%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP118^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:11 AM UTC 2026
% Result : Theorem 7.09s 1.51s
% Output : CNFRefutation 7.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 56
% Syntax : Number of formulae : 870 ( 331 unt; 0 typ; 0 def)
% Number of atoms : 6116 (2741 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 6182 (1187 ~;1459 |; 3 &;3488 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 19 con; 0-3 aty)
% Number of variables : 1640 ( 22 ^;1597 !; 21 ?;1640 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_finite1183840848l_num1,type,
finite1183840848l_num1: $tType ).
thf(tp_finite121157254l_num1,type,
finite121157254l_num1: $tType ).
thf(tp_finite1489363574real_n,type,
finite1489363574real_n: $tType ).
thf(tp_finite2063899472l_num1,type,
finite2063899472l_num1: $tType ).
thf(tp_finite318270636al_n_n,type,
finite318270636al_n_n: $tType ).
thf(tp_finite337957458num1_n,type,
finite337957458num1_n: $tType ).
thf(tp_finite463740460l_num1,type,
finite463740460l_num1: $tType ).
thf(tp_finite964658038_int_n,type,
finite964658038_int_n: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_n,type,
n: $tType ).
thf(tp_numeral_num1,type,
numeral_num1: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_Fi1058188332real_n,type,
set_Fi1058188332real_n: $tType ).
thf(tp_set_Fi1257234438l_num1,type,
set_Fi1257234438l_num1: $tType ).
thf(tp_set_int,type,
set_int: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_a,type,
a: set_Fi1058188332real_n ).
thf(tp_abs_ab1599551059real_n,type,
abs_ab1599551059real_n: finite1489363574real_n > finite1489363574real_n ).
thf(tp_abs_ab948591917l_num1,type,
abs_ab948591917l_num1: finite1183840848l_num1 > finite1183840848l_num1 ).
thf(tp_abs_abs_int,type,
abs_abs_int: int > int ).
thf(tp_abs_abs_real,type,
abs_abs_real: real > real ).
thf(tp_archim1031974863r_real,type,
archim1031974863r_real: real > int ).
thf(tp_archim1371465213g_real,type,
archim1371465213g_real: real > int ).
thf(tp_collec321817931real_n,type,
collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
thf(tp_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(tp_finite1106245191l_num1,type,
finite1106245191l_num1: finite1183840848l_num1 > numeral_num1 > real ).
thf(tp_finite1329045861l_num1,type,
finite1329045861l_num1: real > finite1183840848l_num1 ).
thf(tp_finite1449546019l_num1,type,
finite1449546019l_num1: finite463740460l_num1 > numeral_num1 > finite1183840848l_num1 ).
thf(tp_finite1470207077l_num1,type,
finite1470207077l_num1: int > finite2063899472l_num1 ).
thf(tp_finite1503577981l_num1,type,
finite1503577981l_num1: finite121157254l_num1 > numeral_num1 > finite1489363574real_n ).
thf(tp_finite15144922381_real,type,
finite15144922381_real: numeral_num1 > real > finite1183840848l_num1 ).
thf(tp_finite1639785033num1_n,type,
finite1639785033num1_n: finite337957458num1_n > n > finite1183840848l_num1 ).
thf(tp_finite1800583751l_num1,type,
finite1800583751l_num1: finite2063899472l_num1 > numeral_num1 > int ).
thf(tp_finite1888777460_n_int,type,
finite1888777460_n_int: n > int > finite964658038_int_n ).
thf(tp_finite1961675766l_num1,type,
finite1961675766l_num1: real > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(tp_finite2053577756real_n,type,
finite2053577756real_n: real > finite1489363574real_n > finite1489363574real_n ).
thf(tp_finite55766923_int_n,type,
finite55766923_int_n: int > finite964658038_int_n ).
thf(tp_finite566214509_int_n,type,
finite566214509_int_n: finite964658038_int_n > n > int ).
thf(tp_finite625646243al_n_n,type,
finite625646243al_n_n: finite318270636al_n_n > n > finite1489363574real_n ).
thf(tp_finite627713486m1_int,type,
finite627713486m1_int: numeral_num1 > int > finite2063899472l_num1 ).
thf(tp_finite667548811real_n,type,
finite667548811real_n: real > finite1489363574real_n ).
thf(tp_finite703491444n_real,type,
finite703491444n_real: n > real > finite1489363574real_n ).
thf(tp_finite772340589real_n,type,
finite772340589real_n: finite1489363574real_n > n > real ).
thf(tp_i,type,
i: n ).
thf(tp_if_Fin127821360real_n,type,
if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(tp_if_Fin1570437642l_num1,type,
if_Fin1570437642l_num1: $o > finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).
thf(tp_if_Fin1668193290l_num1,type,
if_Fin1668193290l_num1: $o > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(tp_if_Fin1767949360_int_n,type,
if_Fin1767949360_int_n: $o > finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(tp_m,type,
m: int ).
thf(tp_member1352538125real_n,type,
member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
thf(tp_member1413569767l_num1,type,
member1413569767l_num1: finite1183840848l_num1 > set_Fi1257234438l_num1 > $o ).
thf(tp_member_int,type,
member_int: int > set_int > $o ).
thf(tp_member_real,type,
member_real: real > set_real > $o ).
thf(tp_minkow1134813771n_real,type,
minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
thf(tp_minkow1468704075_n_int,type,
minkow1468704075_n_int: finite964658038_int_n > finite964658038_int_n ).
thf(tp_minkow19073400691_real,type,
minkow19073400691_real: finite2063899472l_num1 > finite1183840848l_num1 ).
thf(tp_minkow2063319845m1_int,type,
minkow2063319845m1_int: finite2063899472l_num1 > finite2063899472l_num1 ).
thf(tp_minkow371489429real_n,type,
minkow371489429real_n: finite964658038_int_n > finite318270636al_n_n ).
thf(tp_minkow781993583real_n,type,
minkow781993583real_n: finite2063899472l_num1 > finite121157254l_num1 ).
thf(tp_minus_1037315151real_n,type,
minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(tp_minus_1196255695_int_n,type,
minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(tp_minus_249161513l_num1,type,
minus_249161513l_num1: finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(tp_minus_779068585l_num1,type,
minus_779068585l_num1: finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).
thf(tp_minus_minus_int,type,
minus_minus_int: int > int > int ).
thf(tp_minus_minus_real,type,
minus_minus_real: real > real > real ).
thf(tp_one_on1253059131real_n,type,
one_on1253059131real_n: finite1489363574real_n ).
thf(tp_one_on1516019131_int_n,type,
one_on1516019131_int_n: finite964658038_int_n ).
thf(tp_one_on1961019669l_num1,type,
one_on1961019669l_num1: finite1183840848l_num1 ).
thf(tp_one_on601734293l_num1,type,
one_on601734293l_num1: finite2063899472l_num1 ).
thf(tp_one_one_Numeral_num1,type,
one_one_Numeral_num1: numeral_num1 ).
thf(tp_one_one_int,type,
one_one_int: int ).
thf(tp_one_one_real,type,
one_one_real: real ).
thf(tp_ord_le1017090250real_n,type,
ord_le1017090250real_n: finite1489363574real_n > finite1489363574real_n > $o ).
thf(tp_ord_le1202326448l_num1,type,
ord_le1202326448l_num1: finite2063899472l_num1 > finite2063899472l_num1 > $o ).
thf(tp_ord_le1724070576l_num1,type,
ord_le1724070576l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).
thf(tp_ord_le1908593622_int_n,type,
ord_le1908593622_int_n: finite964658038_int_n > finite964658038_int_n > $o ).
thf(tp_ord_le2035778724l_num1,type,
ord_le2035778724l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).
thf(tp_ord_le866583254real_n,type,
ord_le866583254real_n: finite1489363574real_n > finite1489363574real_n > $o ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $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_real,type,
ord_less_real: real > real > $o ).
thf(tp_real_V1121707553num1_n,type,
real_V1121707553num1_n: finite337957458num1_n > real ).
thf(tp_real_V1934908667t_real,type,
real_V1934908667t_real: real > real > real ).
thf(tp_real_V1974343547l_num1,type,
real_V1974343547l_num1: finite463740460l_num1 > finite463740460l_num1 > real ).
thf(tp_real_V316032763l_num1,type,
real_V316032763l_num1: finite463740460l_num1 > real ).
thf(tp_real_V400292255l_num1,type,
real_V400292255l_num1: finite1183840848l_num1 > real ).
thf(tp_real_V488409631l_num1,type,
real_V488409631l_num1: finite1183840848l_num1 > finite1183840848l_num1 > real ).
thf(tp_real_V646646907m_real,type,
real_V646646907m_real: real > real ).
thf(tp_real_V739724485real_n,type,
real_V739724485real_n: finite1489363574real_n > real ).
thf(tp_real_V783965509real_n,type,
real_V783965509real_n: finite1489363574real_n > finite1489363574real_n > real ).
thf(tp_real_V845814485l_num1,type,
real_V845814485l_num1: finite121157254l_num1 > finite121157254l_num1 > real ).
thf(tp_ring_11529266783l_num1,type,
ring_11529266783l_num1: set_Fi1257234438l_num1 ).
thf(tp_ring_1154201247l_num1,type,
ring_1154201247l_num1: int > finite1183840848l_num1 ).
thf(tp_ring_11737179077real_n,type,
ring_11737179077real_n: int > finite1489363574real_n ).
thf(tp_ring_1723899781real_n,type,
ring_1723899781real_n: set_Fi1058188332real_n ).
thf(tp_ring_1_Ints_int,type,
ring_1_Ints_int: set_int ).
thf(tp_ring_1_Ints_real,type,
ring_1_Ints_real: set_real ).
thf(tp_ring_1_of_int_int,type,
ring_1_of_int_int: int > int ).
thf(tp_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(tp_sK10_SY151,type,
sK10_SY151: real > int ).
thf(tp_sK11_SY148,type,
sK11_SY148: int > real > int ).
thf(tp_sK12_SY151,type,
sK12_SY151: int > real > int ).
thf(tp_sK13_SY142,type,
sK13_SY142: real > ( n > real > $o ) > finite1489363574real_n ).
thf(tp_sK14_SY142,type,
sK14_SY142: finite1489363574real_n > ( n > real > $o ) > finite1489363574real_n ).
thf(tp_sK15_SY207,type,
sK15_SY207: real > n > ( n > real > $o ) > real ).
thf(tp_sK16_SY208,type,
sK16_SY208: finite1489363574real_n > n > ( n > real > $o ) > real ).
thf(tp_sK1_SX0,type,
sK1_SX0: int ).
thf(tp_sK2_SY133,type,
sK2_SY133: real > int ).
thf(tp_sK3_SY147,type,
sK3_SY147: real > int ).
thf(tp_sK4_SY155,type,
sK4_SY155: real > int ).
thf(tp_sK5_SY140,type,
sK5_SY140: ( n > real > $o ) > n ).
thf(tp_sK6_SV107,type,
sK6_SV107: finite1489363574real_n > finite1489363574real_n > n ).
thf(tp_sK7_SY204,type,
sK7_SY204: finite1489363574real_n > finite1489363574real_n > n ).
thf(tp_sK8_SY206,type,
sK8_SY206: finite1489363574real_n > ( n > real > $o ) > n ).
thf(tp_sK9_SY148,type,
sK9_SY148: real > int ).
thf(tp_x,type,
x: finite1489363574real_n ).
thf(tp_y,type,
y: finite1489363574real_n ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T) ).
thf(120,axiom,
! [X: real] :
? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_ex__le__of__int) ).
thf(123,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_abs__le__D1) ).
thf(124,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_abs__le__D1) ).
thf(125,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_abs__ge__self) ).
thf(126,axiom,
! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_abs__ge__self) ).
thf(130,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ( ord_le866583254real_n @ D @ C )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_diff__mono) ).
thf(134,axiom,
! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ B @ A )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_diff__left__mono) ).
thf(138,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_diff__right__mono) ).
thf(142,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le866583254real_n @ A @ B )
= ( ord_le866583254real_n @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_diff__eq__diff__less__eq) ).
thf(171,axiom,
! [X: finite1183840848l_num1,Y: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V488409631l_num1 @ X @ Y ) )
= ( real_V488409631l_num1 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_real__abs__dist) ).
thf(172,axiom,
! [X: real,Y: real] :
( ( abs_abs_real @ ( real_V1934908667t_real @ X @ Y ) )
= ( real_V1934908667t_real @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_real__abs__dist) ).
thf(173,axiom,
! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( abs_abs_real @ ( real_V783965509real_n @ X @ Y ) )
= ( real_V783965509real_n @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_real__abs__dist) ).
thf(175,axiom,
! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_of__int__floor__cancel) ).
thf(176,axiom,
! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_of__int__ceiling__cancel) ).
thf(180,axiom,
! [A: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ X ) @ ( finite2053577756real_n @ A @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_vec_Oscale__right__diff__distrib) ).
thf(185,axiom,
( ( abs_abs_int @ one_one_int )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_abs__one) ).
thf(186,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_abs__one) ).
thf(190,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__strict__right__mono) ).
thf(194,axiom,
! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ B @ A )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_diff__strict__left__mono) ).
thf(198,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le1017090250real_n @ A @ B )
= ( ord_le1017090250real_n @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__eq__diff__less) ).
thf(202,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ( ord_le1017090250real_n @ D @ C )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_diff__strict__mono) ).
thf(205,axiom,
! [X: real] :
? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ex__of__int__less) ).
thf(206,axiom,
! [X: real] :
? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_ex__less__of__int) ).
thf(207,axiom,
real_V646646907m_real = abs_abs_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_real__norm__def) ).
thf(210,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( real_V739724485real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_norm__minus__commute) ).
thf(245,axiom,
! [C: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ C @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ C @ X ) @ ( finite2053577756real_n @ C @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_vector__ssub__ldistrib) ).
thf(249,axiom,
! [X: real,I: n] :
( ( finite772340589real_n @ ( finite667548811real_n @ X ) @ I )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_vec__component) ).
thf(250,axiom,
! [Z: int] :
( ( archim1371465213g_real @ ( ring_1_of_int_real @ Z ) )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_ceiling__of__int) ).
thf(251,axiom,
! [Z: int] :
( ( archim1031974863r_real @ ( ring_1_of_int_real @ Z ) )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_floor__of__int) ).
thf(254,axiom,
! [A: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V400292255l_num1 @ A ) )
= ( real_V400292255l_num1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_abs__norm__cancel) ).
thf(255,axiom,
! [A: real] :
( ( abs_abs_real @ ( real_V646646907m_real @ A ) )
= ( real_V646646907m_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_abs__norm__cancel) ).
thf(272,axiom,
( ( abs_abs_int @ one_one_int )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_abs__1) ).
thf(273,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_abs__1) ).
thf(281,axiom,
! [I: n,X: real] :
( ( finite772340589real_n @ ( finite703491444n_real @ I @ X ) @ I )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_axis__nth) ).
thf(283,axiom,
! [Z: int] :
( ( real_V646646907m_real @ ( ring_1_of_int_real @ Z ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_norm__of__int) ).
thf(293,axiom,
! [B: $o,X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ X @ I ) ) )
& ( ~ B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ Y @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_cond__component) ).
thf(297,axiom,
! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( ( finite772340589real_n @ X )
= ( finite772340589real_n @ Y ) )
= ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_vec__nth__inject) ).
thf(301,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_diff__eq__diff__eq) ).
thf(305,axiom,
! [A: finite1489363574real_n,C: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_diff__right__commute) ).
thf(327,axiom,
( ( ^ [Y2: finite1489363574real_n,Z2: finite1489363574real_n] : ( Y2 = Z2 ) )
= ( ^ [X3: finite1489363574real_n,Y3: finite1489363574real_n] :
! [I2: n] :
( ( finite772340589real_n @ X3 @ I2 )
= ( finite772340589real_n @ Y3 @ I2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_vec__eq__iff) ).
thf(331,axiom,
! [P: n > real > $o] :
( ( ! [I2: n] :
? [X2: real] : ( P @ I2 @ X2 ) )
= ( ? [X3: finite1489363574real_n] :
! [I2: n] : ( P @ I2 @ ( finite772340589real_n @ X3 @ I2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lambda__skolem) ).
thf(333,axiom,
! [A: int,B: int] :
( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
= ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_abs__minus__commute) ).
thf(334,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_abs__minus__commute) ).
thf(335,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_abs__minus__commute) ).
thf(336,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_abs__idempotent) ).
thf(337,axiom,
! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_abs__idempotent) ).
thf(338,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_abs__abs) ).
thf(339,axiom,
! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_abs__abs) ).
thf(340,axiom,
! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__int__eq__iff) ).
thf(354,axiom,
! [X: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__abs) ).
thf(355,axiom,
! [X: int] :
( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_of__int__abs) ).
thf(357,axiom,
! [X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ X @ Y ) @ I )
= ( minus_minus_real @ ( finite772340589real_n @ X @ I ) @ ( finite772340589real_n @ Y @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_vector__minus__component) ).
thf(360,axiom,
~ ! [M: int] :
( ( ring_1_of_int_real @ M )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(361,axiom,
( ( ring_1_of_int_real @ m )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_m) ).
thf(364,conjecture,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(365,negated_conjecture,
( ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[364]) ).
thf(366,plain,
( ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) )
= $false ),
inference(unfold_def,[status(thm)],[365]) ).
thf(367,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(368,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(369,plain,
( ( ! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(370,plain,
( ( ! [A: int,B: int] :
( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
=> ( ord_less_eq_int @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(371,plain,
( ( ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(372,plain,
( ( ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(373,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ( ord_le866583254real_n @ D @ C )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(374,plain,
( ( ! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ B @ A )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(375,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(376,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le866583254real_n @ A @ B )
= ( ord_le866583254real_n @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(377,plain,
( ( ! [X: finite1183840848l_num1,Y: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V488409631l_num1 @ X @ Y ) )
= ( real_V488409631l_num1 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(378,plain,
( ( ! [X: real,Y: real] :
( ( abs_abs_real @ ( real_V1934908667t_real @ X @ Y ) )
= ( real_V1934908667t_real @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(379,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( abs_abs_real @ ( real_V783965509real_n @ X @ Y ) )
= ( real_V783965509real_n @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(380,plain,
( ( ! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(381,plain,
( ( ! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(382,plain,
( ( ! [A: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ X ) @ ( finite2053577756real_n @ A @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(383,plain,
( ( ( abs_abs_int @ one_one_int )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(384,plain,
( ( ( abs_abs_real @ one_one_real )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(385,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(386,plain,
( ( ! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ B @ A )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(387,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le1017090250real_n @ A @ B )
= ( ord_le1017090250real_n @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(388,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ( ord_le1017090250real_n @ D @ C )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(389,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(390,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(391,plain,
( ( real_V646646907m_real = abs_abs_real )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(392,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( real_V739724485real_n @ ( minus_1037315151real_n @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(393,plain,
( ( ! [C: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ C @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ C @ X ) @ ( finite2053577756real_n @ C @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(394,plain,
( ( ! [X: real,I: n] :
( ( finite772340589real_n @ ( finite667548811real_n @ X ) @ I )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(395,plain,
( ( ! [Z: int] :
( ( archim1371465213g_real @ ( ring_1_of_int_real @ Z ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(396,plain,
( ( ! [Z: int] :
( ( archim1031974863r_real @ ( ring_1_of_int_real @ Z ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(397,plain,
( ( ! [A: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V400292255l_num1 @ A ) )
= ( real_V400292255l_num1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(398,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( real_V646646907m_real @ A ) )
= ( real_V646646907m_real @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(399,plain,
( ( ( abs_abs_int @ one_one_int )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(400,plain,
( ( ( abs_abs_real @ one_one_real )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(401,plain,
( ( ! [I: n,X: real] :
( ( finite772340589real_n @ ( finite703491444n_real @ I @ X ) @ I )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(402,plain,
( ( ! [Z: int] :
( ( real_V646646907m_real @ ( ring_1_of_int_real @ Z ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(403,plain,
( ( ! [B: $o,X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ X @ I ) ) )
& ( ~ B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ Y @ I ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(404,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( ( finite772340589real_n @ X )
= ( finite772340589real_n @ Y ) )
= ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(405,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(406,plain,
( ( ! [A: finite1489363574real_n,C: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(407,plain,
( ( ( ^ [Y2: finite1489363574real_n,Z2: finite1489363574real_n] : ( Y2 = Z2 ) )
= ( ^ [X3: finite1489363574real_n,Y3: finite1489363574real_n] :
! [I2: n] :
( ( finite772340589real_n @ X3 @ I2 )
= ( finite772340589real_n @ Y3 @ I2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(408,plain,
( ( ! [P: n > real > $o] :
( ( ! [I2: n] :
? [X2: real] : ( P @ I2 @ X2 ) )
= ( ? [X3: finite1489363574real_n] :
! [I2: n] : ( P @ I2 @ ( finite772340589real_n @ X3 @ I2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(409,plain,
( ( ! [A: int,B: int] :
( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
= ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(410,plain,
( ( ! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(411,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(412,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(413,plain,
( ( ! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(414,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(415,plain,
( ( ! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(416,plain,
( ( ! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(417,plain,
( ( ! [X: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(418,plain,
( ( ! [X: int] :
( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(419,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ X @ Y ) @ I )
= ( minus_minus_real @ ( finite772340589real_n @ X @ I ) @ ( finite772340589real_n @ Y @ I ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(420,plain,
( ( ~ ! [M: int] :
( ( ring_1_of_int_real @ M )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(421,plain,
( ( ( ring_1_of_int_real @ m )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(422,plain,
( ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[366]) ).
thf(423,plain,
( ( ( ring_1_of_int_real @ m )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(424,plain,
( ( ~ ! [M: int] :
( ( ring_1_of_int_real @ M )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(425,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ X @ Y ) @ I )
= ( minus_minus_real @ ( finite772340589real_n @ X @ I ) @ ( finite772340589real_n @ Y @ I ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(426,plain,
( ( ! [X: int] :
( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(427,plain,
( ( ! [X: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(428,plain,
( ( ! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(429,plain,
( ( ! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(430,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(431,plain,
( ( ! [A: int] :
( ( abs_abs_int @ ( abs_abs_int @ A ) )
= ( abs_abs_int @ A ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(432,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(433,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(434,plain,
( ( ! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(435,plain,
( ( ! [A: int,B: int] :
( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
= ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(436,plain,
( ( ! [P: n > real > $o] :
( ( ! [I2: n] :
? [X2: real] : ( P @ I2 @ X2 ) )
= ( ? [X3: finite1489363574real_n] :
! [I2: n] : ( P @ I2 @ ( finite772340589real_n @ X3 @ I2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(437,plain,
( ( ( ^ [Y2: finite1489363574real_n,Z2: finite1489363574real_n] : ( Y2 = Z2 ) )
= ( ^ [X3: finite1489363574real_n,Y3: finite1489363574real_n] :
! [I2: n] :
( ( finite772340589real_n @ X3 @ I2 )
= ( finite772340589real_n @ Y3 @ I2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(438,plain,
( ( ! [A: finite1489363574real_n,C: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(439,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(440,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( ( finite772340589real_n @ X )
= ( finite772340589real_n @ Y ) )
= ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(441,plain,
( ( ! [B: $o,X: finite1489363574real_n,Y: finite1489363574real_n,I: n] :
( ( B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ X @ I ) ) )
& ( ~ B
=> ( ( finite772340589real_n @ ( if_Fin127821360real_n @ B @ X @ Y ) @ I )
= ( finite772340589real_n @ Y @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(442,plain,
( ( ! [Z: int] :
( ( real_V646646907m_real @ ( ring_1_of_int_real @ Z ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(443,plain,
( ( ! [I: n,X: real] :
( ( finite772340589real_n @ ( finite703491444n_real @ I @ X ) @ I )
= X ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(444,plain,
( ( ( abs_abs_real @ one_one_real )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(445,plain,
( ( ( abs_abs_int @ one_one_int )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(446,plain,
( ( ! [A: real] :
( ( abs_abs_real @ ( real_V646646907m_real @ A ) )
= ( real_V646646907m_real @ A ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(447,plain,
( ( ! [A: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V400292255l_num1 @ A ) )
= ( real_V400292255l_num1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(448,plain,
( ( ! [Z: int] :
( ( archim1031974863r_real @ ( ring_1_of_int_real @ Z ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(449,plain,
( ( ! [Z: int] :
( ( archim1371465213g_real @ ( ring_1_of_int_real @ Z ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(450,plain,
( ( ! [X: real,I: n] :
( ( finite772340589real_n @ ( finite667548811real_n @ X ) @ I )
= X ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(451,plain,
( ( ! [C: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ C @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ C @ X ) @ ( finite2053577756real_n @ C @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(452,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) )
= ( real_V739724485real_n @ ( minus_1037315151real_n @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(453,plain,
( ( real_V646646907m_real = abs_abs_real )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(454,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(455,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(456,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ( ord_le1017090250real_n @ D @ C )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(457,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le1017090250real_n @ A @ B )
= ( ord_le1017090250real_n @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(458,plain,
( ( ! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ B @ A )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(459,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le1017090250real_n @ A @ B )
=> ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(460,plain,
( ( ( abs_abs_real @ one_one_real )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(461,plain,
( ( ( abs_abs_int @ one_one_int )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(462,plain,
( ( ! [A: real,X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ X @ Y ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ X ) @ ( finite2053577756real_n @ A @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(463,plain,
( ( ! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(464,plain,
( ( ! [X: real] :
( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ X ) )
= X )
= ( ? [N2: int] :
( X
= ( ring_1_of_int_real @ N2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(465,plain,
( ( ! [X: finite1489363574real_n,Y: finite1489363574real_n] :
( ( abs_abs_real @ ( real_V783965509real_n @ X @ Y ) )
= ( real_V783965509real_n @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(466,plain,
( ( ! [X: real,Y: real] :
( ( abs_abs_real @ ( real_V1934908667t_real @ X @ Y ) )
= ( real_V1934908667t_real @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(467,plain,
( ( ! [X: finite1183840848l_num1,Y: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V488409631l_num1 @ X @ Y ) )
= ( real_V488409631l_num1 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(468,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( ord_le866583254real_n @ A @ B )
= ( ord_le866583254real_n @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(469,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(470,plain,
( ( ! [B: finite1489363574real_n,A: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ B @ A )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ C @ A ) @ ( minus_1037315151real_n @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(471,plain,
( ( ! [A: finite1489363574real_n,B: finite1489363574real_n,D: finite1489363574real_n,C: finite1489363574real_n] :
( ( ord_le866583254real_n @ A @ B )
=> ( ( ord_le866583254real_n @ D @ C )
=> ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(472,plain,
( ( ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(473,plain,
( ( ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(474,plain,
( ( ! [A: int,B: int] :
( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
=> ( ord_less_eq_int @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(475,plain,
( ( ! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(476,plain,
( ( ! [X: real] :
? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(477,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(478,plain,
( ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(479,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SX0 @ SX1 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SX0 @ SX2 ) @ ( minus_1037315151real_n @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(480,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(481,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SX0 @ SX1 )
!= ( minus_1037315151real_n @ SX2 @ SX3 ) )
| ( ( ord_le866583254real_n @ SX0 @ SX1 )
= ( ord_le866583254real_n @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(482,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SX0 @ SX1 )
| ~ ( ord_le866583254real_n @ SX2 @ SX3 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SX0 @ SX3 ) @ ( minus_1037315151real_n @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(483,plain,
( ( ! [SX0: n > real > $o] :
( ( ! [SX1: n] :
~ ! [SX2: real] :
~ ( SX0 @ SX1 @ SX2 ) )
= ( ~ ! [SX1: finite1489363574real_n] :
~ ! [SX2: n] : ( SX0 @ SX2 @ ( finite772340589real_n @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(484,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SX0 @ SX1 )
| ~ ( ord_le1017090250real_n @ SX2 @ SX3 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SX0 @ SX3 ) @ ( minus_1037315151real_n @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(485,plain,
( ( ~ ! [SX0: int] :
( ( ring_1_of_int_real @ SX0 )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(486,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_real @ SX0 @ ( ring_1_of_int_real @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(487,plain,
( ( ! [SX0: real] :
( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SX0 ) )
= SX0 )
= ( ~ ! [SX1: int] :
( SX0
!= ( ring_1_of_int_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(488,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( abs_abs_int @ SX0 ) @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(489,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ SX0 ) @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(490,plain,
( ( ! [SX0: real] :
( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SX0 ) )
= SX0 )
= ( ~ ! [SX1: int] :
( SX0
!= ( ring_1_of_int_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(491,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SX0 @ SX1 )
!= ( minus_1037315151real_n @ SX2 @ SX3 ) )
| ( ( ord_le1017090250real_n @ SX0 @ SX1 )
= ( ord_le1017090250real_n @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(492,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_eq_real @ SX0 @ ( ring_1_of_int_real @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(493,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SX0 @ SX1 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SX2 @ SX1 ) @ ( minus_1037315151real_n @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(494,plain,
( ( ! [SX0: $o,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: n] :
~ ( ~ ( ~ SX0
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( finite772340589real_n @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ SX0
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( finite772340589real_n @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(495,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SX0 @ SX1 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SX2 @ SX1 ) @ ( minus_1037315151real_n @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(496,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n,SX3: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SX0 @ SX1 )
!= ( minus_1037315151real_n @ SX2 @ SX3 ) )
| ( ( SX0 = SX1 )
= ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(497,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SX0 @ SX1 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SX0 @ SX2 ) @ ( minus_1037315151real_n @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(498,plain,
! [SV1: finite1489363574real_n] :
( ( ! [SY109: finite1489363574real_n,SY110: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ SV1 @ SY109 ) @ SY110 )
= ( minus_minus_real @ ( finite772340589real_n @ SV1 @ SY110 ) @ ( finite772340589real_n @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(499,plain,
! [SV2: int] :
( ( ( ring_1_of_int_int @ ( abs_abs_int @ SV2 ) )
= ( abs_abs_int @ ( ring_1_of_int_int @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(500,plain,
! [SV3: int] :
( ( ( ring_1_of_int_real @ ( abs_abs_int @ SV3 ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(501,plain,
! [SV4: int] :
( ( ! [SY111: int] :
( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SY111 ) )
= ( SV4 = SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(502,plain,
! [SV5: int] :
( ( ( abs_abs_int @ ( abs_abs_int @ SV5 ) )
= ( abs_abs_int @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(503,plain,
! [SV6: real] :
( ( ( abs_abs_real @ ( abs_abs_real @ SV6 ) )
= ( abs_abs_real @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(504,plain,
! [SV7: int] :
( ( ( abs_abs_int @ ( abs_abs_int @ SV7 ) )
= ( abs_abs_int @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(505,plain,
! [SV8: real] :
( ( ( abs_abs_real @ ( abs_abs_real @ SV8 ) )
= ( abs_abs_real @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(506,plain,
! [SV9: finite1489363574real_n] :
( ( ! [SY112: finite1489363574real_n] :
( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ SV9 @ SY112 ) )
= ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ SY112 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(507,plain,
! [SV10: real] :
( ( ! [SY113: real] :
( ( abs_abs_real @ ( minus_minus_real @ SV10 @ SY113 ) )
= ( abs_abs_real @ ( minus_minus_real @ SY113 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(508,plain,
! [SV11: int] :
( ( ! [SY114: int] :
( ( abs_abs_int @ ( minus_minus_int @ SV11 @ SY114 ) )
= ( abs_abs_int @ ( minus_minus_int @ SY114 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(509,plain,
( ( ! [SV12: finite1489363574real_n] :
( ( ^ [SY115: finite1489363574real_n] : ( SV12 = SY115 ) )
= ( ^ [SY116: finite1489363574real_n] :
! [SY117: n] :
( ( finite772340589real_n @ SV12 @ SY117 )
= ( finite772340589real_n @ SY116 @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(510,plain,
( ( ( ^ [Y2: finite1489363574real_n,Z2: finite1489363574real_n] : ( Y2 = Z2 ) )
= ( ^ [X3: finite1489363574real_n,Y3: finite1489363574real_n] :
! [I2: n] :
( ( finite772340589real_n @ X3 @ I2 )
= ( finite772340589real_n @ Y3 @ I2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(511,plain,
! [SV13: finite1489363574real_n] :
( ( ! [SY118: finite1489363574real_n,SY119: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SY118 ) @ SY119 )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SY119 ) @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(512,plain,
! [SV14: finite1489363574real_n] :
( ( ! [SY120: finite1489363574real_n] :
( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SY120 ) )
= ( SV14 = SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(513,plain,
! [SV15: int] :
( ( ( real_V646646907m_real @ ( ring_1_of_int_real @ SV15 ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(514,plain,
! [SV16: n] :
( ( ! [SY121: real] :
( ( finite772340589real_n @ ( finite703491444n_real @ SV16 @ SY121 ) @ SV16 )
= SY121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(515,plain,
! [SV17: real] :
( ( ( abs_abs_real @ ( real_V646646907m_real @ SV17 ) )
= ( real_V646646907m_real @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(516,plain,
! [SV18: finite1183840848l_num1] :
( ( ( abs_abs_real @ ( real_V400292255l_num1 @ SV18 ) )
= ( real_V400292255l_num1 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(517,plain,
! [SV19: int] :
( ( ( archim1031974863r_real @ ( ring_1_of_int_real @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(518,plain,
! [SV20: int] :
( ( ( archim1371465213g_real @ ( ring_1_of_int_real @ SV20 ) )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(519,plain,
! [SV21: real] :
( ( ! [SY122: n] :
( ( finite772340589real_n @ ( finite667548811real_n @ SV21 ) @ SY122 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(520,plain,
! [SV22: real] :
( ( ! [SY123: finite1489363574real_n,SY124: finite1489363574real_n] :
( ( finite2053577756real_n @ SV22 @ ( minus_1037315151real_n @ SY123 @ SY124 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV22 @ SY123 ) @ ( finite2053577756real_n @ SV22 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(521,plain,
! [SV23: finite1489363574real_n] :
( ( ! [SY125: finite1489363574real_n] :
( ( real_V739724485real_n @ ( minus_1037315151real_n @ SV23 @ SY125 ) )
= ( real_V739724485real_n @ ( minus_1037315151real_n @ SY125 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(522,plain,
( ( ! [SV24: real] :
( ( real_V646646907m_real @ SV24 )
= ( abs_abs_real @ SV24 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[453]) ).
thf(523,plain,
( ( real_V646646907m_real = abs_abs_real )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[453]) ).
thf(524,plain,
! [SV25: real] :
( ( ! [SY126: finite1489363574real_n,SY127: finite1489363574real_n] :
( ( finite2053577756real_n @ SV25 @ ( minus_1037315151real_n @ SY126 @ SY127 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV25 @ SY126 ) @ ( finite2053577756real_n @ SV25 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(525,plain,
! [SV26: finite1489363574real_n] :
( ( ! [SY128: finite1489363574real_n] :
( ( abs_abs_real @ ( real_V783965509real_n @ SV26 @ SY128 ) )
= ( real_V783965509real_n @ SV26 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(526,plain,
! [SV27: real] :
( ( ! [SY129: real] :
( ( abs_abs_real @ ( real_V1934908667t_real @ SV27 @ SY129 ) )
= ( real_V1934908667t_real @ SV27 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(527,plain,
! [SV28: finite1183840848l_num1] :
( ( ! [SY130: finite1183840848l_num1] :
( ( abs_abs_real @ ( real_V488409631l_num1 @ SV28 @ SY130 ) )
= ( real_V488409631l_num1 @ SV28 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(528,plain,
! [SV29: int] :
( ( ord_less_eq_int @ SV29 @ ( abs_abs_int @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(529,plain,
! [SV30: real] :
( ( ord_less_eq_real @ SV30 @ ( abs_abs_real @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(530,plain,
! [SV31: $o] :
( ( ( SV31 = $true )
| ( SV31 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[477]) ).
thf(531,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[477]) ).
thf(532,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[477]) ).
thf(533,plain,
( ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(534,plain,
! [SV32: finite1489363574real_n] :
( ( ! [SY131: finite1489363574real_n,SY132: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV32 @ SY131 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV32 @ SY132 ) @ ( minus_1037315151real_n @ SY131 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(535,plain,
! [SV33: real] :
( ( ~ ! [SY133: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SY133 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(536,plain,
! [SV34: finite1489363574real_n] :
( ( ! [SY134: finite1489363574real_n,SY135: finite1489363574real_n,SY136: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV34 @ SY134 )
!= ( minus_1037315151real_n @ SY135 @ SY136 ) )
| ( ( ord_le866583254real_n @ SV34 @ SY134 )
= ( ord_le866583254real_n @ SY135 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(537,plain,
! [SV35: finite1489363574real_n] :
( ( ! [SY137: finite1489363574real_n,SY138: finite1489363574real_n,SY139: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV35 @ SY137 )
| ~ ( ord_le866583254real_n @ SY138 @ SY139 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SY139 ) @ ( minus_1037315151real_n @ SY137 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(538,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= ( ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(539,plain,
! [SV37: finite1489363574real_n] :
( ( ! [SY144: finite1489363574real_n,SY145: finite1489363574real_n,SY146: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV37 @ SY144 )
| ~ ( ord_le1017090250real_n @ SY145 @ SY146 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SY146 ) @ ( minus_1037315151real_n @ SY144 @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(540,plain,
( ( ! [SX0: int] :
( ( ring_1_of_int_real @ SX0 )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(541,plain,
! [SV38: real] :
( ( ~ ! [SY147: int] :
~ ( ord_less_real @ SV38 @ ( ring_1_of_int_real @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(542,plain,
! [SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= ( ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(543,plain,
! [SV40: int] :
( ( ! [SY149: int] :
( ~ ( ord_less_eq_int @ ( abs_abs_int @ SV40 ) @ SY149 )
| ( ord_less_eq_int @ SV40 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(544,plain,
! [SV41: real] :
( ( ! [SY150: real] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ SV41 ) @ SY150 )
| ( ord_less_eq_real @ SV41 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(545,plain,
! [SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= ( ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(546,plain,
! [SV43: finite1489363574real_n] :
( ( ! [SY152: finite1489363574real_n,SY153: finite1489363574real_n,SY154: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV43 @ SY152 )
!= ( minus_1037315151real_n @ SY153 @ SY154 ) )
| ( ( ord_le1017090250real_n @ SV43 @ SY152 )
= ( ord_le1017090250real_n @ SY153 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(547,plain,
! [SV44: real] :
( ( ~ ! [SY155: int] :
~ ( ord_less_eq_real @ SV44 @ ( ring_1_of_int_real @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(548,plain,
! [SV45: finite1489363574real_n] :
( ( ! [SY156: finite1489363574real_n,SY157: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV45 @ SY156 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SY157 @ SY156 ) @ ( minus_1037315151real_n @ SY157 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(549,plain,
! [SV46: $o] :
( ( ! [SY158: finite1489363574real_n,SY159: finite1489363574real_n,SY160: n] :
~ ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SY158 @ SY159 ) @ SY160 )
= ( finite772340589real_n @ SY158 @ SY160 ) ) )
| ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SY158 @ SY159 ) @ SY160 )
= ( finite772340589real_n @ SY159 @ SY160 ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[494]) ).
thf(550,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: n] :
~ ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SX0 @ SX1 ) @ SX2 )
= ( finite772340589real_n @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SX0 @ SX1 ) @ SX2 )
= ( finite772340589real_n @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[494]) ).
thf(551,plain,
( ( ! [SX0: finite1489363574real_n,SX1: finite1489363574real_n,SX2: n] :
~ ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SX0 @ SX1 ) @ SX2 )
= ( finite772340589real_n @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SX0 @ SX1 ) @ SX2 )
= ( finite772340589real_n @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[494]) ).
thf(552,plain,
! [SV47: finite1489363574real_n] :
( ( ! [SY161: finite1489363574real_n,SY162: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV47 @ SY161 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SY162 @ SY161 ) @ ( minus_1037315151real_n @ SY162 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(553,plain,
! [SV48: finite1489363574real_n] :
( ( ! [SY163: finite1489363574real_n,SY164: finite1489363574real_n,SY165: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV48 @ SY163 )
!= ( minus_1037315151real_n @ SY164 @ SY165 ) )
| ( ( SV48 = SY163 )
= ( SY164 = SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(554,plain,
! [SV49: finite1489363574real_n] :
( ( ! [SY166: finite1489363574real_n,SY167: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV49 @ SY166 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV49 @ SY167 ) @ ( minus_1037315151real_n @ SY166 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(555,plain,
! [SV50: finite1489363574real_n,SV1: finite1489363574real_n] :
( ( ! [SY168: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ SV1 @ SV50 ) @ SY168 )
= ( minus_minus_real @ ( finite772340589real_n @ SV1 @ SY168 ) @ ( finite772340589real_n @ SV50 @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(556,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= ( SV4 = SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(557,plain,
! [SV52: finite1489363574real_n,SV9: finite1489363574real_n] :
( ( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ SV9 @ SV52 ) )
= ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ SV52 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(558,plain,
! [SV53: real,SV10: real] :
( ( ( abs_abs_real @ ( minus_minus_real @ SV10 @ SV53 ) )
= ( abs_abs_real @ ( minus_minus_real @ SV53 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(559,plain,
! [SV54: int,SV11: int] :
( ( ( abs_abs_int @ ( minus_minus_int @ SV11 @ SV54 ) )
= ( abs_abs_int @ ( minus_minus_int @ SV54 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(560,plain,
! [SV55: finite1489363574real_n] :
( ( ( ^ [SY169: finite1489363574real_n] : ( SV55 = SY169 ) )
= ( ^ [SY170: finite1489363574real_n] :
! [SY171: n] :
( ( finite772340589real_n @ SV55 @ SY171 )
= ( finite772340589real_n @ SY170 @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(561,plain,
! [SV56: finite1489363574real_n,SV13: finite1489363574real_n] :
( ( ! [SY172: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SV56 ) @ SY172 )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SY172 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(562,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= ( SV14 = SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(563,plain,
! [SV58: real,SV16: n] :
( ( ( finite772340589real_n @ ( finite703491444n_real @ SV16 @ SV58 ) @ SV16 )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(564,plain,
! [SV59: n,SV21: real] :
( ( ( finite772340589real_n @ ( finite667548811real_n @ SV21 ) @ SV59 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(565,plain,
! [SV60: finite1489363574real_n,SV22: real] :
( ( ! [SY173: finite1489363574real_n] :
( ( finite2053577756real_n @ SV22 @ ( minus_1037315151real_n @ SV60 @ SY173 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV22 @ SV60 ) @ ( finite2053577756real_n @ SV22 @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(566,plain,
! [SV61: finite1489363574real_n,SV23: finite1489363574real_n] :
( ( ( real_V739724485real_n @ ( minus_1037315151real_n @ SV23 @ SV61 ) )
= ( real_V739724485real_n @ ( minus_1037315151real_n @ SV61 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(567,plain,
! [SV62: real] :
( ( ( real_V646646907m_real @ SV62 )
= ( abs_abs_real @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(568,plain,
! [SV63: finite1489363574real_n,SV25: real] :
( ( ! [SY174: finite1489363574real_n] :
( ( finite2053577756real_n @ SV25 @ ( minus_1037315151real_n @ SV63 @ SY174 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV25 @ SV63 ) @ ( finite2053577756real_n @ SV25 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(569,plain,
! [SV64: finite1489363574real_n,SV26: finite1489363574real_n] :
( ( ( abs_abs_real @ ( real_V783965509real_n @ SV26 @ SV64 ) )
= ( real_V783965509real_n @ SV26 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(570,plain,
! [SV65: real,SV27: real] :
( ( ( abs_abs_real @ ( real_V1934908667t_real @ SV27 @ SV65 ) )
= ( real_V1934908667t_real @ SV27 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(571,plain,
! [SV66: finite1183840848l_num1,SV28: finite1183840848l_num1] :
( ( ( abs_abs_real @ ( real_V488409631l_num1 @ SV28 @ SV66 ) )
= ( real_V488409631l_num1 @ SV28 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(572,plain,
! [SV31: $o] :
( ( ( SV31 = $true )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(573,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(574,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(575,plain,
! [SV67: finite1489363574real_n,SV32: finite1489363574real_n] :
( ( ! [SY175: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV32 @ SV67 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV32 @ SY175 ) @ ( minus_1037315151real_n @ SV67 @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(576,plain,
! [SV33: real] :
( ( ! [SY133: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SY133 ) @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(577,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ! [SY176: finite1489363574real_n,SY177: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV34 @ SV68 )
!= ( minus_1037315151real_n @ SY176 @ SY177 ) )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SY176 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(578,plain,
! [SV69: finite1489363574real_n,SV35: finite1489363574real_n] :
( ( ! [SY178: finite1489363574real_n,SY179: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV35 @ SV69 )
| ~ ( ord_le866583254real_n @ SY178 @ SY179 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SY179 ) @ ( minus_1037315151real_n @ SV69 @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(579,plain,
! [SV36: n > real > $o] :
( ( ~ ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
| ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[538]) ).
thf(580,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= ( ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[538]) ).
thf(581,plain,
! [SV70: finite1489363574real_n,SV37: finite1489363574real_n] :
( ( ! [SY180: finite1489363574real_n,SY181: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV37 @ SV70 )
| ~ ( ord_le1017090250real_n @ SY180 @ SY181 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SY181 ) @ ( minus_1037315151real_n @ SV70 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(582,plain,
( ( ( ring_1_of_int_real @ sK1_SX0 )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[540]) ).
thf(583,plain,
! [SV38: real] :
( ( ! [SY147: int] :
~ ( ord_less_real @ SV38 @ ( ring_1_of_int_real @ SY147 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(584,plain,
! [SV39: real] :
( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
| ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
| ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[542]) ).
thf(585,plain,
! [SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= ( ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[542]) ).
thf(586,plain,
! [SV71: int,SV40: int] :
( ( ~ ( ord_less_eq_int @ ( abs_abs_int @ SV40 ) @ SV71 )
| ( ord_less_eq_int @ SV40 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(587,plain,
! [SV72: real,SV41: real] :
( ( ~ ( ord_less_eq_real @ ( abs_abs_real @ SV41 ) @ SV72 )
| ( ord_less_eq_real @ SV41 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(588,plain,
! [SV42: real] :
( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
| ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
| ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(589,plain,
! [SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= ( ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(590,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ! [SY182: finite1489363574real_n,SY183: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV43 @ SV73 )
!= ( minus_1037315151real_n @ SY182 @ SY183 ) )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SY182 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(591,plain,
! [SV44: real] :
( ( ! [SY155: int] :
~ ( ord_less_eq_real @ SV44 @ ( ring_1_of_int_real @ SY155 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(592,plain,
! [SV74: finite1489363574real_n,SV45: finite1489363574real_n] :
( ( ! [SY184: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV45 @ SV74 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SY184 @ SV74 ) @ ( minus_1037315151real_n @ SY184 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(593,plain,
! [SV75: finite1489363574real_n,SV46: $o] :
( ( ! [SY185: finite1489363574real_n,SY186: n] :
~ ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SY185 ) @ SY186 )
= ( finite772340589real_n @ SV75 @ SY186 ) ) )
| ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SY185 ) @ SY186 )
= ( finite772340589real_n @ SY185 @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(594,plain,
! [SV76: finite1489363574real_n] :
( ( ! [SY187: finite1489363574real_n,SY188: n] :
~ ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SY187 ) @ SY188 )
= ( finite772340589real_n @ SV76 @ SY188 ) ) )
| ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SY187 ) @ SY188 )
= ( finite772340589real_n @ SY187 @ SY188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(595,plain,
! [SV77: finite1489363574real_n] :
( ( ! [SY189: finite1489363574real_n,SY190: n] :
~ ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SY189 ) @ SY190 )
= ( finite772340589real_n @ SV77 @ SY190 ) ) )
| ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SY189 ) @ SY190 )
= ( finite772340589real_n @ SY189 @ SY190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(596,plain,
! [SV78: finite1489363574real_n,SV47: finite1489363574real_n] :
( ( ! [SY191: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV47 @ SV78 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SY191 @ SV78 ) @ ( minus_1037315151real_n @ SY191 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(597,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ! [SY192: finite1489363574real_n,SY193: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV48 @ SV79 )
!= ( minus_1037315151real_n @ SY192 @ SY193 ) )
| ( ( SV48 = SV79 )
= ( SY192 = SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(598,plain,
! [SV80: finite1489363574real_n,SV49: finite1489363574real_n] :
( ( ! [SY194: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV49 @ SV80 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV49 @ SY194 ) @ ( minus_1037315151real_n @ SV80 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(599,plain,
! [SV81: n,SV50: finite1489363574real_n,SV1: finite1489363574real_n] :
( ( ( finite772340589real_n @ ( minus_1037315151real_n @ SV1 @ SV50 ) @ SV81 )
= ( minus_minus_real @ ( finite772340589real_n @ SV1 @ SV81 ) @ ( finite772340589real_n @ SV50 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(600,plain,
! [SV51: int,SV4: int] :
( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 = SV51 ) )
| ~ ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[556]) ).
thf(601,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= ( SV4 = SV51 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[556]) ).
thf(602,plain,
! [SV55: finite1489363574real_n] :
( ( ! [SV82: finite1489363574real_n] :
( ( SV55 = SV82 )
= ( ! [SY195: n] :
( ( finite772340589real_n @ SV55 @ SY195 )
= ( finite772340589real_n @ SV82 @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[560]) ).
thf(603,plain,
! [SV55: finite1489363574real_n] :
( ( ( ^ [SY169: finite1489363574real_n] : ( SV55 = SY169 ) )
= ( ^ [SY170: finite1489363574real_n] :
! [SY171: n] :
( ( finite772340589real_n @ SV55 @ SY171 )
= ( finite772340589real_n @ SY170 @ SY171 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[560]) ).
thf(604,plain,
! [SV83: finite1489363574real_n,SV56: finite1489363574real_n,SV13: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SV56 ) @ SV83 )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ SV13 @ SV83 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(605,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ~ ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
| ( SV14 = SV57 ) )
| ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(606,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= ( SV14 = SV57 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(607,plain,
! [SV84: finite1489363574real_n,SV60: finite1489363574real_n,SV22: real] :
( ( ( finite2053577756real_n @ SV22 @ ( minus_1037315151real_n @ SV60 @ SV84 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV22 @ SV60 ) @ ( finite2053577756real_n @ SV22 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(608,plain,
! [SV85: finite1489363574real_n,SV63: finite1489363574real_n,SV25: real] :
( ( ( finite2053577756real_n @ SV25 @ ( minus_1037315151real_n @ SV63 @ SV85 ) )
= ( minus_1037315151real_n @ ( finite2053577756real_n @ SV25 @ SV63 ) @ ( finite2053577756real_n @ SV25 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(609,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $true )
| ~ ( ~ SV31
| ~ $true ) )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(610,plain,
! [SV31: $o] :
( ( ( SV31 = $true )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(611,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[573]) ).
thf(612,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[573]) ).
thf(613,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[574]) ).
thf(614,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[574]) ).
thf(615,plain,
! [SV86: finite1489363574real_n,SV67: finite1489363574real_n,SV32: finite1489363574real_n] :
( ( ~ ( ord_le866583254real_n @ SV32 @ SV67 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV32 @ SV86 ) @ ( minus_1037315151real_n @ SV67 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(616,plain,
! [SV33: real] :
( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ ( sK2_SY133 @ SV33 ) ) @ SV33 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[576]) ).
thf(617,plain,
! [SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ! [SY196: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV34 @ SV68 )
!= ( minus_1037315151real_n @ SV87 @ SY196 ) )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SV87 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(618,plain,
! [SV88: finite1489363574real_n,SV69: finite1489363574real_n,SV35: finite1489363574real_n] :
( ( ! [SY197: finite1489363574real_n] :
( ~ ( ord_le866583254real_n @ SV35 @ SV69 )
| ~ ( ord_le866583254real_n @ SV88 @ SY197 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SY197 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(619,plain,
! [SV36: n > real > $o] :
( ( ( ~ ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(620,plain,
! [SV89: finite1489363574real_n,SV70: finite1489363574real_n,SV37: finite1489363574real_n] :
( ( ! [SY198: finite1489363574real_n] :
( ~ ( ord_le1017090250real_n @ SV37 @ SV70 )
| ~ ( ord_le1017090250real_n @ SV89 @ SY198 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SY198 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(621,plain,
( ( ( ring_1_of_int_real @ sK1_SX0 )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(622,plain,
! [SV38: real] :
( ( ~ ( ord_less_real @ SV38 @ ( ring_1_of_int_real @ ( sK3_SY147 @ SV38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[583]) ).
thf(623,plain,
! [SV39: real] :
( ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
| ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(624,plain,
! [SV71: int,SV40: int] :
( ( ( ~ ( ord_less_eq_int @ ( abs_abs_int @ SV40 ) @ SV71 ) )
= $true )
| ( ( ord_less_eq_int @ SV40 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(625,plain,
! [SV72: real,SV41: real] :
( ( ( ~ ( ord_less_eq_real @ ( abs_abs_real @ SV41 ) @ SV72 ) )
= $true )
| ( ( ord_less_eq_real @ SV41 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(626,plain,
! [SV42: real] :
( ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
| ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(627,plain,
! [SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ! [SY199: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV43 @ SV73 )
!= ( minus_1037315151real_n @ SV90 @ SY199 ) )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SV90 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(628,plain,
! [SV44: real] :
( ( ~ ( ord_less_eq_real @ SV44 @ ( ring_1_of_int_real @ ( sK4_SY155 @ SV44 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[591]) ).
thf(629,plain,
! [SV91: finite1489363574real_n,SV74: finite1489363574real_n,SV45: finite1489363574real_n] :
( ( ~ ( ord_le866583254real_n @ SV45 @ SV74 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV91 @ SV74 ) @ ( minus_1037315151real_n @ SV91 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(630,plain,
! [SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ! [SY200: n] :
~ ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SY200 )
= ( finite772340589real_n @ SV75 @ SY200 ) ) )
| ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SY200 )
= ( finite772340589real_n @ SV92 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(631,plain,
! [SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ! [SY201: n] :
~ ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SY201 )
= ( finite772340589real_n @ SV76 @ SY201 ) ) )
| ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SY201 )
= ( finite772340589real_n @ SV93 @ SY201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(632,plain,
! [SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ! [SY202: n] :
~ ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SY202 )
= ( finite772340589real_n @ SV77 @ SY202 ) ) )
| ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SY202 )
= ( finite772340589real_n @ SV94 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(633,plain,
! [SV95: finite1489363574real_n,SV78: finite1489363574real_n,SV47: finite1489363574real_n] :
( ( ~ ( ord_le1017090250real_n @ SV47 @ SV78 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV95 @ SV78 ) @ ( minus_1037315151real_n @ SV95 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(634,plain,
! [SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ! [SY203: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ SV48 @ SV79 )
!= ( minus_1037315151real_n @ SV96 @ SY203 ) )
| ( ( SV48 = SV79 )
= ( SV96 = SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(635,plain,
! [SV97: finite1489363574real_n,SV80: finite1489363574real_n,SV49: finite1489363574real_n] :
( ( ~ ( ord_le1017090250real_n @ SV49 @ SV80 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV49 @ SV97 ) @ ( minus_1037315151real_n @ SV80 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(636,plain,
! [SV51: int,SV4: int] :
( ( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 = SV51 ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(637,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 = SV98 )
= ( ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(638,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ~ ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
| ( SV14 = SV57 ) ) )
= $true )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(639,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $true ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $true ) )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(640,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false )
| ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[610]) ).
thf(641,plain,
! [SV31: $o] :
( ( ( SV31 = $false )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[610]) ).
thf(642,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(643,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(644,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(645,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(646,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(647,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(648,plain,
! [SV86: finite1489363574real_n,SV67: finite1489363574real_n,SV32: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV32 @ SV67 ) )
= $true )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV32 @ SV86 ) @ ( minus_1037315151real_n @ SV67 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(649,plain,
! [SV33: real] :
( ( ord_less_real @ ( ring_1_of_int_real @ ( sK2_SY133 @ SV33 ) ) @ SV33 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(650,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
!= ( minus_1037315151real_n @ SV87 @ SV99 ) )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(651,plain,
! [SV100: finite1489363574real_n,SV88: finite1489363574real_n,SV69: finite1489363574real_n,SV35: finite1489363574real_n] :
( ( ~ ( ord_le866583254real_n @ SV35 @ SV69 )
| ~ ( ord_le866583254real_n @ SV88 @ SV100 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SV100 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(652,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(653,plain,
! [SV101: finite1489363574real_n,SV89: finite1489363574real_n,SV70: finite1489363574real_n,SV37: finite1489363574real_n] :
( ( ~ ( ord_le1017090250real_n @ SV37 @ SV70 )
| ~ ( ord_le1017090250real_n @ SV89 @ SV101 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SV101 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(654,plain,
! [SV38: real] :
( ( ord_less_real @ SV38 @ ( ring_1_of_int_real @ ( sK3_SY147 @ SV38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(655,plain,
! [SV39: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
| ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(656,plain,
! [SV71: int,SV40: int] :
( ( ( ord_less_eq_int @ ( abs_abs_int @ SV40 ) @ SV71 )
= $false )
| ( ( ord_less_eq_int @ SV40 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(657,plain,
! [SV72: real,SV41: real] :
( ( ( ord_less_eq_real @ ( abs_abs_real @ SV41 ) @ SV72 )
= $false )
| ( ( ord_less_eq_real @ SV41 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(658,plain,
! [SV42: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
| ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(659,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
!= ( minus_1037315151real_n @ SV90 @ SV102 ) )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(660,plain,
! [SV44: real] :
( ( ord_less_eq_real @ SV44 @ ( ring_1_of_int_real @ ( sK4_SY155 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(661,plain,
! [SV91: finite1489363574real_n,SV74: finite1489363574real_n,SV45: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV45 @ SV74 ) )
= $true )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV91 @ SV74 ) @ ( minus_1037315151real_n @ SV91 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(662,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) ) )
| ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(663,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) ) )
| ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(664,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) ) )
| ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(665,plain,
! [SV95: finite1489363574real_n,SV78: finite1489363574real_n,SV47: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV47 @ SV78 ) )
= $true )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV95 @ SV78 ) @ ( minus_1037315151real_n @ SV95 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(666,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
!= ( minus_1037315151real_n @ SV96 @ SV106 ) )
| ( ( SV48 = SV79 )
= ( SV96 = SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(667,plain,
! [SV97: finite1489363574real_n,SV80: finite1489363574real_n,SV49: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV49 @ SV80 ) )
= $true )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV49 @ SV97 ) @ ( minus_1037315151real_n @ SV80 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(668,plain,
! [SV51: int,SV4: int] :
( ( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 = SV51 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(669,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ~ ( ( SV55 = SV98 )
| ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
| ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[637]) ).
thf(670,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 = SV98 )
= ( ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[637]) ).
thf(671,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
| ( SV14 = SV57 ) )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(672,plain,
! [SV31: $o] :
( ( ( SV31
| $true )
= $false )
| ( ( ~ ( ~ SV31
| ~ $true ) )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(673,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(674,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(675,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(676,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(677,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(678,plain,
! [SV86: finite1489363574real_n,SV67: finite1489363574real_n,SV32: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV32 @ SV67 )
= $false )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV32 @ SV86 ) @ ( minus_1037315151real_n @ SV67 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(679,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
!= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $true )
| ( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(680,plain,
! [SV100: finite1489363574real_n,SV88: finite1489363574real_n,SV69: finite1489363574real_n,SV35: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV35 @ SV69 ) )
= $true )
| ( ( ~ ( ord_le866583254real_n @ SV88 @ SV100 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SV100 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(681,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(682,plain,
! [SV36: n > real > $o] :
( ( ( ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(683,plain,
! [SV101: finite1489363574real_n,SV89: finite1489363574real_n,SV70: finite1489363574real_n,SV37: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV37 @ SV70 ) )
= $true )
| ( ( ~ ( ord_le1017090250real_n @ SV89 @ SV101 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SV101 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(684,plain,
! [SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(685,plain,
! [SV39: real] :
( ( ( ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(686,plain,
! [SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(687,plain,
! [SV42: real] :
( ( ( ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(688,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
!= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $true )
| ( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(689,plain,
! [SV91: finite1489363574real_n,SV74: finite1489363574real_n,SV45: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV45 @ SV74 )
= $false )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV91 @ SV74 ) @ ( minus_1037315151real_n @ SV91 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(690,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) ) )
| ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(691,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) ) )
| ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(692,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) ) )
| ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(693,plain,
! [SV95: finite1489363574real_n,SV78: finite1489363574real_n,SV47: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV47 @ SV78 )
= $false )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV95 @ SV78 ) @ ( minus_1037315151real_n @ SV95 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(694,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
!= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $true )
| ( ( ( SV48 = SV79 )
= ( SV96 = SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(695,plain,
! [SV97: finite1489363574real_n,SV80: finite1489363574real_n,SV49: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV49 @ SV80 )
= $false )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV49 @ SV97 ) @ ( minus_1037315151real_n @ SV80 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(696,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(697,plain,
! [SV51: int,SV4: int] :
( ( ( SV4 = SV51 )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(698,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ~ ( ( SV55 = SV98 )
| ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true )
| ( ( ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(699,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(700,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 = SV57 )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(701,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $true ) )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(702,plain,
! [SV31: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV31
| ~ $true ) )
= $true )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(703,plain,
! [SV31: $o] :
( ( ( SV31
| $false )
= $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(704,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(705,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(706,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(707,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(708,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(709,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(710,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(711,plain,
! [SV100: finite1489363574real_n,SV88: finite1489363574real_n,SV69: finite1489363574real_n,SV35: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV35 @ SV69 )
= $false )
| ( ( ~ ( ord_le866583254real_n @ SV88 @ SV100 )
| ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SV100 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(712,plain,
! [SV36: n > real > $o] :
( ( ( ~ ! [SY205: real] :
~ ( SV36 @ ( sK5_SY140 @ SV36 ) @ SY205 ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[681]) ).
thf(713,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(714,plain,
! [SV101: finite1489363574real_n,SV89: finite1489363574real_n,SV70: finite1489363574real_n,SV37: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV37 @ SV70 )
= $false )
| ( ( ~ ( ord_le1017090250real_n @ SV89 @ SV101 )
| ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SV101 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(715,plain,
! [SV39: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(716,plain,
! [SV39: real] :
( ( ( ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(717,plain,
! [SV42: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(718,plain,
! [SV42: real] :
( ( ( ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(719,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(720,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(721,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(722,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(723,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(724,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(725,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(726,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false )
| ( ( ( SV48 = SV79 )
= ( SV96 = SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(727,plain,
! [SV51: int,SV4: int] :
( ( ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(728,plain,
! [SV51: int,SV4: int] :
( ( ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
| ( SV4 != SV51 ) )
= $false )
| ( ( SV4 = SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(729,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ( SV55 = SV98 )
| ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(730,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ! [SV107: n] :
( ( finite772340589real_n @ SV14 @ SV107 )
= ( finite772340589real_n @ SV57 @ SV107 ) ) )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[699]) ).
thf(731,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[699]) ).
thf(732,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) )
= $false )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(733,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $true )
= $false )
| ( SV31 = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(734,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(735,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(736,plain,
! [SV31: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(737,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(738,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(739,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(740,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(741,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(742,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(743,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(744,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(745,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ( ord_le866583254real_n @ SV34 @ SV68 )
| ( ord_le866583254real_n @ SV87 @ SV99 ) )
| ~ ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(746,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(747,plain,
! [SV69: finite1489363574real_n,SV35: finite1489363574real_n,SV100: finite1489363574real_n,SV88: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV88 @ SV100 ) )
= $true )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SV100 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) )
= $true )
| ( ( ord_le866583254real_n @ SV35 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(748,plain,
! [SV36: n > real > $o] :
( ( ( ! [SY205: real] :
~ ( SV36 @ ( sK5_SY140 @ SV36 ) @ SY205 ) )
= $true )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(749,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ! [SY206: n] : ( SV36 @ SY206 @ ( finite772340589real_n @ SV108 @ SY206 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(750,plain,
! [SV70: finite1489363574real_n,SV37: finite1489363574real_n,SV101: finite1489363574real_n,SV89: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV89 @ SV101 ) )
= $true )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SV101 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) )
= $true )
| ( ( ord_le1017090250real_n @ SV37 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(751,plain,
! [SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(752,plain,
! [SV39: real] :
( ( ( ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(753,plain,
! [SV109: int,SV39: real] :
( ( ( SV39
!= ( ring_1_of_int_real @ SV109 ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(754,plain,
! [SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(755,plain,
! [SV42: real] :
( ( ( ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(756,plain,
! [SV110: int,SV42: real] :
( ( ( SV42
!= ( ring_1_of_int_real @ SV110 ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(757,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ( ord_le1017090250real_n @ SV43 @ SV73 )
| ( ord_le1017090250real_n @ SV90 @ SV102 ) )
| ~ ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(758,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(759,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(760,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ~ ~ SV46
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(761,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(762,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ~ ~ $true
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(763,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(764,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ~ ~ $false
| ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(765,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ~ ( ( SV48 = SV79 )
| ( SV96 = SV106 ) )
| ~ ( ( SV48 != SV79 )
| ( SV96 != SV106 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(766,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( SV48 = SV79 )
= ( SV96 = SV106 ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(767,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(768,plain,
! [SV51: int,SV4: int] :
( ( ( SV4 != SV51 )
= $false )
| ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(769,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
!= ( ring_1_of_int_real @ SV51 ) )
= $false )
| ( ( SV4 = SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(770,plain,
! [SV51: int,SV4: int] :
( ( ( SV4 != SV51 )
= $false )
| ( ( SV4 = SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(771,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 = SV98 )
= $false )
| ( ( ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(772,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(773,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false )
| ( ( ~ ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[730]) ).
thf(774,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) )
= $false )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(775,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
= $false )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(776,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 != SV57 )
= $false )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(777,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(778,plain,
! [SV31: $o] :
( ( ( ~ $true ) = $false )
| ( SV31 = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(779,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $true = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(780,plain,
! [SV31: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(781,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( SV31 = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(782,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(783,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(784,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(785,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(786,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(787,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(788,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(789,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(790,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(791,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(792,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(793,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(794,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(795,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ( ord_le866583254real_n @ SV34 @ SV68 )
| ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(796,plain,
! [SV69: finite1489363574real_n,SV35: finite1489363574real_n,SV100: finite1489363574real_n,SV88: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV88 @ SV100 )
= $false )
| ( ( ord_le866583254real_n @ ( minus_1037315151real_n @ SV35 @ SV100 ) @ ( minus_1037315151real_n @ SV69 @ SV88 ) )
= $true )
| ( ( ord_le866583254real_n @ SV35 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(797,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 ) )
= $true )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(798,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ! [SY206: n] : ( SV36 @ SY206 @ ( finite772340589real_n @ SV108 @ SY206 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(799,plain,
! [SV70: finite1489363574real_n,SV37: finite1489363574real_n,SV101: finite1489363574real_n,SV89: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV89 @ SV101 )
= $false )
| ( ( ord_le1017090250real_n @ ( minus_1037315151real_n @ SV37 @ SV101 ) @ ( minus_1037315151real_n @ SV70 @ SV89 ) )
= $true )
| ( ( ord_le1017090250real_n @ SV37 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(800,plain,
! [SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(801,plain,
! [SV39: real] :
( ( ( ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(802,plain,
! [SV109: int,SV39: real] :
( ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(803,plain,
! [SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(804,plain,
! [SV42: real] :
( ( ( ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(805,plain,
! [SV110: int,SV42: real] :
( ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(806,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ( ord_le1017090250real_n @ SV43 @ SV73 )
| ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(807,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ( ~ SV46 ) = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(808,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ( ~ ~ SV46 )
= $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(809,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ( ~ $true ) = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(810,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(811,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ( ~ $false ) = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(812,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(813,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ~ ( ( SV48 = SV79 )
| ( SV96 = SV106 ) ) )
= $true )
| ( ( ~ ( ( SV48 != SV79 )
| ( SV96 != SV106 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(814,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $true )
| ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(815,plain,
! [SV51: int,SV4: int] :
( ( ( SV4 = SV51 )
= $true )
| ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(816,plain,
! [SV51: int,SV4: int] :
( ( ( ( ring_1_of_int_real @ SV4 )
= ( ring_1_of_int_real @ SV51 ) )
= $true )
| ( ( SV4 = SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(817,plain,
! [SV51: int,SV4: int] :
( ( ( SV4 = SV51 )
= $true )
| ( ( SV4 = SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(818,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(819,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false )
| ( ( ~ ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[772]) ).
thf(820,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
| ( SV14 != SV57 ) )
= $false )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(821,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
= $false )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(822,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 != SV57 )
= $false )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(823,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(824,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 = SV57 )
= $true )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(825,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(826,plain,
! [SV31: $o] :
( ( $true = $true )
| ( SV31 = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(827,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $true = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(828,plain,
! [SV31: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV31 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(829,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[781]) ).
thf(830,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( SV31 = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[781]) ).
thf(831,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $false = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(832,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(833,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(834,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(835,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(836,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(837,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(838,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(839,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(840,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(841,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(842,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(843,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(844,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(845,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(846,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(847,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(848,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(849,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ( ord_le866583254real_n @ SV34 @ SV68 )
| ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ~ ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(850,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(851,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[798]) ).
thf(852,plain,
! [SV39: real] :
( ( ( ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(853,plain,
! [SV109: int,SV39: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
| ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(854,plain,
! [SV42: real] :
( ( ( ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(855,plain,
! [SV110: int,SV42: real] :
( ( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
| ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(856,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
| ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(857,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( SV46 = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV75 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(858,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( ( ~ SV46 ) = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(859,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( $true = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV76 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(860,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( ( ~ $true ) = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(861,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( $false = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV77 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(862,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( ( ~ $false ) = $false )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(863,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( SV48 = SV79 )
| ( SV96 = SV106 ) )
= $false )
| ( ( ~ ( ( SV48 != SV79 )
| ( SV96 != SV106 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(864,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 != SV98 )
= $false )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(865,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(866,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ( SV55 != SV98 )
| ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(867,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
!= ( finite772340589real_n @ SV57 ) )
= $false )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(868,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 != SV57 )
= $false )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(869,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(870,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 = SV57 )
= $true )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(871,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ! [SV112: n] :
( ( finite772340589real_n @ SV14 @ SV112 )
= ( finite772340589real_n @ SV57 @ SV112 ) ) )
= $true )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[823]) ).
thf(872,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[823]) ).
thf(873,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false )
| ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[825]) ).
thf(874,plain,
! [SV31: $o] :
( ( ( SV31 = $false )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[825]) ).
thf(875,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false )
| ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[826]) ).
thf(876,plain,
! [SV31: $o] :
( ( ( SV31 = $false )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[826]) ).
thf(877,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false )
| ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[827]) ).
thf(878,plain,
! [SV31: $o] :
( ( ( SV31 = $false )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[827]) ).
thf(879,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false )
| ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[828]) ).
thf(880,plain,
! [SV31: $o] :
( ( ( SV31 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[828]) ).
thf(881,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(882,plain,
! [SV31: $o] :
( ( $false = $true )
| ( SV31 = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(883,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $false = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(884,plain,
! [SV31: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV31 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(885,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(886,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(887,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[834]) ).
thf(888,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[834]) ).
thf(889,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[835]) ).
thf(890,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[835]) ).
thf(891,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(892,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(893,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(894,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(895,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(896,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(897,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(898,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(899,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[842]) ).
thf(900,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[842]) ).
thf(901,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(902,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(903,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[844]) ).
thf(904,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[844]) ).
thf(905,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(906,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(907,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(908,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(909,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ~ ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(910,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n,SV99: finite1489363574real_n,SV87: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ~ ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(911,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(912,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 )
| ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(913,plain,
! [SV39: real] :
( ( ( SV39
!= ( ring_1_of_int_real @ ( sK9_SY148 @ SV39 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[852]) ).
thf(914,plain,
! [SV109: int,SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
!= SV39 )
= $false )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(915,plain,
! [SV109: int,SV39: real] :
( ( ( ~ ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(916,plain,
! [SV42: real] :
( ( ( SV42
!= ( ring_1_of_int_real @ ( sK10_SY151 @ SV42 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[854]) ).
thf(917,plain,
! [SV110: int,SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
!= SV42 )
= $false )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(918,plain,
! [SV110: int,SV42: real] :
( ( ( ~ ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(919,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ~ ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(920,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n,SV102: finite1489363574real_n,SV90: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ~ ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(921,plain,
! [SV103: n,SV92: finite1489363574real_n,SV75: finite1489363574real_n,SV46: $o] :
( ( SV46 = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ SV46 @ SV75 @ SV92 ) @ SV103 )
= ( finite772340589real_n @ SV92 @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(922,plain,
! [SV104: n,SV93: finite1489363574real_n,SV76: finite1489363574real_n] :
( ( $true = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $true @ SV76 @ SV93 ) @ SV104 )
= ( finite772340589real_n @ SV93 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(923,plain,
! [SV105: n,SV94: finite1489363574real_n,SV77: finite1489363574real_n] :
( ( $false = $true )
| ( ( ( finite772340589real_n @ ( if_Fin127821360real_n @ $false @ SV77 @ SV94 ) @ SV105 )
= ( finite772340589real_n @ SV94 @ SV105 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(924,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( SV48 = SV79 )
= $false )
| ( ( ~ ( ( SV48 != SV79 )
| ( SV96 != SV106 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(925,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n,SV106: finite1489363574real_n,SV96: finite1489363574real_n] :
( ( ( SV96 = SV106 )
= $false )
| ( ( ~ ( ( SV48 != SV79 )
| ( SV96 != SV106 ) ) )
= $true )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(926,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 = SV98 )
= $true )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(927,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $true )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(928,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 != SV98 )
= $false )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(929,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ~ ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $false )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(930,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(931,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( SV14 = SV57 )
= $true )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(932,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ! [SV113: n] :
( ( finite772340589real_n @ SV14 @ SV113 )
= ( finite772340589real_n @ SV57 @ SV113 ) ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[869]) ).
thf(933,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[869]) ).
thf(934,plain,
! [SV57: finite1489363574real_n,SV114: n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 @ SV114 )
= ( finite772340589real_n @ SV57 @ SV114 ) )
= $true )
| ( ( SV14 = SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(935,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(936,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(937,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(938,plain,
! [SV31: $o] :
( ( ( ~ ( SV31
| $false ) )
= $true )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(939,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(940,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(941,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(942,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(943,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(944,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(945,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(946,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(947,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(948,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV34 @ SV68 )
| ~ ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(949,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(950,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(951,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(952,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(953,plain,
! [SV39: real] :
( ( ( SV39
= ( ring_1_of_int_real @ ( sK9_SY148 @ SV39 ) ) )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(954,plain,
! [SV109: int,SV39: real] :
( ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ SV39 ) )
= SV39 )
= $true )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(955,plain,
! [SV109: int,SV39: real] :
( ( ( ~ ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $true )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(956,plain,
! [SV42: real] :
( ( ( SV42
= ( ring_1_of_int_real @ ( sK10_SY151 @ SV42 ) ) )
= $true )
| ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(957,plain,
! [SV110: int,SV42: real] :
( ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ SV42 ) )
= SV42 )
= $true )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(958,plain,
! [SV110: int,SV42: real] :
( ( ( ~ ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $true )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(959,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(960,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 )
| ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(961,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( SV48 != SV79 )
| ( SV96 != SV106 ) )
= $false )
| ( ( SV48 = SV79 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(962,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( ( SV48 != SV79 )
| ( SV96 != SV106 ) )
= $false )
| ( ( SV96 = SV106 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(963,plain,
! [SV98: finite1489363574real_n,SV115: n,SV55: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV55 @ SV115 )
= ( finite772340589real_n @ SV98 @ SV115 ) )
= $true )
| ( ( SV55 = SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(964,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( SV55 = SV98 )
= $true )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(965,plain,
! [SV98: finite1489363574real_n,SV55: finite1489363574real_n] :
( ( ( ! [SY204: n] :
( ( finite772340589real_n @ SV55 @ SY204 )
= ( finite772340589real_n @ SV98 @ SY204 ) ) )
= $true )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(966,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ! [SV116: n] :
( ( finite772340589real_n @ SV14 @ SV116 )
= ( finite772340589real_n @ SV57 @ SV116 ) ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(967,plain,
! [SV57: finite1489363574real_n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(968,plain,
! [SV57: finite1489363574real_n,SV117: n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 @ SV117 )
= ( finite772340589real_n @ SV57 @ SV117 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 )
= ( finite772340589real_n @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(969,plain,
! [SV31: $o] :
( ( ( SV31
| $false )
= $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(970,plain,
! [SV31: $o] :
( ( ( SV31
| $false )
= $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(971,plain,
! [SV31: $o] :
( ( ( SV31
| $false )
= $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(972,plain,
! [SV31: $o] :
( ( ( SV31
| $false )
= $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(973,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(974,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(975,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(976,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(977,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(978,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(979,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(980,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(981,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV34 @ SV68 ) )
= $false )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(982,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n,SV99: finite1489363574real_n,SV87: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(983,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV34 @ SV68 ) )
= $false )
| ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(984,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n,SV99: finite1489363574real_n,SV87: finite1489363574real_n] :
( ( ( ~ ( ord_le866583254real_n @ SV87 @ SV99 ) )
= $false )
| ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(985,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(986,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(987,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ! [SY140: n] :
~ ! [SY141: real] :
~ ( SV36 @ SY140 @ SY141 ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(988,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(989,plain,
! [SV109: int,SV39: real] :
( ( ( ! [SY148: int] :
( SV39
!= ( ring_1_of_int_real @ SY148 ) ) )
= $false )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(990,plain,
! [SV110: int,SV42: real] :
( ( ( ! [SY151: int] :
( SV42
!= ( ring_1_of_int_real @ SY151 ) ) )
= $false )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(991,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(992,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n,SV102: finite1489363574real_n,SV90: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(993,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV43 @ SV73 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(994,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n,SV102: finite1489363574real_n,SV90: finite1489363574real_n] :
( ( ( ~ ( ord_le1017090250real_n @ SV90 @ SV102 ) )
= $false )
| ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(995,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( SV48 != SV79 )
= $false )
| ( ( SV48 = SV79 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(996,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n,SV106: finite1489363574real_n,SV96: finite1489363574real_n] :
( ( ( SV96 != SV106 )
= $false )
| ( ( SV48 = SV79 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(997,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( SV48 != SV79 )
= $false )
| ( ( SV96 = SV106 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(998,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n,SV106: finite1489363574real_n,SV96: finite1489363574real_n] :
( ( ( SV96 != SV106 )
= $false )
| ( ( SV96 = SV106 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(999,plain,
! [SV98: finite1489363574real_n,SV118: n,SV55: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV55 @ SV118 )
= ( finite772340589real_n @ SV98 @ SV118 ) )
= $true )
| ( ( ( finite772340589real_n @ SV55 @ ( sK7_SY204 @ SV98 @ SV55 ) )
= ( finite772340589real_n @ SV98 @ ( sK7_SY204 @ SV98 @ SV55 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1000,plain,
! [SV57: finite1489363574real_n,SV119: n,SV14: finite1489363574real_n] :
( ( ( ( finite772340589real_n @ SV14 @ SV119 )
= ( finite772340589real_n @ SV57 @ SV119 ) )
= $true )
| ( ( ( finite772340589real_n @ SV14 @ ( sK6_SV107 @ SV57 @ SV14 ) )
= ( finite772340589real_n @ SV57 @ ( sK6_SV107 @ SV57 @ SV14 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1001,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1002,plain,
! [SV31: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1003,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1004,plain,
! [SV31: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1005,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1006,plain,
! [SV31: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1007,plain,
! [SV31: $o] :
( ( SV31 = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[972]) ).
thf(1008,plain,
! [SV31: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV31
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[972]) ).
thf(1009,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1010,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1011,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1012,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1013,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1014,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1015,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1016,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1017,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1018,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1019,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1020,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1021,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1022,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1023,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1024,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1025,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $true )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1026,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n,SV99: finite1489363574real_n,SV87: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $true )
| ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1027,plain,
! [SV99: finite1489363574real_n,SV87: finite1489363574real_n,SV68: finite1489363574real_n,SV34: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV34 @ SV68 )
= $true )
| ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1028,plain,
! [SV68: finite1489363574real_n,SV34: finite1489363574real_n,SV99: finite1489363574real_n,SV87: finite1489363574real_n] :
( ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $true )
| ( ( ord_le866583254real_n @ SV87 @ SV99 )
= $false )
| ( ( ( minus_1037315151real_n @ SV34 @ SV68 )
= ( minus_1037315151real_n @ SV87 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1029,plain,
! [SV111: real,SV120: n,SV36: n > real > $o] :
( ( ( ~ ! [SY207: real] :
~ ( SV36 @ SV120 @ SY207 ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1030,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1031,plain,
! [SV108: finite1489363574real_n,SV121: n,SV36: n > real > $o] :
( ( ( ~ ! [SY208: real] :
~ ( SV36 @ SV121 @ SY208 ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1032,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ! [SY142: finite1489363574real_n] :
~ ! [SY143: n] : ( SV36 @ SY143 @ ( finite772340589real_n @ SY142 @ SY143 ) ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1033,plain,
! [SV109: int,SV39: real] :
( ( ( SV39
!= ( ring_1_of_int_real @ ( sK11_SY148 @ SV109 @ SV39 ) ) )
= $false )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[989]) ).
thf(1034,plain,
! [SV110: int,SV42: real] :
( ( ( SV42
!= ( ring_1_of_int_real @ ( sK12_SY151 @ SV110 @ SV42 ) ) )
= $false )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[990]) ).
thf(1035,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $true )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1036,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n,SV102: finite1489363574real_n,SV90: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $true )
| ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1037,plain,
! [SV102: finite1489363574real_n,SV90: finite1489363574real_n,SV73: finite1489363574real_n,SV43: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV43 @ SV73 )
= $true )
| ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1038,plain,
! [SV73: finite1489363574real_n,SV43: finite1489363574real_n,SV102: finite1489363574real_n,SV90: finite1489363574real_n] :
( ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $true )
| ( ( ord_le1017090250real_n @ SV90 @ SV102 )
= $false )
| ( ( ( minus_1037315151real_n @ SV43 @ SV73 )
= ( minus_1037315151real_n @ SV90 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1039,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( SV48 = SV79 )
= $true )
| ( ( SV48 = SV79 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1040,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n,SV106: finite1489363574real_n,SV96: finite1489363574real_n] :
( ( ( SV96 = SV106 )
= $true )
| ( ( SV48 = SV79 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1041,plain,
! [SV106: finite1489363574real_n,SV96: finite1489363574real_n,SV79: finite1489363574real_n,SV48: finite1489363574real_n] :
( ( ( SV48 = SV79 )
= $true )
| ( ( SV96 = SV106 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1042,plain,
! [SV79: finite1489363574real_n,SV48: finite1489363574real_n,SV106: finite1489363574real_n,SV96: finite1489363574real_n] :
( ( ( SV96 = SV106 )
= $true )
| ( ( SV96 = SV106 )
= $false )
| ( ( ( minus_1037315151real_n @ SV48 @ SV79 )
= ( minus_1037315151real_n @ SV96 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1043,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1044,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( $false = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1045,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1046,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( $false = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1047,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( SV31 = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1048,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1049,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( SV31 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1050,plain,
! [SV31: $o] :
( ( ( ~ SV31
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1051,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1052,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1053,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1054,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1055,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1056,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1057,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1058,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1059,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1060,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1061,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1062,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1063,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1064,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1065,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1066,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1067,plain,
! [SV111: real,SV120: n,SV36: n > real > $o] :
( ( ( ! [SY207: real] :
~ ( SV36 @ SV120 @ SY207 ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1068,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ~ ! [SY209: n] : ( SV36 @ SY209 @ ( finite772340589real_n @ ( sK13_SY142 @ SV111 @ SV36 ) @ SY209 ) ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1030]) ).
thf(1069,plain,
! [SV108: finite1489363574real_n,SV121: n,SV36: n > real > $o] :
( ( ( ! [SY208: real] :
~ ( SV36 @ SV121 @ SY208 ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1070,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ~ ! [SY210: n] : ( SV36 @ SY210 @ ( finite772340589real_n @ ( sK14_SY142 @ SV108 @ SV36 ) @ SY210 ) ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1032]) ).
thf(1071,plain,
! [SV109: int,SV39: real] :
( ( ( SV39
= ( ring_1_of_int_real @ ( sK11_SY148 @ SV109 @ SV39 ) ) )
= $true )
| ( ( SV39
= ( ring_1_of_int_real @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1072,plain,
! [SV110: int,SV42: real] :
( ( ( SV42
= ( ring_1_of_int_real @ ( sK12_SY151 @ SV110 @ SV42 ) ) )
= $true )
| ( ( SV42
= ( ring_1_of_int_real @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1073,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1074,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1075,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $false = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1076,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1077,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1078,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( SV31 = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1079,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $false = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1080,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1081,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1082,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( SV31 = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1083,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1084,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1085,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( SV31 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1086,plain,
! [SV31: $o] :
( ( ( ~ $false ) = $false )
| ( SV31 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1087,plain,
! [SV31: $o] :
( ( ( ~ SV31 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1088,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1089,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1090,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1091,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1092,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1093,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1094,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1095,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1096,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1097,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1098,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1099,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1100,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1101,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1102,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1103,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1104,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1105,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1106,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1107,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1108,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1109,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1110,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1111,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1112,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1113,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1114,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1115,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1116,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1117,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1118,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1119,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1120,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1121,plain,
! [SV111: real,SV120: n,SV36: n > real > $o] :
( ( ( ~ ( SV36 @ SV120 @ ( sK15_SY207 @ SV111 @ SV120 @ SV36 ) ) )
= $false )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1067]) ).
thf(1122,plain,
! [SV111: real,SV36: n > real > $o] :
( ( ( ! [SY209: n] : ( SV36 @ SY209 @ ( finite772340589real_n @ ( sK13_SY142 @ SV111 @ SV36 ) @ SY209 ) ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1123,plain,
! [SV108: finite1489363574real_n,SV121: n,SV36: n > real > $o] :
( ( ( ~ ( SV36 @ SV121 @ ( sK16_SY208 @ SV108 @ SV121 @ SV36 ) ) )
= $false )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1069]) ).
thf(1124,plain,
! [SV108: finite1489363574real_n,SV36: n > real > $o] :
( ( ( ! [SY210: n] : ( SV36 @ SY210 @ ( finite772340589real_n @ ( sK14_SY142 @ SV108 @ SV36 ) @ SY210 ) ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1125,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1126,plain,
! [SV31: $o] :
( ( $false = $true )
| ( SV31 = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1127,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $false = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1128,plain,
! [SV31: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV31 = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1129,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1130,plain,
! [SV31: $o] :
( ( $false = $true )
| ( SV31 = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1131,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $false = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1132,plain,
! [SV31: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV31 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1133,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1134,plain,
! [SV31: $o] :
( ( $false = $true )
| ( SV31 = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1135,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1136,plain,
! [SV31: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV31 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1137,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( SV31 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1138,plain,
! [SV31: $o] :
( ( $false = $true )
| ( SV31 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1139,plain,
! [SV31: $o] :
( ( SV31 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1140,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1141,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1142,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1143,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1144,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1145,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1146,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1147,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1148,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1149,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1150,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1151,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1152,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1153,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1154,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1155,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1156,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1157,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1158,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1159,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1160,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1161,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1162,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1163,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1164,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1165,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1166,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1167,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1168,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1169,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1170,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1171,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1172,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1173,plain,
! [SV111: real,SV120: n,SV36: n > real > $o] :
( ( ( SV36 @ SV120 @ ( sK15_SY207 @ SV111 @ SV120 @ SV36 ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1174,plain,
! [SV111: real,SV122: n,SV36: n > real > $o] :
( ( ( SV36 @ SV122 @ ( finite772340589real_n @ ( sK13_SY142 @ SV111 @ SV36 ) @ SV122 ) )
= $true )
| ( ( SV36 @ ( sK5_SY140 @ SV36 ) @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1175,plain,
! [SV108: finite1489363574real_n,SV121: n,SV36: n > real > $o] :
( ( ( SV36 @ SV121 @ ( sK16_SY208 @ SV108 @ SV121 @ SV36 ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1176,plain,
! [SV108: finite1489363574real_n,SV123: n,SV36: n > real > $o] :
( ( ( SV36 @ SV123 @ ( finite772340589real_n @ ( sK14_SY142 @ SV108 @ SV36 ) @ SV123 ) )
= $true )
| ( ( SV36 @ ( sK8_SY206 @ SV108 @ SV36 ) @ ( finite772340589real_n @ SV108 @ ( sK8_SY206 @ SV108 @ SV36 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1177,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[423,1176,1175,1174,1173,1172,1171,1170,1169,1168,1167,1166,1165,1164,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1151,1150,1149,1148,1147,1146,1145,1144,1143,1142,1141,1140,1139,1138,1137,1136,1135,1134,1133,1132,1131,1130,1129,1128,1127,1126,1125,1072,1071,1042,1041,1040,1039,1038,1037,1036,1035,1028,1027,1026,1025,1000,999,968,967,964,963,957,956,954,953,934,933,931,926,923,922,921,908,907,906,905,904,902,900,898,896,895,894,893,892,890,888,886,884,883,882,881,880,878,876,874,872,870,861,859,857,824,817,816,815,814,803,800,799,796,766,758,746,695,693,689,678,670,660,657,656,654,649,647,644,641,621,608,607,606,604,603,601,599,589,585,580,571,570,569,567,566,564,563,559,558,557,533,529,528,523,518,517,516,515,513,510,505,504,503,502,500,499,461,460,445,444]) ).
thf(1178,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP118^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24 % Computer : n014.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8046.5625MB
% 0.08/0.24 % OS : Linux 6.8.0-71-generic
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Oct 6 11:17:56 UTC 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.09/1.51 ..
% 7.09/1.51
% 7.09/1.51 No.of.Axioms: 55
% 7.09/1.51
% 7.09/1.51 Length.of.Defs: 0
% 7.09/1.51
% 7.09/1.51 Contains.Choice.Funs: false
% 7.09/1.51 ..................
% 7.09/1.51
% 7.09/1.51 ********************************
% 7.09/1.51 * All subproblems solved! *
% 7.09/1.51 ********************************
% 7.09/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:55,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1177,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.09/1.51
% 7.09/1.51 %**** Beginning of derivation protocol ****
% 7.09/1.51 % SZS output start CNFRefutation
% See solution above
% 7.09/1.52
% 7.09/1.52 %**** End of derivation protocol ****
% 7.09/1.52 %**** no. of clauses in derivation: 870 ****
% 7.09/1.52 %**** clause counter: 1177 ****
% 7.09/1.52
% 7.09/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:55,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1177,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------