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1140,plain,
! [SV26: list_list_a] :
( ( ( SV26 = nil_list_a )
= $false )
| ( ( ~ ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1141,plain,
! [SV26: list_list_a] :
( ( ( null_list_a @ SV26 )
= $false )
| ( ( ~ ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1142,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1143,plain,
! [SV35: list_list_a] :
( ( ( SV35 = nil_list_a )
= $false )
| ( ( ~ ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1144,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1145,plain,
! [SV36: list_a] :
( ( ( SV36 = nil_a )
= $false )
| ( ( ~ ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1146,plain,
! [SV37: nat,SV132: list_list_a] :
( ( ( SV132 = nil_list_a )
= $false )
| ( ( ord_less_nat @ SV37 @ ( size_s1427607542list_a @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1147,plain,
! [SV38: nat,SV133: list_a] :
( ( ( SV133 = nil_a )
= $false )
| ( ( ord_less_nat @ SV38 @ ( size_size_list_a @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1148,plain,
! [SV42: $o] :
( ( ( SV42
| $true )
= $false )
| ( ( ~ ( ~ SV42
| ~ $true ) )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1149,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1150,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1151,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1152,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1153,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1154,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 = nil_list_list_a )
= $false )
| ( ( ~ ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1155,plain,
! [SV50: list_list_list_a] :
( ( ( null_list_list_a @ SV50 )
= $false )
| ( ( ~ ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1156,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1157,plain,
! [SV52: list_list_list_a] :
( ( ( SV52 = nil_list_list_a )
= $false )
| ( ( ~ ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1158,plain,
! [SV53: list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1159,plain,
! [SV53: list_list_a] :
( ( ( SV53 != nil_list_a )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1160,plain,
! [SV54: list_list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1161,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 != nil_list_list_a )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1162,plain,
! [SV55: list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1163,plain,
! [SV55: list_a] :
( ( ( SV55 != nil_a )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1164,plain,
! [SV60: nat] :
( ( ( SV60 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1165,plain,
! [SV60: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false )
| ( ( ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1166,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1167,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1168,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1169,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1170,plain,
! [SV64: nat,SV139: list_list_list_a] :
( ( ( SV139 = nil_list_list_a )
= $false )
| ( ( ord_less_nat @ SV64 @ ( size_s575106428list_a @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1171,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1172,plain,
! [SV66: nat] :
( ( ( SV66 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1173,plain,
! [SV69: nat,SV140: nat] :
( ( ( SV140 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV69 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1174,plain,
! [SV70: nat] :
( ( ( zero_zero_nat = SV70 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1175,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1176,plain,
! [SV142: nat,SV73: nat] :
( ( ( SV73 = SV142 )
= $false )
| ( ( ord_less_nat @ SV73 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1177,plain,
! [SV74: nat,SV143: nat] :
( ( ( SV143 = SV74 )
= $false )
| ( ( ord_less_nat @ SV74 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1178,plain,
! [SV144: nat,SV76: nat] :
( ( ( ( SV76 != SV144 )
| ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
= $false )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1179,plain,
! [SV78: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1180,plain,
! [SV78: nat] :
( ( ( SV78 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1181,plain,
! [SV79: nat,SV146: nat] :
( ( ( SV146 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV79 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1182,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1183,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1184,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1185,plain,
! [SV87: nat] :
( ( ( zero_zero_nat = SV87 )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1186,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1187,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1188,plain,
! [SV149: nat,SV89: nat] :
( ( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ( ord_less_nat @ SV89 @ SV149 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1189,plain,
! [SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1190,plain,
! [SV96: nat] :
( ( ( SV96 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1191,plain,
! [SV153: nat,SV97: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1192,plain,
! [SV101: nat] :
( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1193,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1194,plain,
! [SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1195,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1196,plain,
! [SV154: nat,SV104: nat] :
( ( ( SV104 = SV154 )
= $true )
| ( ( ord_less_nat @ SV104 @ SV154 )
= $true )
| ( ( ord_less_eq_nat @ SV104 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1197,plain,
! [SV182: nat,SV155: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV155 @ SV182 )
| ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1109]) ).
thf(1198,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1109]) ).
thf(1199,plain,
! [SV193: nat,SV184: nat,SV108: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SV184 ) @ ( power_power_nat @ SV108 @ SV193 ) )
| ( ord_less_nat @ SV184 @ SV193 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1200,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
| ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1201,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
| ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1202,plain,
! [SV115: nat > $o] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
| ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1203,plain,
! [SV185: nat,SV162: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV162 @ SV185 )
| ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1117]) ).
thf(1204,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1117]) ).
thf(1205,plain,
! [SV163: set_nat,SV117: nat,SV194: nat > $o] :
( ( ( ~ ( SV194 @ SV117 )
| ~ ( ~ ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) )
| ~ ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) ) )
= $true )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1206,plain,
! [SV118: nat > $o] :
( ( ( ~ ( SV118 @ ( sK10_N2 @ SV118 ) ) )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1207,plain,
! [SV118: nat > $o] :
( ( ( ! [SY259: nat] :
( ~ ( ord_less_nat @ SY259 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SY259 ) ) )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1208,plain,
! [SV186: nat,SV164: nat] :
( ( ~ ( ( ord_less_nat @ SV164 @ SV186 )
| ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
| ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1121]) ).
thf(1209,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_nat @ SV164 @ SV186 )
= ( ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1121]) ).
thf(1210,plain,
! [SV120: nat > nat] :
( ( ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
= $true )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1211,plain,
! [SV120: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) ) )
= $true )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1212,plain,
! [SV121: nat > $o] :
( ( ( ! [SY264: nat] :
( ~ ( ord_less_nat @ SY264 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SY264 ) ) )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1213,plain,
! [SV121: nat > $o] :
( ( ( ~ ( SV121 @ ( sK9_N2 @ SV121 ) ) )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1214,plain,
! [SV122: set_nat,SV187: nat,SV165: nat > $o] :
( ( ( ~ ( SV165 @ SV187 ) )
= $true )
| ( ( ~ ( member_nat @ SV187 @ SV122 ) )
= $true )
| ( ( ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1215,plain,
! [SV188: nat,SV166: nat] :
( ( ~ ( ( ord_less_nat @ SV166 @ SV188 )
| ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
| ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1127]) ).
thf(1216,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1127]) ).
thf(1217,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
| ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1218,plain,
! [SV125: list_a > $o] :
( ( ( ! [SY272: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY272 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SY272 ) ) )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1219,plain,
! [SV125: list_a > $o] :
( ( ( ~ ( SV125 @ ( sK12_Xs2 @ SV125 ) ) )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1220,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ! [SY297: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY297 @ SV126 )
| ~ ( ord_less_nat @ SY297 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SY297 ) ) )
= $false )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1221,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ~ ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $false )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1222,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) ) )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1223,plain,
! [SV195: nat,SV189: nat] :
( ( ( SV189 != SV195 )
| ( ord_less_eq_nat @ SV189 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1224,plain,
! [SV196: nat,SV190: nat] :
( ( ~ ( ord_less_nat @ SV190 @ SV196 )
| ( ord_less_eq_nat @ SV190 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1225,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY300 @ SV128 )
| ~ ( ord_less_nat @ SY300 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SY300 ) ) )
= $false )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1226,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ~ ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $false )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1227,plain,
! [SV191: nat,SV171: nat] :
( ( ~ ( ( ord_less_nat @ SV171 @ SV191 )
| ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
| ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1136]) ).
thf(1228,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1136]) ).
thf(1229,plain,
! [SV192: nat,SV172: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV172 @ SV192 )
| ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1137]) ).
thf(1230,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1137]) ).
thf(1231,plain,
! [SV25: list_a] :
( ( ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) )
= $false )
| ( ( SV25 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1232,plain,
! [SV25: list_a] :
( ( ( ( SV25 != nil_a )
| ~ ( null_a @ SV25 ) )
= $false )
| ( ( null_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1233,plain,
! [SV26: list_list_a] :
( ( ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) )
= $false )
| ( ( SV26 = nil_list_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1234,plain,
! [SV26: list_list_a] :
( ( ( ( SV26 != nil_list_a )
| ~ ( null_list_a @ SV26 ) )
= $false )
| ( ( null_list_a @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1235,plain,
! [SV35: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1236,plain,
! [SV35: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
| ( SV35 != nil_list_a ) )
= $false )
| ( ( SV35 = nil_list_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1237,plain,
! [SV36: list_a] :
( ( ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) )
= $false )
| ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1238,plain,
! [SV36: list_a] :
( ( ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
| ( SV36 != nil_a ) )
= $false )
| ( ( SV36 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1239,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $true ) )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1240,plain,
! [SV42: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV42
| ~ $true ) )
= $true )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1241,plain,
! [SV42: $o] :
( ( ( SV42
| $false )
= $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1242,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1243,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1244,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1245,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1246,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1247,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1248,plain,
! [SV50: list_list_list_a] :
( ( ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) )
= $false )
| ( ( SV50 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1249,plain,
! [SV50: list_list_list_a] :
( ( ( ( SV50 != nil_list_list_a )
| ~ ( null_list_list_a @ SV50 ) )
= $false )
| ( ( null_list_list_a @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1250,plain,
! [SV52: list_list_list_a] :
( ( ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) )
= $false )
| ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1251,plain,
! [SV52: list_list_list_a] :
( ( ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
| ( SV52 != nil_list_list_a ) )
= $false )
| ( ( SV52 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1252,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1253,plain,
! [SV53: list_list_a] :
( ( ( SV53 = nil_list_a )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1254,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1255,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 = nil_list_list_a )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1256,plain,
! [SV55: list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1257,plain,
! [SV55: list_a] :
( ( ( SV55 = nil_a )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1258,plain,
! [SV60: nat] :
( ( ( SV60 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1259,plain,
! [SV60: nat] :
( ( ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1260,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1261,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1262,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1263,plain,
! [SV63: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1264,plain,
! [SV66: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1265,plain,
! [SV66: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1266,plain,
! [SV70: nat] :
( ( ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1267,plain,
! [SV70: nat] :
( ( ( ( zero_zero_nat != SV70 )
| ( SV70 != zero_zero_nat ) )
= $false )
| ( ( SV70 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1268,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= $false )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1269,plain,
! [SV144: nat,SV76: nat] :
( ( ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
= $false )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1270,plain,
! [SV78: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1271,plain,
! [SV78: nat] :
( ( ( SV78 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1272,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1273,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1274,plain,
! [SV87: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1275,plain,
! [SV87: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
| ( zero_zero_nat != SV87 ) )
= $false )
| ( ( zero_zero_nat = SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1276,plain,
! [SV88: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) )
= $false )
| ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1277,plain,
! [SV88: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
| ( SV88 != zero_zero_nat ) )
= $false )
| ( ( SV88 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1278,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1279,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ SV89 @ SV149 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1280,plain,
! [SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1281,plain,
! [SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
| ( SV96 != zero_zero_nat ) )
= $false )
| ( ( SV96 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1282,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1283,plain,
! [SV97: nat,SV153: nat] :
( ( ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1284,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1285,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
| ( SV101 != zero_zero_nat ) )
= $false )
| ( ( SV101 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1286,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1287,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
| ( SV102 != zero_zero_nat ) )
= $false )
| ( ( SV102 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1288,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV155 @ SV182 )
| ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1289,plain,
! [SV193: nat,SV184: nat,SV108: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV108 @ SV184 ) @ ( power_power_nat @ SV108 @ SV193 ) ) )
= $true )
| ( ( ord_less_nat @ SV184 @ SV193 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1290,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1291,plain,
! [SV113: nat,SV160: nat] :
( ( ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1292,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1293,plain,
! [SV114: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1294,plain,
! [SV115: nat > $o] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1295,plain,
! [SV115: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1296,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV162 @ SV185 )
| ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1297,plain,
! [SV163: set_nat,SV117: nat,SV194: nat > $o] :
( ( ( ~ ( SV194 @ SV117 ) )
= $true )
| ( ( ~ ( ~ ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) )
| ~ ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) ) )
= $true )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1298,plain,
! [SV118: nat > $o] :
( ( ( SV118 @ ( sK10_N2 @ SV118 ) )
= $false )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1299,plain,
! [SV118: nat > $o,SV197: nat] :
( ( ( ~ ( ord_less_nat @ SV197 @ ( sK10_N2 @ SV118 ) )
| ( SV118 @ SV197 ) )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1300,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( ord_less_nat @ SV164 @ SV186 )
| ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1301,plain,
! [SV120: nat > nat,SV198: nat] :
( ( ( ! [SY318: nat] :
( ~ ( ord_less_eq_nat @ SV198 @ SY318 )
| ( ord_less_eq_nat @ ( SV120 @ SV198 ) @ ( SV120 @ SY318 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1302,plain,
! [SV120: nat > nat] :
( ( ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) )
= $false )
| ( ( ! [SY262: nat,SY263: nat] :
( ~ ( ord_less_eq_nat @ SY262 @ SY263 )
| ( ord_less_eq_nat @ ( SV120 @ SY262 ) @ ( SV120 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1303,plain,
! [SV121: nat > $o,SV199: nat] :
( ( ( ~ ( ord_less_nat @ SV199 @ ( sK9_N2 @ SV121 ) )
| ( SV121 @ SV199 ) )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1304,plain,
! [SV121: nat > $o] :
( ( ( SV121 @ ( sK9_N2 @ SV121 ) )
= $false )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1305,plain,
! [SV122: set_nat,SV187: nat,SV165: nat > $o] :
( ( ( SV165 @ SV187 )
= $false )
| ( ( ~ ( member_nat @ SV187 @ SV122 ) )
= $true )
| ( ( ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1306,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ( ord_less_nat @ SV166 @ SV188 )
| ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1307,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1308,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1309,plain,
! [SV125: list_a > $o,SV200: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV200 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
| ( SV125 @ SV200 ) )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1310,plain,
! [SV125: list_a > $o] :
( ( ( SV125 @ ( sK12_Xs2 @ SV125 ) )
= $false )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1311,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ! [SY297: nat] :
( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SY297 @ SV126 )
| ~ ( ord_less_nat @ SY297 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SY297 ) ) )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1312,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1313,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1314,plain,
! [SV195: nat,SV189: nat] :
( ( ( SV189 != SV195 )
= $true )
| ( ( ord_less_eq_nat @ SV189 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1315,plain,
! [SV196: nat,SV190: nat] :
( ( ( ~ ( ord_less_nat @ SV190 @ SV196 ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1316,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SY300 @ SV128 )
| ~ ( ord_less_nat @ SY300 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SY300 ) ) )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1317,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1318,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ( ord_less_nat @ SV171 @ SV191 )
| ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1319,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV172 @ SV192 )
| ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1320,plain,
! [SV25: list_a] :
( ( ( SV25 != nil_a )
= $false )
| ( ( SV25 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1321,plain,
! [SV25: list_a] :
( ( ( ~ ( null_a @ SV25 ) )
= $false )
| ( ( SV25 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1322,plain,
! [SV25: list_a] :
( ( ( SV25 != nil_a )
= $false )
| ( ( null_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1323,plain,
! [SV25: list_a] :
( ( ( ~ ( null_a @ SV25 ) )
= $false )
| ( ( null_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1324,plain,
! [SV26: list_list_a] :
( ( ( SV26 != nil_list_a )
= $false )
| ( ( SV26 = nil_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1325,plain,
! [SV26: list_list_a] :
( ( ( ~ ( null_list_a @ SV26 ) )
= $false )
| ( ( SV26 = nil_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1326,plain,
! [SV26: list_list_a] :
( ( ( SV26 != nil_list_a )
= $false )
| ( ( null_list_a @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1327,plain,
! [SV26: list_list_a] :
( ( ( ~ ( null_list_a @ SV26 ) )
= $false )
| ( ( null_list_a @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1328,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
= $false )
| ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1329,plain,
! [SV35: list_list_a] :
( ( ( SV35 != nil_list_a )
= $false )
| ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1330,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
!= zero_zero_nat )
= $false )
| ( ( SV35 = nil_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1331,plain,
! [SV35: list_list_a] :
( ( ( SV35 != nil_list_a )
= $false )
| ( ( SV35 = nil_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1332,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
= $false )
| ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1333,plain,
! [SV36: list_a] :
( ( ( SV36 != nil_a )
= $false )
| ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1334,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
!= zero_zero_nat )
= $false )
| ( ( SV36 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1335,plain,
! [SV36: list_a] :
( ( ( SV36 != nil_a )
= $false )
| ( ( SV36 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1336,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $true )
= $false )
| ( SV42 = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1337,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1338,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1339,plain,
! [SV42: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1340,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1341,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1342,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1343,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1344,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1345,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1346,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1347,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1348,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 != nil_list_list_a )
= $false )
| ( ( SV50 = nil_list_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1349,plain,
! [SV50: list_list_list_a] :
( ( ( ~ ( null_list_list_a @ SV50 ) )
= $false )
| ( ( SV50 = nil_list_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1350,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 != nil_list_list_a )
= $false )
| ( ( null_list_list_a @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1351,plain,
! [SV50: list_list_list_a] :
( ( ( ~ ( null_list_list_a @ SV50 ) )
= $false )
| ( ( null_list_list_a @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1352,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
= $false )
| ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1250]) ).
thf(1353,plain,
! [SV52: list_list_list_a] :
( ( ( SV52 != nil_list_list_a )
= $false )
| ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1250]) ).
thf(1354,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
!= zero_zero_nat )
= $false )
| ( ( SV52 = nil_list_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1355,plain,
! [SV52: list_list_list_a] :
( ( ( SV52 != nil_list_list_a )
= $false )
| ( ( SV52 = nil_list_list_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1356,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1252]) ).
thf(1357,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ( SV53 != nil_list_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1252]) ).
thf(1358,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
| ~ ( ( SV53 != nil_list_a ) ) )
= $false )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1359,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1254]) ).
thf(1360,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ( SV54 != nil_list_list_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1254]) ).
thf(1361,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
| ~ ( ( SV54 != nil_list_list_a ) ) )
= $false )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1362,plain,
! [SV55: list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1363,plain,
! [SV55: list_a] :
( ( ( ~ ( ( SV55 != nil_a ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1364,plain,
! [SV55: list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
| ~ ( ( SV55 != nil_a ) ) )
= $false )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1365,plain,
! [SV60: nat] :
( ( ( ~ ( ( SV60 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $false )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1366,plain,
! [SV60: nat] :
( ( ( ~ ( ( SV60 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1367,plain,
! [SV60: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1368,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1369,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1370,plain,
! [SV62: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1371,plain,
! [SV63: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( SV63 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1372,plain,
! [SV63: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1373,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= $false )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1374,plain,
! [SV66: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 )
| ( SV66 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1375,plain,
! [SV66: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1376,plain,
! [SV66: nat] :
( ( ( SV66 != zero_zero_nat )
= $false )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1377,plain,
! [SV70: nat] :
( ( ( zero_zero_nat != SV70 )
= $false )
| ( ( zero_zero_nat = SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1378,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1379,plain,
! [SV70: nat] :
( ( ( zero_zero_nat != SV70 )
= $false )
| ( ( SV70 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1380,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= $false )
| ( ( SV70 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1381,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 = SV144 )
= $true )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1382,plain,
! [SV144: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ SV144 )
= $false )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1383,plain,
! [SV76: nat,SV144: nat] :
( ( ( ord_less_nat @ SV144 @ SV76 )
= $false )
| ( ( ~ ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1384,plain,
! [SV78: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1385,plain,
! [SV78: nat] :
( ( ( ~ ( ( SV78 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1386,plain,
! [SV78: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 )
| ~ ( ( SV78 != zero_zero_nat ) ) )
= $false )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1387,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1388,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1389,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1390,plain,
! [SV85: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV85 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1391,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1392,plain,
! [SV87: nat] :
( ( ( zero_zero_nat != SV87 )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1393,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV87 ) )
= $false )
| ( ( zero_zero_nat = SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1394,plain,
! [SV87: nat] :
( ( ( zero_zero_nat != SV87 )
= $false )
| ( ( zero_zero_nat = SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1395,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1396,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1397,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
!= zero_zero_nat )
= $false )
| ( ( SV88 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1398,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= $false )
| ( ( SV88 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1399,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) )
= $false )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1400,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
| ~ ( ord_less_nat @ SV89 @ SV149 ) )
= $false )
| ( ( ord_less_nat @ SV89 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1401,plain,
! [SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1402,plain,
! [SV96: nat] :
( ( ( SV96 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1403,plain,
! [SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ zero_zero_nat ) )
= $false )
| ( ( SV96 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1404,plain,
! [SV96: nat] :
( ( ( SV96 != zero_zero_nat )
= $false )
| ( ( SV96 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1405,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1406,plain,
! [SV97: nat,SV153: nat] :
( ( ( SV153 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1407,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1408,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1409,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1410,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV101 @ zero_zero_nat ) )
= $false )
| ( ( SV101 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1285]) ).
thf(1411,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= $false )
| ( ( SV101 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1285]) ).
thf(1412,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1413,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1414,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV102 @ zero_zero_nat ) )
= $false )
| ( ( SV102 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1415,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= $false )
| ( ( SV102 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1416,plain,
! [SV182: nat,SV155: nat] :
( ( ( ( ord_less_eq_nat @ SV155 @ SV182 )
| ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1417,plain,
! [SV193: nat,SV184: nat,SV108: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV108 @ SV184 ) @ ( power_power_nat @ SV108 @ SV193 ) )
= $false )
| ( ( ord_less_nat @ SV184 @ SV193 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1418,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1419,plain,
! [SV113: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1420,plain,
! [SV160: nat,SV113: nat] :
( ( ( ord_less_nat @ SV113 @ SV160 )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1421,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1422,plain,
! [SV114: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1423,plain,
! [SV161: nat,SV114: nat] :
( ( ( ord_less_nat @ SV114 @ SV161 )
= $false )
| ( ( ~ ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1424,plain,
! [SV115: nat > $o] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1425,plain,
! [SV115: nat > $o] :
( ( ( ~ ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1426,plain,
! [SV185: nat,SV162: nat] :
( ( ( ( ord_less_eq_nat @ SV162 @ SV185 )
| ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1427,plain,
! [SV163: set_nat,SV117: nat,SV194: nat > $o] :
( ( ( SV194 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) )
| ~ ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) ) )
= $true )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1428,plain,
! [SV201: nat,SV118: nat > $o] :
( ( ( SV118 @ SV201 )
= $true )
| ( ( SV118 @ ( sK10_N2 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1429,plain,
! [SV118: nat > $o,SV197: nat] :
( ( ( ~ ( ord_less_nat @ SV197 @ ( sK10_N2 @ SV118 ) ) )
= $true )
| ( ( SV118 @ SV197 )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1430,plain,
! [SV186: nat,SV164: nat] :
( ( ( ( ord_less_nat @ SV164 @ SV186 )
| ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1431,plain,
! [SV120: nat > nat,SV202: nat,SV198: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV198 @ SV202 )
| ( ord_less_eq_nat @ ( SV120 @ SV198 ) @ ( SV120 @ SV202 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1432,plain,
! [SV120: nat > nat,SV203: nat] :
( ( ( ! [SY319: nat] :
( ~ ( ord_less_eq_nat @ SV203 @ SY319 )
| ( ord_less_eq_nat @ ( SV120 @ SV203 ) @ ( SV120 @ SY319 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1433,plain,
! [SV121: nat > $o,SV199: nat] :
( ( ( ~ ( ord_less_nat @ SV199 @ ( sK9_N2 @ SV121 ) ) )
= $true )
| ( ( SV121 @ SV199 )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1434,plain,
! [SV204: nat,SV121: nat > $o] :
( ( ( SV121 @ SV204 )
= $true )
| ( ( SV121 @ ( sK9_N2 @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1435,plain,
! [SV165: nat > $o,SV122: set_nat,SV187: nat] :
( ( ( member_nat @ SV187 @ SV122 )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( ~ ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1436,plain,
! [SV188: nat,SV166: nat] :
( ( ( ( ord_less_nat @ SV166 @ SV188 )
| ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1437,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1438,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1439,plain,
! [SV125: list_a > $o,SV200: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV200 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) ) )
= $true )
| ( ( SV125 @ SV200 )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1440,plain,
! [SV205: list_a,SV125: list_a > $o] :
( ( ( SV125 @ SV205 )
= $true )
| ( ( SV125 @ ( sK12_Xs2 @ SV125 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1441,plain,
! [SV206: nat,SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SV206 @ SV126 )
| ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) )
| ( SV168 @ SV206 ) )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1442,plain,
! [SV126: set_nat,SV168: nat > $o] :
( ( ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) )
= $false )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1443,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1444,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ( ~ ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1445,plain,
! [SV195: nat,SV189: nat] :
( ( ( SV189 = SV195 )
= $false )
| ( ( ord_less_eq_nat @ SV189 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1446,plain,
! [SV196: nat,SV190: nat] :
( ( ( ord_less_nat @ SV190 @ SV196 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1447,plain,
! [SV207: nat,SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SV207 @ SV128 )
| ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) )
| ( SV170 @ SV207 ) )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1448,plain,
! [SV128: set_nat,SV170: nat > $o] :
( ( ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) )
= $false )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1449,plain,
! [SV191: nat,SV171: nat] :
( ( ( ( ord_less_nat @ SV171 @ SV191 )
| ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1450,plain,
! [SV192: nat,SV172: nat] :
( ( ( ( ord_less_eq_nat @ SV172 @ SV192 )
| ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1451,plain,
! [SV25: list_a] :
( ( ( SV25 = nil_a )
= $true )
| ( ( SV25 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1452,plain,
! [SV25: list_a] :
( ( ( null_a @ SV25 )
= $true )
| ( ( SV25 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1453,plain,
! [SV25: list_a] :
( ( ( SV25 = nil_a )
= $true )
| ( ( null_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1454,plain,
! [SV25: list_a] :
( ( ( null_a @ SV25 )
= $true )
| ( ( null_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1455,plain,
! [SV26: list_list_a] :
( ( ( SV26 = nil_list_a )
= $true )
| ( ( SV26 = nil_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1456,plain,
! [SV26: list_list_a] :
( ( ( null_list_a @ SV26 )
= $true )
| ( ( SV26 = nil_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1457,plain,
! [SV26: list_list_a] :
( ( ( SV26 = nil_list_a )
= $true )
| ( ( null_list_a @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1458,plain,
! [SV26: list_list_a] :
( ( ( null_list_a @ SV26 )
= $true )
| ( ( null_list_a @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1459,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $true )
| ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1460,plain,
! [SV35: list_list_a] :
( ( ( SV35 = nil_list_a )
= $true )
| ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1461,plain,
! [SV35: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV35 )
= zero_zero_nat )
= $true )
| ( ( SV35 = nil_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1462,plain,
! [SV35: list_list_a] :
( ( ( SV35 = nil_list_a )
= $true )
| ( ( SV35 = nil_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1331]) ).
thf(1463,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $true )
| ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1464,plain,
! [SV36: list_a] :
( ( ( SV36 = nil_a )
= $true )
| ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1465,plain,
! [SV36: list_a] :
( ( ( ( size_size_list_a @ SV36 )
= zero_zero_nat )
= $true )
| ( ( SV36 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1466,plain,
! [SV36: list_a] :
( ( ( SV36 = nil_a )
= $true )
| ( ( SV36 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1467,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1468,plain,
! [SV42: $o] :
( ( ( ~ $true ) = $false )
| ( SV42 = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1469,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $true = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1470,plain,
! [SV42: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1471,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( SV42 = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1472,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1473,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1474,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1475,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1476,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1477,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1478,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1479,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1480,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1481,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1482,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1483,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1484,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1485,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 = nil_list_list_a )
= $true )
| ( ( SV50 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1486,plain,
! [SV50: list_list_list_a] :
( ( ( null_list_list_a @ SV50 )
= $true )
| ( ( SV50 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1487,plain,
! [SV50: list_list_list_a] :
( ( ( SV50 = nil_list_list_a )
= $true )
| ( ( null_list_list_a @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1488,plain,
! [SV50: list_list_list_a] :
( ( ( null_list_list_a @ SV50 )
= $true )
| ( ( null_list_list_a @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1489,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $true )
| ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1490,plain,
! [SV52: list_list_list_a] :
( ( ( SV52 = nil_list_list_a )
= $true )
| ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1491,plain,
! [SV52: list_list_list_a] :
( ( ( ( size_s575106428list_a @ SV52 )
= zero_zero_nat )
= $true )
| ( ( SV52 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1492,plain,
! [SV52: list_list_list_a] :
( ( ( SV52 = nil_list_list_a )
= $true )
| ( ( SV52 = nil_list_list_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1493,plain,
! [SV53: list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1494,plain,
! [SV53: list_list_a] :
( ( ( SV53 != nil_list_a )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1357]) ).
thf(1495,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) ) )
= $false )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1496,plain,
! [SV53: list_list_a] :
( ( ( ~ ( ( SV53 != nil_list_a ) ) )
= $false )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1497,plain,
! [SV54: list_list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1498,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 != nil_list_list_a )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1499,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) ) )
= $false )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1500,plain,
! [SV54: list_list_list_a] :
( ( ( ~ ( ( SV54 != nil_list_list_a ) ) )
= $false )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1501,plain,
! [SV55: list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1502,plain,
! [SV55: list_a] :
( ( ( SV55 != nil_a )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1503,plain,
! [SV55: list_a] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) ) )
= $false )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1504,plain,
! [SV55: list_a] :
( ( ( ~ ( ( SV55 != nil_a ) ) )
= $false )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1505,plain,
! [SV60: nat] :
( ( ( ~ ( ( SV60 != zero_zero_nat ) ) )
= $false )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1506,plain,
! [SV60: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $false )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1507,plain,
! [SV60: nat] :
( ( ( SV60 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1508,plain,
! [SV60: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1509,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1510,plain,
! [SV62: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1511,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1512,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1513,plain,
! [SV63: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1514,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1515,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1516,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $true )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1517,plain,
! [SV66: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1518,plain,
! [SV66: nat] :
( ( ( SV66 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1519,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1520,plain,
! [SV66: nat] :
( ( ( SV66 = zero_zero_nat )
= $true )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1521,plain,
! [SV70: nat] :
( ( ( zero_zero_nat = SV70 )
= $true )
| ( ( zero_zero_nat = SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1522,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1523,plain,
! [SV70: nat] :
( ( ( zero_zero_nat = SV70 )
= $true )
| ( ( SV70 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1524,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $true )
| ( ( SV70 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1525,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1526,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1527,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) )
| ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1528,plain,
! [SV78: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1529,plain,
! [SV78: nat] :
( ( ( SV78 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1530,plain,
! [SV78: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV78 ) )
= $false )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1531,plain,
! [SV78: nat] :
( ( ( ~ ( ( SV78 != zero_zero_nat ) ) )
= $false )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1532,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1533,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1534,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV85 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1535,plain,
! [SV85: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1536,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1537,plain,
! [SV87: nat] :
( ( ( zero_zero_nat = SV87 )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1538,plain,
! [SV87: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV87 ) )
= $true )
| ( ( zero_zero_nat = SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1539,plain,
! [SV87: nat] :
( ( ( zero_zero_nat = SV87 )
= $true )
| ( ( zero_zero_nat = SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1540,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1541,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1542,plain,
! [SV88: nat] :
( ( ( ( semiri1382578993at_nat @ SV88 )
= zero_zero_nat )
= $true )
| ( ( SV88 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1543,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $true )
| ( ( SV88 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1544,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) ) )
= $false )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1545,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ SV89 @ SV149 ) )
= $false )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1546,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) ) )
= $false )
| ( ( ord_less_nat @ SV89 @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1547,plain,
! [SV149: nat,SV89: nat] :
( ( ( ~ ( ord_less_nat @ SV89 @ SV149 ) )
= $false )
| ( ( ord_less_nat @ SV89 @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1548,plain,
! [SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1549,plain,
! [SV96: nat] :
( ( ( SV96 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1550,plain,
! [SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ zero_zero_nat )
= $true )
| ( ( SV96 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1551,plain,
! [SV96: nat] :
( ( ( SV96 = zero_zero_nat )
= $true )
| ( ( SV96 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1552,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1553,plain,
! [SV97: nat,SV153: nat] :
( ( ( ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1554,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1555,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
| ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1556,plain,
! [SV101: nat] :
( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1557,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1558,plain,
! [SV101: nat] :
( ( ( ord_less_eq_nat @ SV101 @ zero_zero_nat )
= $true )
| ( ( SV101 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1559,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $true )
| ( ( SV101 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1560,plain,
! [SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1561,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1562,plain,
! [SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ zero_zero_nat )
= $true )
| ( ( SV102 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1563,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $true )
| ( ( SV102 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1564,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1565,plain,
! [SV182: nat,SV155: nat] :
( ( ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1566,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
= $false )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1567,plain,
! [SV113: nat,SV160: nat] :
( ( ( ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1568,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1569,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
| ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1570,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1571,plain,
! [SV114: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1572,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1573,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1574,plain,
! [SV208: nat,SV115: nat > $o] :
( ( ( SV115 @ SV208 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK8_N2 @ SV115 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1575,plain,
! [SV115: nat > $o] :
( ( ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1576,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1577,plain,
! [SV185: nat,SV162: nat] :
( ( ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1578,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat] :
( ( ( ~ ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) )
| ~ ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1579,plain,
! [SV118: nat > $o,SV197: nat] :
( ( ( ord_less_nat @ SV197 @ ( sK10_N2 @ SV118 ) )
= $false )
| ( ( SV118 @ SV197 )
= $true )
| ( ( ! [SY260: nat] : ( SV118 @ SY260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1580,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_nat @ SV164 @ SV186 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1581,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1582,plain,
! [SV120: nat > nat,SV202: nat,SV198: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV198 @ SV202 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV120 @ SV198 ) @ ( SV120 @ SV202 ) )
= $true )
| ( ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1583,plain,
! [SV120: nat > nat,SV209: nat,SV203: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV203 @ SV209 )
| ( ord_less_eq_nat @ ( SV120 @ SV203 ) @ ( SV120 @ SV209 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1584,plain,
! [SV121: nat > $o,SV199: nat] :
( ( ( ord_less_nat @ SV199 @ ( sK9_N2 @ SV121 ) )
= $false )
| ( ( SV121 @ SV199 )
= $true )
| ( ( ! [SY265: nat] : ( SV121 @ SY265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1585,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat] :
( ( ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) )
| ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1586,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1587,plain,
! [SV188: nat,SV166: nat] :
( ( ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1588,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1589,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1590,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 != zero_zero_nat )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1591,plain,
! [SV125: list_a > $o,SV200: list_a] :
( ( ( ord_less_nat @ ( size_size_list_a @ SV200 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
= $false )
| ( ( SV125 @ SV200 )
= $true )
| ( ( ! [SY273: list_a] : ( SV125 @ SY273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1592,plain,
! [SV206: nat,SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SV206 @ SV126 )
| ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1593,plain,
! [SV126: set_nat,SV210: nat,SV168: nat > $o] :
( ( ( SV168 @ SV210 )
= $true )
| ( ( SV168 @ ( sK6_X3 @ SV168 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1594,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1595,plain,
! [SV169: nat,SV127: nat > $o] :
( ( ( SV127 @ ( sK1_K3 @ SV169 @ SV127 ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1596,plain,
! [SV207: nat,SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SV207 @ SV128 )
| ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1597,plain,
! [SV128: set_nat,SV211: nat,SV170: nat > $o] :
( ( ( SV170 @ SV211 )
= $true )
| ( ( SV170 @ ( sK7_X3 @ SV170 @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1598,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1599,plain,
! [SV171: nat,SV191: nat] :
( ( ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1600,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1601,plain,
! [SV172: nat,SV192: nat] :
( ( ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1602,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1603,plain,
! [SV42: $o] :
( ( $true = $true )
| ( SV42 = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1604,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $true = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1605,plain,
! [SV42: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV42 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1606,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1607,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( SV42 = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1608,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $false = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1609,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1610,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1611,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1612,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1613,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1614,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1615,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1616,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1617,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1618,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1619,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1620,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1621,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1622,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1623,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1624,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1625,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1626,plain,
! [SV53: list_list_a] :
( ( ( SV53 = nil_list_a )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1627,plain,
! [SV53: list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ SV53 ) )
= $true )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1628,plain,
! [SV53: list_list_a] :
( ( ( SV53 != nil_list_a )
= $true )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1629,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 = nil_list_list_a )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1630,plain,
! [SV54: list_list_list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ SV54 ) )
= $true )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1631,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 != nil_list_list_a )
= $true )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1632,plain,
! [SV55: list_a] :
( ( ( SV55 = nil_a )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1633,plain,
! [SV55: list_a] :
( ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ SV55 ) )
= $true )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1634,plain,
! [SV55: list_a] :
( ( ( SV55 != nil_a )
= $true )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1635,plain,
! [SV60: nat] :
( ( ( SV60 != zero_zero_nat )
= $true )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1636,plain,
! [SV60: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $true )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1637,plain,
! [SV60: nat] :
( ( ( SV60 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1638,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1639,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1640,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1641,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1642,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1643,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1644,plain,
! [SV66: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV66 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1645,plain,
! [SV66: nat] :
( ( ( SV66 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1646,plain,
! [SV66: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1647,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) ) )
= $false )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1648,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1649,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) ) )
= $false )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1526]) ).
thf(1650,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1526]) ).
thf(1651,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( SV76 != SV144 ) ) )
= $false )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1652,plain,
! [SV144: nat,SV76: nat] :
( ( ( ~ ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1653,plain,
! [SV78: nat] :
( ( ( SV78 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1654,plain,
! [SV78: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV78 )
= $true )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1655,plain,
! [SV78: nat] :
( ( ( SV78 != zero_zero_nat )
= $true )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1656,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $true )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1657,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ SV89 @ SV149 )
= $true )
| ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1658,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ ( semiri1382578993at_nat @ SV89 ) @ ( semiri1382578993at_nat @ SV149 ) )
= $true )
| ( ( ord_less_nat @ SV89 @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1659,plain,
! [SV149: nat,SV89: nat] :
( ( ( ord_less_nat @ SV89 @ SV149 )
= $true )
| ( ( ord_less_nat @ SV89 @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1660,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1661,plain,
! [SV97: nat,SV153: nat] :
( ( ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1662,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) ) )
= $false )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1663,plain,
! [SV97: nat,SV153: nat] :
( ( ( ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1664,plain,
! [SV153: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1665,plain,
! [SV97: nat,SV153: nat] :
( ( ( ~ ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1666,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1667,plain,
! [SV182: nat,SV155: nat] :
( ( ( SV155 = SV182 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1668,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV182 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1669,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $true )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1670,plain,
! [SV113: nat,SV160: nat] :
( ( ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
= $true )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1567]) ).
thf(1671,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1672,plain,
! [SV113: nat,SV160: nat] :
( ( ( ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1673,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
!= zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1674,plain,
! [SV113: nat,SV160: nat] :
( ( ( ~ ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1675,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1676,plain,
! [SV114: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
= $true )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1677,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1678,plain,
! [SV114: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1679,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1680,plain,
! [SV114: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) ) )
= $false )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1681,plain,
! [SV115: nat > $o] :
( ( ( ~ ~ ( SV115 @ ( sK8_N2 @ SV115 ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1682,plain,
! [SV115: nat > $o] :
( ( ( ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1683,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1684,plain,
! [SV162: nat,SV185: nat] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
| ( SV185
!= ( sK13_SY311 @ SV185 @ SV162 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1577]) ).
thf(1685,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat] :
( ( ( ~ ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1686,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( ~ ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1687,plain,
! [SV197: nat,SV212: nat,SV118: nat > $o] :
( ( ( SV118 @ SV212 )
= $true )
| ( ( SV118 @ SV197 )
= $true )
| ( ( ord_less_nat @ SV197 @ ( sK10_N2 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1688,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1689,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1690,plain,
! [SV120: nat > nat,SV202: nat,SV198: nat] :
( ( ( ord_less_eq_nat @ SV198 @ SV202 )
= $false )
| ( ( ord_less_eq_nat @ ( SV120 @ SV198 ) @ ( SV120 @ SV202 ) )
= $true )
| ( ( ord_less_nat @ ( sK2_I3 @ SV120 ) @ ( sK3_SY210 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1691,plain,
! [SV120: nat > nat,SV209: nat,SV203: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV203 @ SV209 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV120 @ SV203 ) @ ( SV120 @ SV209 ) )
= $true )
| ( ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1692,plain,
! [SV199: nat,SV213: nat,SV121: nat > $o] :
( ( ( SV121 @ SV213 )
= $true )
| ( ( SV121 @ SV199 )
= $true )
| ( ( ord_less_nat @ SV199 @ ( sK9_N2 @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1693,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat] :
( ( ( ~ ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1694,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1695,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1696,plain,
! [SV166: nat,SV188: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
| ( SV188
!= ( sK14_SY312 @ SV188 @ SV166 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1587]) ).
thf(1697,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1698,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $true )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1699,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1700,plain,
! [SV200: list_a,SV214: list_a,SV125: list_a > $o] :
( ( ( SV125 @ SV214 )
= $true )
| ( ( SV125 @ SV200 )
= $true )
| ( ( ord_less_nat @ ( size_size_list_a @ SV200 ) @ ( size_size_list_a @ ( sK12_Xs2 @ SV125 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1701,plain,
! [SV206: nat,SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
| ~ ( member_nat @ SV206 @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1702,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) )
| ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1703,plain,
! [SV207: nat,SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
| ~ ( member_nat @ SV207 @ SV128 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1704,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1705,plain,
! [SV171: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
| ( SV171
!= ( sK15_SY315 @ SV171 @ SV191 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1599]) ).
thf(1706,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1707,plain,
! [SV172: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
| ( SV172
!= ( sK16_SY316 @ SV172 @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1601]) ).
thf(1708,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false )
| ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1602]) ).
thf(1709,plain,
! [SV42: $o] :
( ( ( SV42 = $false )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1602]) ).
thf(1710,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false )
| ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1603]) ).
thf(1711,plain,
! [SV42: $o] :
( ( ( SV42 = $false )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1603]) ).
thf(1712,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false )
| ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1604]) ).
thf(1713,plain,
! [SV42: $o] :
( ( ( SV42 = $false )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1604]) ).
thf(1714,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false )
| ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1605]) ).
thf(1715,plain,
! [SV42: $o] :
( ( ( SV42 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1605]) ).
thf(1716,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1717,plain,
! [SV42: $o] :
( ( $false = $true )
| ( SV42 = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1718,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $false = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1719,plain,
! [SV42: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV42 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1720,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1610]) ).
thf(1721,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1610]) ).
thf(1722,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1611]) ).
thf(1723,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1611]) ).
thf(1724,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1612]) ).
thf(1725,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1612]) ).
thf(1726,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1613]) ).
thf(1727,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1613]) ).
thf(1728,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1729,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1730,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1731,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1732,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1618]) ).
thf(1733,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1618]) ).
thf(1734,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1619]) ).
thf(1735,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1619]) ).
thf(1736,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1620]) ).
thf(1737,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1620]) ).
thf(1738,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1621]) ).
thf(1739,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1621]) ).
thf(1740,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1741,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1742,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1743,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1744,plain,
! [SV53: list_list_a] :
( ( ( SV53 = nil_list_a )
= $false )
| ( ( SV53 = nil_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1745,plain,
! [SV54: list_list_list_a] :
( ( ( SV54 = nil_list_list_a )
= $false )
| ( ( SV54 = nil_list_list_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1746,plain,
! [SV55: list_a] :
( ( ( SV55 = nil_a )
= $false )
| ( ( SV55 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1747,plain,
! [SV60: nat] :
( ( ( SV60 = zero_zero_nat )
= $false )
| ( ( SV60 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1748,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1749,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1750,plain,
! [SV66: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1751,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= $true )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1752,plain,
! [SV144: nat,SV76: nat] :
( ( ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
= $true )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1753,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= $true )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1754,plain,
! [SV144: nat,SV76: nat] :
( ( ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
= $true )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1755,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 != SV144 )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1756,plain,
! [SV144: nat,SV76: nat] :
( ( ( ( ord_less_nat @ SV76 @ SV144 )
| ( ord_less_nat @ SV144 @ SV76 ) )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1757,plain,
! [SV78: nat] :
( ( ( SV78 = zero_zero_nat )
= $false )
| ( ( SV78 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1758,plain,
! [SV97: nat,SV153: nat] :
( ( ( SV153 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1759,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $true )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1760,plain,
! [SV97: nat,SV153: nat] :
( ( ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1761,plain,
! [SV153: nat,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV97 @ SV153 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1762,plain,
! [SV97: nat,SV153: nat] :
( ( ( ( SV153 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1763,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1764,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1765,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1766,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 )
| ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1767,plain,
! [SV113: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $true )
| ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1768,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1769,plain,
! [SV113: nat,SV160: nat] :
( ( ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1770,plain,
! [SV160: nat,SV113: nat] :
( ( ( ( divide_divide_nat @ SV113 @ SV160 )
= zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1771,plain,
! [SV113: nat,SV160: nat] :
( ( ( ( SV160 = zero_zero_nat )
| ( ord_less_nat @ SV113 @ SV160 ) )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1772,plain,
! [SV114: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $true )
| ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1773,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1774,plain,
! [SV114: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1775,plain,
! [SV161: nat,SV114: nat] :
( ( ( ( divide_divide_nat @ SV114 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1776,plain,
! [SV114: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( ord_less_nat @ SV114 @ SV161 ) )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1777,plain,
! [SV115: nat > $o] :
( ( ( ~ ( SV115 @ ( sK8_N2 @ SV115 ) ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1778,plain,
! [SV115: nat > $o] :
( ( ( ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SY252 ) ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1779,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1780,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1781,plain,
! [SV162: nat,SV185: nat] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1782,plain,
! [SV162: nat,SV185: nat] :
( ( ( SV185
!= ( sK13_SY311 @ SV185 @ SV162 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1783,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat] :
( ( ( ! [SY317: nat] :
( ~ ( member_nat @ SY317 @ SV163 )
| ~ ( ord_less_nat @ SY317 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SY317 ) ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1784,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( ~ ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1785,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_nat @ SV164 @ SV186 ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1786,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1787,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1788,plain,
! [SV120: nat > nat,SV209: nat,SV203: nat] :
( ( ( ord_less_eq_nat @ SV203 @ SV209 )
= $false )
| ( ( ord_less_eq_nat @ ( SV120 @ SV203 ) @ ( SV120 @ SV209 ) )
= $true )
| ( ( ord_less_nat @ ( SV120 @ ( sK2_I3 @ SV120 ) ) @ ( SV120 @ ( sK3_SY210 @ SV120 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1789,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat] :
( ( ( ! [SY294: nat] :
( ~ ( member_nat @ SY294 @ SV122 )
| ~ ( ord_less_nat @ SY294 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SY294 ) ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1790,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( ~ ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1791,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 ) )
= $false )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1792,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1793,plain,
! [SV166: nat,SV188: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1794,plain,
! [SV166: nat,SV188: nat] :
( ( ( SV188
!= ( sK14_SY312 @ SV188 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1795,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1796,plain,
! [SV124: nat,SV167: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1797,plain,
! [SV206: nat,SV126: set_nat,SV168: nat > $o] :
( ( ( ~ ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 ) )
= $true )
| ( ( ~ ( member_nat @ SV206 @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1798,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1799,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1800,plain,
! [SV207: nat,SV128: set_nat,SV170: nat > $o] :
( ( ( ~ ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 ) )
= $true )
| ( ( ~ ( member_nat @ SV207 @ SV128 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1801,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1802,plain,
! [SV171: nat,SV191: nat] :
( ( ( ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1803,plain,
! [SV171: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1804,plain,
! [SV191: nat,SV171: nat] :
( ( ( SV171
!= ( sK15_SY315 @ SV171 @ SV191 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1805,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 ) )
= $false )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1806,plain,
! [SV172: nat,SV192: nat] :
( ( ( ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1807,plain,
! [SV172: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1808,plain,
! [SV192: nat,SV172: nat] :
( ( ( SV172
!= ( sK16_SY316 @ SV172 @ SV192 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1809,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1810,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1811,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1812,plain,
! [SV42: $o] :
( ( ( ~ ( SV42
| $false ) )
= $true )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1813,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1814,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1815,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1816,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1817,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1818,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1819,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1820,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1821,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 = SV144 )
= $false )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1822,plain,
! [SV144: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ SV144 )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $true )
| ( ( SV76 = SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1823,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 = SV144 )
= $false )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1824,plain,
! [SV144: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ SV144 )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $true )
| ( ( ord_less_nat @ SV76 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1825,plain,
! [SV144: nat,SV76: nat] :
( ( ( SV76 = SV144 )
= $false )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1826,plain,
! [SV144: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ SV144 )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $true )
| ( ( ord_less_nat @ SV144 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1827,plain,
! [SV97: nat,SV153: nat] :
( ( ( SV153 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $true )
| ( ( SV153 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1828,plain,
! [SV97: nat,SV153: nat] :
( ( ( SV153 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1829,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1830,plain,
! [SV182: nat,SV155: nat] :
( ( ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1831,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 ) )
= $false )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1832,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1833,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV182 ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1834,plain,
! [SV182: nat,SV155: nat] :
( ( ( ~ ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1835,plain,
! [SV113: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1836,plain,
! [SV113: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $true )
| ( ( ord_less_nat @ SV113 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1837,plain,
! [SV114: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1838,plain,
! [SV114: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $true )
| ( ( ord_less_nat @ SV114 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(1839,plain,
! [SV115: nat > $o] :
( ( ( SV115 @ ( sK8_N2 @ SV115 ) )
= $false )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1840,plain,
! [SV115: nat > $o,SV215: nat] :
( ( ( ~ ( ord_less_nat @ SV215 @ ( sK8_N2 @ SV115 ) )
| ( SV115 @ SV215 ) )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1841,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $true )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1842,plain,
! [SV185: nat,SV162: nat] :
( ( ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1843,plain,
! [SV162: nat,SV185: nat] :
( ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1844,plain,
! [SV162: nat,SV185: nat] :
( ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1845,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat,SV216: nat] :
( ( ( ~ ( member_nat @ SV216 @ SV163 )
| ~ ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SV216 ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1846,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1847,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_nat @ SV164 @ SV186 )
= $true )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1848,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $true )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1849,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 != SV186 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1850,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat,SV217: nat] :
( ( ( ~ ( member_nat @ SV217 @ SV122 )
| ~ ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SV217 ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1851,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1852,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= $true )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1853,plain,
! [SV188: nat,SV166: nat] :
( ( ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $true )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1854,plain,
! [SV166: nat,SV188: nat] :
( ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1855,plain,
! [SV166: nat,SV188: nat] :
( ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1856,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 != zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1857,plain,
! [SV124: nat,SV167: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $false )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1858,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
| ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1859,plain,
! [SV206: nat,SV126: set_nat,SV168: nat > $o] :
( ( ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
= $false )
| ( ( ~ ( member_nat @ SV206 @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1860,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SY299 ) ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1861,plain,
! [SV127: nat > $o,SV169: nat] :
( ( ( ord_less_eq_nat @ ( sK1_K3 @ SV169 @ SV127 ) @ SV169 )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1862,plain,
! [SV207: nat,SV128: set_nat,SV170: nat > $o] :
( ( ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
= $false )
| ( ( ~ ( member_nat @ SV207 @ SV128 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1863,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= $true )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1864,plain,
! [SV171: nat,SV191: nat] :
( ( ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1865,plain,
! [SV171: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1866,plain,
! [SV191: nat,SV171: nat] :
( ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1867,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1868,plain,
! [SV172: nat,SV192: nat] :
( ( ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1869,plain,
! [SV172: nat,SV192: nat] :
( ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1870,plain,
! [SV192: nat,SV172: nat] :
( ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1871,plain,
! [SV42: $o] :
( ( ( SV42
| $false )
= $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1872,plain,
! [SV42: $o] :
( ( ( SV42
| $false )
= $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1873,plain,
! [SV42: $o] :
( ( ( SV42
| $false )
= $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1874,plain,
! [SV42: $o] :
( ( ( SV42
| $false )
= $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1875,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1876,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1877,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1878,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1879,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1880,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1881,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1882,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1883,plain,
! [SV182: nat,SV155: nat] :
( ( ( SV155 = SV182 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1884,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $true )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1885,plain,
! [SV182: nat,SV155: nat] :
( ( ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
= $true )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1886,plain,
! [SV182: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV182 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1887,plain,
! [SV182: nat,SV155: nat] :
( ( ( ( SV155 = SV182 )
| ( ord_less_nat @ SV155 @ SV182 ) )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1888,plain,
! [SV218: nat,SV115: nat > $o] :
( ( ( SV115 @ SV218 )
= $true )
| ( ( SV115 @ ( sK8_N2 @ SV115 ) )
= $false )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1889,plain,
! [SV115: nat > $o,SV215: nat] :
( ( ( ~ ( ord_less_nat @ SV215 @ ( sK8_N2 @ SV115 ) ) )
= $true )
| ( ( SV115 @ SV215 )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1890,plain,
! [SV185: nat,SV162: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ SV219 @ SV162 )
| ( SV185 != SV219 ) )
= $true )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(1891,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1892,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 )
| ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1893,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat,SV216: nat] :
( ( ( ~ ( member_nat @ SV216 @ SV163 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SV216 ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1894,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( ~ ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(1895,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( ~ ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 ) )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(1896,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1897,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 = SV186 )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1898,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat,SV217: nat] :
( ( ( ~ ( member_nat @ SV217 @ SV122 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SV217 ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1899,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( ~ ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1900,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( ~ ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 ) )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1901,plain,
! [SV188: nat,SV166: nat,SV220: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV220 @ SV166 )
| ( SV188 != SV220 ) )
= $true )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(1902,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1903,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 )
| ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1904,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1905,plain,
! [SV124: nat,SV167: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $true )
| ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1906,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
!= zero_zero_nat )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1907,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1908,plain,
! [SV168: nat > $o,SV126: set_nat,SV206: nat] :
( ( ( member_nat @ SV206 @ SV126 )
= $false )
| ( ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
= $false )
| ( ( ~ ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) ) )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1909,plain,
! [SV127: nat > $o,SV169: nat,SV221: nat] :
( ( ( ~ ( ord_less_nat @ SV221 @ ( sK1_K3 @ SV169 @ SV127 ) )
| ~ ( SV127 @ SV221 ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(1910,plain,
! [SV170: nat > $o,SV128: set_nat,SV207: nat] :
( ( ( member_nat @ SV207 @ SV128 )
= $false )
| ( ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
= $false )
| ( ( ~ ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) ) )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1911,plain,
! [SV171: nat,SV222: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV222 )
| ( SV171 != SV222 ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(1912,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1913,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1914,plain,
! [SV172: nat,SV223: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV223 )
| ( SV172 != SV223 ) )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(1915,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1916,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 )
| ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1917,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1918,plain,
! [SV42: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1919,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1920,plain,
! [SV42: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1921,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1922,plain,
! [SV42: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1923,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1924,plain,
! [SV42: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV42
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1925,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1926,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1927,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1928,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1929,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1930,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1931,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(1932,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(1933,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1934,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1935,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1936,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1937,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1938,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1939,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1940,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1941,plain,
! [SV182: nat,SV155: nat] :
( ( ( SV155 = SV182 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $true )
| ( ( SV155 = SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(1942,plain,
! [SV182: nat,SV155: nat] :
( ( ( SV155 = SV182 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(1943,plain,
! [SV115: nat > $o,SV215: nat] :
( ( ( ord_less_nat @ SV215 @ ( sK8_N2 @ SV115 ) )
= $false )
| ( ( SV115 @ SV215 )
= $true )
| ( ( ! [SY253: nat] : ( SV115 @ SY253 ) )
= $true )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1944,plain,
! [SV185: nat,SV162: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ SV219 @ SV162 ) )
= $true )
| ( ( SV185 != SV219 )
= $true )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1945,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(1946,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(1947,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV162 @ SV185 ) )
= $false )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1948,plain,
! [SV185: nat,SV162: nat] :
( ( ( ~ ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $false )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1949,plain,
! [SV117: nat,SV194: nat > $o,SV163: set_nat,SV216: nat] :
( ( ( member_nat @ SV216 @ SV163 )
= $false )
| ( ( ~ ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
| ~ ( SV194 @ SV216 ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1950,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( SV194 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1951,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o] :
( ( ( member_nat @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) @ SV163 )
= $true )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1952,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1953,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1954,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1955,plain,
! [SV187: nat,SV165: nat > $o,SV122: set_nat,SV217: nat] :
( ( ( member_nat @ SV217 @ SV122 )
= $false )
| ( ( ~ ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) )
| ~ ( SV165 @ SV217 ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(1956,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( SV165 @ ( sK4_X3 @ SV165 @ SV122 ) )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1957,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o] :
( ( ( member_nat @ ( sK4_X3 @ SV165 @ SV122 ) @ SV122 )
= $true )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1958,plain,
! [SV188: nat,SV166: nat,SV220: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV220 @ SV166 ) )
= $true )
| ( ( SV188 != SV220 )
= $true )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1959,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1960,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1961,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV188 ) )
= $false )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1962,plain,
! [SV188: nat,SV166: nat] :
( ( ( ~ ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $false )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1963,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( power_power_nat @ SV124 @ SV167 )
= zero_zero_nat )
= $true )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1964,plain,
! [SV167: nat,SV124: nat] :
( ( ( ~ ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) ) )
= $true )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1965,plain,
! [SV126: set_nat,SV168: nat > $o,SV206: nat] :
( ( ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) )
= $false )
| ( ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
= $false )
| ( ( member_nat @ SV206 @ SV126 )
= $false )
| ( ( SV168 @ SV206 )
= $true )
| ( ( ! [SY298: nat] : ( SV168 @ SY298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1966,plain,
! [SV127: nat > $o,SV169: nat,SV221: nat] :
( ( ( ~ ( ord_less_nat @ SV221 @ ( sK1_K3 @ SV169 @ SV127 ) ) )
= $true )
| ( ( ~ ( SV127 @ SV221 ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1967,plain,
! [SV128: set_nat,SV170: nat > $o,SV207: nat] :
( ( ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) )
= $false )
| ( ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
= $false )
| ( ( member_nat @ SV207 @ SV128 )
= $false )
| ( ( SV170 @ SV207 )
= $true )
| ( ( ! [SY301: nat] : ( SV170 @ SY301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1968,plain,
! [SV171: nat,SV222: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV222 ) )
= $true )
| ( ( SV171 != SV222 )
= $true )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1969,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 ) )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1912]) ).
thf(1970,plain,
! [SV171: nat,SV191: nat] :
( ( ( ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1912]) ).
thf(1971,plain,
! [SV191: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV191 ) )
= $false )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(1972,plain,
! [SV171: nat,SV191: nat] :
( ( ( ~ ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $false )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(1973,plain,
! [SV172: nat,SV223: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV223 ) )
= $true )
| ( ( SV172 != SV223 )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1974,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 ) )
= $false )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1975,plain,
! [SV172: nat,SV192: nat] :
( ( ( ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1976,plain,
! [SV192: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV192 ) )
= $false )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(1977,plain,
! [SV172: nat,SV192: nat] :
( ( ( ~ ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $false )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(1978,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1979,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( $false = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1980,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1981,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( $false = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1982,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( SV42 = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1983,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1984,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( SV42 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1985,plain,
! [SV42: $o] :
( ( ( ~ SV42
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1986,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1987,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1988,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(1989,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1990,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1991,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1992,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1993,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1994,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1995,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1996,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1997,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1998,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(1999,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2000,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2001,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2002,plain,
! [SV215: nat,SV224: nat,SV115: nat > $o] :
( ( ( SV115 @ SV224 )
= $true )
| ( ( SV115 @ SV215 )
= $true )
| ( ( ord_less_nat @ SV215 @ ( sK8_N2 @ SV115 ) )
= $false )
| ( ( SV115 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2003,plain,
! [SV185: nat,SV162: nat,SV219: nat] :
( ( ( ord_less_nat @ SV219 @ SV162 )
= $false )
| ( ( SV185 != SV219 )
= $true )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2004,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $true )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2005,plain,
! [SV185: nat,SV162: nat] :
( ( ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1946]) ).
thf(2006,plain,
! [SV185: nat,SV162: nat] :
( ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $true )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2007,plain,
! [SV185: nat,SV162: nat] :
( ( ( ! [SY311: nat] :
( ~ ( ord_less_nat @ SY311 @ SV162 )
| ( SV185 != SY311 ) ) )
= $true )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2008,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o,SV216: nat] :
( ( ( ~ ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) ) )
= $true )
| ( ( ~ ( SV194 @ SV216 ) )
= $true )
| ( ( member_nat @ SV216 @ SV163 )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2009,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 != SV186 )
= $true )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2010,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $true )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2011,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_nat @ SV164 @ SV186 )
| ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2012,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o,SV217: nat] :
( ( ( ~ ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) ) )
= $true )
| ( ( ~ ( SV165 @ SV217 ) )
= $true )
| ( ( member_nat @ SV217 @ SV122 )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2013,plain,
! [SV188: nat,SV166: nat,SV220: nat] :
( ( ( ord_less_eq_nat @ SV220 @ SV166 )
= $false )
| ( ( SV188 != SV220 )
= $true )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2014,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2015,plain,
! [SV188: nat,SV166: nat] :
( ( ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2016,plain,
! [SV188: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV188 )
= $true )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2017,plain,
! [SV188: nat,SV166: nat] :
( ( ( ! [SY312: nat] :
( ~ ( ord_less_eq_nat @ SY312 @ SV166 )
| ( SV188 != SY312 ) ) )
= $true )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2018,plain,
! [SV167: nat,SV124: nat] :
( ( ( ( SV124 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2019,plain,
! [SV126: set_nat,SV206: nat,SV225: nat,SV168: nat > $o] :
( ( ( SV168 @ SV225 )
= $true )
| ( ( SV168 @ SV206 )
= $true )
| ( ( member_nat @ SV206 @ SV126 )
= $false )
| ( ( member_nat @ ( sK6_X3 @ SV168 @ SV126 ) @ SV126 )
= $false )
| ( ( ord_less_nat @ SV206 @ ( sK6_X3 @ SV168 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2020,plain,
! [SV127: nat > $o,SV169: nat,SV221: nat] :
( ( ( ord_less_nat @ SV221 @ ( sK1_K3 @ SV169 @ SV127 ) )
= $false )
| ( ( ~ ( SV127 @ SV221 ) )
= $true )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2021,plain,
! [SV128: set_nat,SV207: nat,SV226: nat,SV170: nat > $o] :
( ( ( SV170 @ SV226 )
= $true )
| ( ( SV170 @ SV207 )
= $true )
| ( ( member_nat @ SV207 @ SV128 )
= $false )
| ( ( member_nat @ ( sK7_X3 @ SV170 @ SV128 ) @ SV128 )
= $false )
| ( ( ord_less_nat @ SV207 @ ( sK7_X3 @ SV170 @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2022,plain,
! [SV171: nat,SV222: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ SV222 )
= $false )
| ( ( SV171 != SV222 )
= $true )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2023,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2024,plain,
! [SV171: nat,SV191: nat] :
( ( ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2025,plain,
! [SV191: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV191 )
= $true )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2026,plain,
! [SV171: nat,SV191: nat] :
( ( ( ! [SY315: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY315 )
| ( SV171 != SY315 ) ) )
= $true )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2027,plain,
! [SV172: nat,SV223: nat,SV192: nat] :
( ( ( ord_less_nat @ SV192 @ SV223 )
= $false )
| ( ( SV172 != SV223 )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2028,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $true )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2029,plain,
! [SV172: nat,SV192: nat] :
( ( ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $true )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2030,plain,
! [SV192: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $true )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2031,plain,
! [SV172: nat,SV192: nat] :
( ( ( ! [SY316: nat] :
( ~ ( ord_less_nat @ SV192 @ SY316 )
| ( SV172 != SY316 ) ) )
= $true )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2032,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2033,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2034,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $false = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2035,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2036,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2037,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( SV42 = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2038,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $false = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2039,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2040,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2041,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( SV42 = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2042,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2043,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2044,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( SV42 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2045,plain,
! [SV42: $o] :
( ( ( ~ $false ) = $false )
| ( SV42 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2046,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1985]) ).
thf(2047,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1985]) ).
thf(2048,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2049,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2050,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2051,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2052,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2053,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2054,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2055,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2056,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2057,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2058,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2059,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2060,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2061,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2062,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2063,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2064,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2065,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2066,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2067,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2068,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2069,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2070,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2071,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2072,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1998]) ).
thf(2073,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1998]) ).
thf(2074,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2075,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2076,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2077,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2078,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2079,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2080,plain,
! [SV162: nat,SV219: nat,SV185: nat] :
( ( ( SV185 = SV219 )
= $false )
| ( ( ord_less_nat @ SV219 @ SV162 )
= $false )
| ( ( ord_less_eq_nat @ SV162 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2081,plain,
! [SV185: nat,SV162: nat,SV227: nat] :
( ( ( ~ ( ord_less_nat @ SV227 @ SV162 )
| ( SV185 != SV227 ) )
= $true )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2082,plain,
! [SV185: nat,SV162: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV162 )
| ( SV185 != SV228 ) )
= $true )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2083,plain,
! [SV117: nat,SV163: set_nat,SV194: nat > $o,SV216: nat] :
( ( ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
= $false )
| ( ( ~ ( SV194 @ SV216 ) )
= $true )
| ( ( member_nat @ SV216 @ SV163 )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2084,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 = SV186 )
= $false )
| ( ( ord_less_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2085,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_nat @ SV164 @ SV186 ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2011]) ).
thf(2086,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2011]) ).
thf(2087,plain,
! [SV187: nat,SV122: set_nat,SV165: nat > $o,SV217: nat] :
( ( ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) )
= $false )
| ( ( ~ ( SV165 @ SV217 ) )
= $true )
| ( ( member_nat @ SV217 @ SV122 )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2088,plain,
! [SV166: nat,SV220: nat,SV188: nat] :
( ( ( SV188 = SV220 )
= $false )
| ( ( ord_less_eq_nat @ SV220 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV166 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2089,plain,
! [SV188: nat,SV166: nat,SV229: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV229 @ SV166 )
| ( SV188 != SV229 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2090,plain,
! [SV188: nat,SV166: nat,SV230: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV230 @ SV166 )
| ( SV188 != SV230 ) )
= $true )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2091,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 != zero_zero_nat )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2092,plain,
! [SV124: nat,SV167: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV167 ) )
= $false )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2093,plain,
! [SV169: nat,SV221: nat,SV127: nat > $o] :
( ( ( SV127 @ SV221 )
= $false )
| ( ( ord_less_nat @ SV221 @ ( sK1_K3 @ SV169 @ SV127 ) )
= $false )
| ( ( SV127 @ zero_zero_nat )
= $true )
| ( ( SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2094,plain,
! [SV191: nat,SV222: nat,SV171: nat] :
( ( ( SV171 = SV222 )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ SV222 )
= $false )
| ( ( ord_less_nat @ SV171 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2095,plain,
! [SV171: nat,SV231: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV231 )
| ( SV171 != SV231 ) )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2096,plain,
! [SV171: nat,SV232: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV232 )
| ( SV171 != SV232 ) )
= $true )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2097,plain,
! [SV192: nat,SV223: nat,SV172: nat] :
( ( ( SV172 = SV223 )
= $false )
| ( ( ord_less_nat @ SV192 @ SV223 )
= $false )
| ( ( ord_less_eq_nat @ SV172 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2098,plain,
! [SV172: nat,SV233: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV233 )
| ( SV172 != SV233 ) )
= $true )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2099,plain,
! [SV172: nat,SV234: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV234 )
| ( SV172 != SV234 ) )
= $true )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2100,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2101,plain,
! [SV42: $o] :
( ( $false = $true )
| ( SV42 = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2102,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $false = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2103,plain,
! [SV42: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV42 = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2104,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2036]) ).
thf(2105,plain,
! [SV42: $o] :
( ( $false = $true )
| ( SV42 = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2106,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $false = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2107,plain,
! [SV42: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV42 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2108,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2109,plain,
! [SV42: $o] :
( ( $false = $true )
| ( SV42 = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2110,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2111,plain,
! [SV42: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV42 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2112,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( SV42 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2113,plain,
! [SV42: $o] :
( ( $false = $true )
| ( SV42 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2114,plain,
! [SV42: $o] :
( ( SV42 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2115,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2116,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2117,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2118,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2119,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2120,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2121,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2122,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2123,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2124,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2125,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2126,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2127,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2128,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2129,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2130,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2131,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2132,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2133,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2134,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2135,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2136,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2137,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2138,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2139,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2140,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2141,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2142,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2143,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2144,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2145,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2146,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2147,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2148,plain,
! [SV185: nat,SV162: nat,SV227: nat] :
( ( ( ~ ( ord_less_nat @ SV227 @ SV162 ) )
= $true )
| ( ( SV185 != SV227 )
= $true )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2149,plain,
! [SV185: nat,SV162: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV162 ) )
= $true )
| ( ( SV185 != SV228 )
= $true )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2150,plain,
! [SV117: nat,SV163: set_nat,SV216: nat,SV194: nat > $o] :
( ( ( SV194 @ SV216 )
= $false )
| ( ( ord_less_nat @ SV216 @ ( sK5_X3 @ SV194 @ SV163 @ SV117 ) )
= $false )
| ( ( member_nat @ SV216 @ SV163 )
= $false )
| ( ( SV194 @ SV117 )
= $false )
| ( ( member_nat @ SV117 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2151,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_nat @ SV164 @ SV186 )
= $true )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2152,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) ) )
= $true )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2153,plain,
! [SV187: nat,SV122: set_nat,SV217: nat,SV165: nat > $o] :
( ( ( SV165 @ SV217 )
= $false )
| ( ( ord_less_nat @ SV217 @ ( sK4_X3 @ SV165 @ SV122 ) )
= $false )
| ( ( member_nat @ SV217 @ SV122 )
= $false )
| ( ( SV165 @ SV187 )
= $false )
| ( ( member_nat @ SV187 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2154,plain,
! [SV188: nat,SV166: nat,SV229: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV229 @ SV166 ) )
= $true )
| ( ( SV188 != SV229 )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2155,plain,
! [SV188: nat,SV166: nat,SV230: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV230 @ SV166 ) )
= $true )
| ( ( SV188 != SV230 )
= $true )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2156,plain,
! [SV167: nat,SV124: nat] :
( ( ( SV124 = zero_zero_nat )
= $true )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2157,plain,
! [SV124: nat,SV167: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $true )
| ( ( SV124 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2158,plain,
! [SV171: nat,SV231: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV231 ) )
= $true )
| ( ( SV171 != SV231 )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2159,plain,
! [SV171: nat,SV232: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV232 ) )
= $true )
| ( ( SV171 != SV232 )
= $true )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2160,plain,
! [SV172: nat,SV233: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV233 ) )
= $true )
| ( ( SV172 != SV233 )
= $true )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2161,plain,
! [SV172: nat,SV234: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV234 ) )
= $true )
| ( ( SV172 != SV234 )
= $true )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2162,plain,
! [SV185: nat,SV162: nat,SV227: nat] :
( ( ( ord_less_nat @ SV227 @ SV162 )
= $false )
| ( ( SV185 != SV227 )
= $true )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2163,plain,
! [SV185: nat,SV162: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV162 )
= $false )
| ( ( SV185 != SV228 )
= $true )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2164,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) )
| ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2165,plain,
! [SV188: nat,SV166: nat,SV229: nat] :
( ( ( ord_less_eq_nat @ SV229 @ SV166 )
= $false )
| ( ( SV188 != SV229 )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2166,plain,
! [SV188: nat,SV166: nat,SV230: nat] :
( ( ( ord_less_eq_nat @ SV230 @ SV166 )
= $false )
| ( ( SV188 != SV230 )
= $true )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2167,plain,
! [SV171: nat,SV231: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ SV231 )
= $false )
| ( ( SV171 != SV231 )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2168,plain,
! [SV171: nat,SV232: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ SV232 )
= $false )
| ( ( SV171 != SV232 )
= $true )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2169,plain,
! [SV172: nat,SV233: nat,SV192: nat] :
( ( ( ord_less_nat @ SV192 @ SV233 )
= $false )
| ( ( SV172 != SV233 )
= $true )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2170,plain,
! [SV172: nat,SV234: nat,SV192: nat] :
( ( ( ord_less_nat @ SV192 @ SV234 )
= $false )
| ( ( SV172 != SV234 )
= $true )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2171,plain,
! [SV162: nat,SV227: nat,SV185: nat] :
( ( ( SV185 = SV227 )
= $false )
| ( ( ord_less_nat @ SV227 @ SV162 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY311 @ SV185 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2172,plain,
! [SV162: nat,SV228: nat,SV185: nat] :
( ( ( SV185 = SV228 )
= $false )
| ( ( ord_less_nat @ SV228 @ SV162 )
= $false )
| ( ( SV185
= ( sK13_SY311 @ SV185 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2173,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ( SV164 != SV186 ) ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2174,plain,
! [SV186: nat,SV164: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV164 @ SV186 ) )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2175,plain,
! [SV166: nat,SV229: nat,SV188: nat] :
( ( ( SV188 = SV229 )
= $false )
| ( ( ord_less_eq_nat @ SV229 @ SV166 )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY312 @ SV188 @ SV166 ) @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2176,plain,
! [SV166: nat,SV230: nat,SV188: nat] :
( ( ( SV188 = SV230 )
= $false )
| ( ( ord_less_eq_nat @ SV230 @ SV166 )
= $false )
| ( ( SV188
= ( sK14_SY312 @ SV188 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2177,plain,
! [SV191: nat,SV231: nat,SV171: nat] :
( ( ( SV171 = SV231 )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ SV231 )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2178,plain,
! [SV191: nat,SV232: nat,SV171: nat] :
( ( ( SV171 = SV232 )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ SV232 )
= $false )
| ( ( SV171
= ( sK15_SY315 @ SV171 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2179,plain,
! [SV192: nat,SV233: nat,SV172: nat] :
( ( ( SV172 = SV233 )
= $false )
| ( ( ord_less_nat @ SV192 @ SV233 )
= $false )
| ( ( ord_less_nat @ SV192 @ ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2180,plain,
! [SV192: nat,SV234: nat,SV172: nat] :
( ( ( SV172 = SV234 )
= $false )
| ( ( ord_less_nat @ SV192 @ SV234 )
= $false )
| ( ( SV172
= ( sK16_SY316 @ SV172 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2181,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 != SV186 )
= $true )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2173]) ).
thf(2182,plain,
! [SV186: nat,SV164: nat] :
( ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $true )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2174]) ).
thf(2183,plain,
! [SV186: nat,SV164: nat] :
( ( ( SV164 = SV186 )
= $false )
| ( ( SV164 = SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV164 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2184,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[551,2183,2182,2180,2179,2178,2177,2176,2175,2172,2171,2157,2156,2153,2151,2150,2147,2146,2145,2144,2143,2142,2141,2140,2139,2138,2137,2136,2135,2134,2133,2132,2131,2130,2129,2128,2127,2126,2125,2124,2123,2122,2121,2120,2119,2118,2117,2116,2115,2114,2113,2112,2111,2110,2109,2108,2107,2106,2105,2104,2103,2102,2101,2100,2097,2094,2093,2088,2084,2080,2030,2028,2025,2023,2021,2019,2016,2014,2010,2006,2004,2002,1963,1957,1956,1951,1950,1942,1941,1905,1904,1888,1886,1884,1883,1867,1863,1861,1852,1847,1841,1838,1837,1836,1835,1829,1828,1827,1826,1825,1824,1823,1822,1821,1788,1775,1773,1772,1770,1768,1767,1761,1759,1758,1757,1750,1749,1748,1747,1746,1745,1744,1743,1742,1741,1740,1739,1737,1735,1733,1731,1730,1729,1728,1727,1725,1723,1721,1719,1718,1717,1716,1715,1713,1711,1709,1700,1697,1692,1690,1687,1675,1669,1660,1659,1658,1657,1656,1654,1653,1646,1645,1643,1642,1640,1639,1637,1636,1633,1632,1630,1629,1627,1626,1597,1595,1593,1574,1563,1562,1561,1560,1559,1558,1557,1556,1551,1550,1549,1548,1543,1542,1541,1540,1539,1538,1537,1536,1535,1534,1533,1532,1528,1524,1523,1522,1521,1520,1516,1512,1508,1501,1497,1493,1492,1491,1490,1489,1488,1487,1486,1485,1466,1465,1464,1463,1462,1461,1460,1459,1458,1457,1456,1455,1454,1453,1452,1451,1446,1445,1440,1434,1428,1417,1230,1228,1216,1209,1204,1198,1196,1181,1177,1176,1173,1170,1147,1146,1113,1111,1110,1105,1102,1101,1100,1095,1092,1088,1080,1074,1073,1070,1067,1058,1057,1055,1047,1045,1040,1036,1033,1031,1028,1024,1019,1017,1014,1010,1001,948,947,940,938,933,928,926,924,922,920,918,917,916,914,910,907,905,902,901,900,898,896,894,892,891,888,887,886,884,882,880,878,876,874,870,867,865,863,861,859,858,856,855,854,852,844,839,835,832,822,819,815,811,810,809,801,798,772,771,769,763,761,760,758,755,751,750,744,743,742,741,740,739,738,737,734,733,732,731,730,729,728,727,726,725,722,721,720,719,718,717,716,715,711,669,652,651,612,605,591,590,577,576,552]) ).
thf(2185,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n020.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 11:18:21 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.36/4.16 ..
% 21.36/4.16
% 21.36/4.16 No.of.Axioms: 349
% 21.36/4.16
% 21.36/4.16 Length.of.Defs: 0
% 21.36/4.16
% 21.36/4.16 Contains.Choice.Funs: false
% 21.36/4.16 ..........................................
% 21.36/4.16
% 21.36/4.16 ********************************
% 21.36/4.16 * All subproblems solved! *
% 21.36/4.16 ********************************
% 21.36/4.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:143,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2184,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 21.36/4.16
% 21.36/4.16 %**** Beginning of derivation protocol ****
% 21.36/4.16 % SZS output start CNFRefutation
% See solution above
% 3.74/4.17
% 3.74/4.17 %**** End of derivation protocol ****
% 3.74/4.17 %**** no. of clauses in derivation: 1979 ****
% 3.74/4.17 %**** clause counter: 2184 ****
% 3.74/4.17
% 3.74/4.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:143,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2184,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------