%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP094^1 : 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 : n009.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 10:24:05 AM UTC 2026
% Result : Theorem 4.24s 1.02s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 26
% Syntax : Number of formulae : 409 ( 137 unt; 0 typ; 0 def)
% Number of atoms : 2950 (1335 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 5345 (1261 ~; 875 |; 30 &;3134 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 104 usr; 21 con; 0-6 aty)
% Number of variables : 989 ( 108 ^; 866 !; 15 ?; 989 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_poly_nat,type,
poly_nat: $tType ).
thf(tp_poly_poly_nat,type,
poly_poly_nat: $tType ).
thf(tp_poly_poly_poly_real,type,
poly_poly_poly_real: $tType ).
thf(tp_poly_poly_real,type,
poly_poly_real: $tType ).
thf(tp_poly_real,type,
poly_real: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_poly_poly_real,type,
set_poly_poly_real: $tType ).
thf(tp_set_poly_real,type,
set_poly_real: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_algebraic_int_real,type,
algebraic_int_real: real > $o ).
thf(tp_algebraic_real,type,
algebraic_real: real > $o ).
thf(tp_coeff_nat,type,
coeff_nat: poly_nat > nat > nat ).
thf(tp_coeff_poly_nat,type,
coeff_poly_nat: poly_poly_nat > nat > poly_nat ).
thf(tp_coeff_poly_poly_real,type,
coeff_poly_poly_real: poly_poly_poly_real > nat > poly_poly_real ).
thf(tp_coeff_poly_real,type,
coeff_poly_real: poly_poly_real > nat > poly_real ).
thf(tp_coeff_real,type,
coeff_real: poly_real > nat > real ).
thf(tp_collec927113489y_real,type,
collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_poly_real,type,
collect_poly_real: ( poly_real > $o ) > set_poly_real ).
thf(tp_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(tp_cr_poly_real,type,
cr_poly_real: ( nat > real ) > poly_real > $o ).
thf(tp_degree360860553y_real,type,
degree360860553y_real: poly_poly_poly_real > nat ).
thf(tp_degree_nat,type,
degree_nat: poly_nat > nat ).
thf(tp_degree_poly_nat,type,
degree_poly_nat: poly_poly_nat > nat ).
thf(tp_degree_poly_real,type,
degree_poly_real: poly_poly_real > nat ).
thf(tp_degree_real,type,
degree_real: poly_real > nat ).
thf(tp_divide1142363123y_real,type,
divide1142363123y_real: poly_real > poly_poly_real > poly_poly_real > poly_poly_real > nat > nat > poly_poly_real ).
thf(tp_divide1561404011n_real,type,
divide1561404011n_real: real > poly_real > poly_real > poly_real > nat > nat > poly_real ).
thf(tp_divide924636027y_real,type,
divide924636027y_real: poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > poly_poly_poly_real > nat > nat > poly_poly_poly_real ).
thf(tp_dvd_dv1946063458y_real,type,
dvd_dv1946063458y_real: poly_poly_real > poly_poly_real > $o ).
thf(tp_dvd_dvd_nat,type,
dvd_dvd_nat: nat > nat > $o ).
thf(tp_dvd_dvd_poly_nat,type,
dvd_dvd_poly_nat: poly_nat > poly_nat > $o ).
thf(tp_dvd_dvd_poly_real,type,
dvd_dvd_poly_real: poly_real > poly_real > $o ).
thf(tp_dvd_dvd_real,type,
dvd_dvd_real: real > real > $o ).
thf(tp_field_1537545994s_real,type,
field_1537545994s_real: set_real ).
thf(tp_finite1328464339y_real,type,
finite1328464339y_real: set_poly_poly_real > $o ).
thf(tp_finite1810960971y_real,type,
finite1810960971y_real: set_poly_real > $o ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_finite_finite_real,type,
finite_finite_real: set_real > $o ).
thf(tp_inverse_inverse_real,type,
inverse_inverse_real: real > real ).
thf(tp_is_zero_nat,type,
is_zero_nat: poly_nat > $o ).
thf(tp_is_zero_poly_real,type,
is_zero_poly_real: poly_poly_real > $o ).
thf(tp_is_zero_real,type,
is_zero_real: poly_real > $o ).
thf(tp_member1159720147y_real,type,
member1159720147y_real: poly_poly_real > set_poly_poly_real > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_poly_real,type,
member_poly_real: poly_real > set_poly_real > $o ).
thf(tp_member_real,type,
member_real: real > set_real > $o ).
thf(tp_n,type,
n: nat ).
thf(tp_one_on501200385y_real,type,
one_on501200385y_real: poly_poly_real ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_one_one_poly_nat,type,
one_one_poly_nat: poly_nat ).
thf(tp_one_one_poly_real,type,
one_one_poly_real: poly_real ).
thf(tp_one_one_real,type,
one_one_real: real ).
thf(tp_ord_le38482960y_real,type,
ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_poly_real,type,
ord_less_poly_real: poly_real > poly_real > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_order_poly_poly_real,type,
order_poly_poly_real: poly_poly_real > poly_poly_poly_real > nat ).
thf(tp_order_poly_real,type,
order_poly_real: poly_real > poly_poly_real > nat ).
thf(tp_order_real,type,
order_real: real > poly_real > nat ).
thf(tp_p,type,
p: poly_real ).
thf(tp_pcr_po1200519205y_real,type,
pcr_po1200519205y_real: ( poly_poly_real > poly_poly_real > $o ) > ( nat > poly_poly_real ) > poly_poly_poly_real > $o ).
thf(tp_pcr_po1314690837y_real,type,
pcr_po1314690837y_real: ( poly_real > poly_real > $o ) > ( nat > poly_real ) > poly_poly_real > $o ).
thf(tp_pcr_po273983709ly_nat,type,
pcr_po273983709ly_nat: ( poly_nat > poly_nat > $o ) > ( nat > poly_nat ) > poly_poly_nat > $o ).
thf(tp_pcr_poly_nat_nat,type,
pcr_poly_nat_nat: ( nat > nat > $o ) > ( nat > nat ) > poly_nat > $o ).
thf(tp_pcr_poly_real_real,type,
pcr_poly_real_real: ( real > real > $o ) > ( nat > real ) > poly_real > $o ).
thf(tp_pderiv_nat,type,
pderiv_nat: poly_nat > poly_nat ).
thf(tp_pderiv_poly_real,type,
pderiv_poly_real: poly_poly_real > poly_poly_real ).
thf(tp_pderiv_real,type,
pderiv_real: poly_real > poly_real ).
thf(tp_poly_c1404107022y_real,type,
poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
thf(tp_poly_cutoff_nat,type,
poly_cutoff_nat: nat > poly_nat > poly_nat ).
thf(tp_poly_cutoff_real,type,
poly_cutoff_real: nat > poly_real > poly_real ).
thf(tp_poly_nat2,type,
poly_nat2: poly_nat > nat > nat ).
thf(tp_poly_poly_nat2,type,
poly_poly_nat2: poly_poly_nat > poly_nat > poly_nat ).
thf(tp_poly_poly_poly_real2,type,
poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
thf(tp_poly_poly_real2,type,
poly_poly_real2: poly_poly_real > poly_real > poly_real ).
thf(tp_poly_real2,type,
poly_real2: poly_real > real > real ).
thf(tp_poly_shift_nat,type,
poly_shift_nat: nat > poly_nat > poly_nat ).
thf(tp_poly_shift_poly_real,type,
poly_shift_poly_real: nat > poly_poly_real > poly_poly_real ).
thf(tp_poly_shift_real,type,
poly_shift_real: nat > poly_real > poly_real ).
thf(tp_reflec144234502y_real,type,
reflec144234502y_real: poly_poly_poly_real > poly_poly_poly_real ).
thf(tp_reflec1522834046y_real,type,
reflec1522834046y_real: poly_poly_real > poly_poly_real ).
thf(tp_reflec781175074ly_nat,type,
reflec781175074ly_nat: poly_poly_nat > poly_poly_nat ).
thf(tp_reflect_poly_nat,type,
reflect_poly_nat: poly_nat > poly_nat ).
thf(tp_reflect_poly_real,type,
reflect_poly_real: poly_real > poly_real ).
thf(tp_ring_1690226883y_real,type,
ring_1690226883y_real: set_poly_real ).
thf(tp_ring_1897377867y_real,type,
ring_1897377867y_real: set_poly_poly_real ).
thf(tp_ring_1_Ints_real,type,
ring_1_Ints_real: set_real ).
thf(tp_rsquar1555552848y_real,type,
rsquar1555552848y_real: poly_poly_real > $o ).
thf(tp_rsquarefree_real,type,
rsquarefree_real: poly_real > $o ).
thf(tp_sK10_SY85,type,
sK10_SY85: real > ( real > real > $o ) > set_real > set_real > real ).
thf(tp_sK1_SY79,type,
sK1_SY79: ( real > $o ) > ( real > $o ) > real ).
thf(tp_sK2_SY44,type,
sK2_SY44: poly_real > real ).
thf(tp_sK3_SY48,type,
sK3_SY48: ( real > $o ) > real ).
thf(tp_sK4_SY72,type,
sK4_SY72: poly_real > real ).
thf(tp_sK5_SV31,type,
sK5_SV31: poly_real > poly_real > real ).
thf(tp_sK6_SY82,type,
sK6_SY82: poly_real > real > real > real ).
thf(tp_sK7_SY83,type,
sK7_SY83: ( real > real > $o ) > set_real > set_real > real ).
thf(tp_sK8_SY87,type,
sK8_SY87: poly_real > real > real > real ).
thf(tp_sK9_SY85,type,
sK9_SY85: ( real > real > $o ) > set_real > set_real > real ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_synthe1498897281y_real,type,
synthe1498897281y_real: poly_poly_real > poly_real > poly_poly_real ).
thf(tp_synthetic_div_nat,type,
synthetic_div_nat: poly_nat > nat > poly_nat ).
thf(tp_synthetic_div_real,type,
synthetic_div_real: poly_real > real > poly_real ).
thf(tp_x,type,
x: real ).
thf(tp_zero_z1059985641ly_nat,type,
zero_z1059985641ly_nat: poly_poly_nat ).
thf(tp_zero_z1423781445y_real,type,
zero_z1423781445y_real: poly_poly_real ).
thf(tp_zero_z935034829y_real,type,
zero_z935034829y_real: poly_poly_poly_real ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_poly_nat,type,
zero_zero_poly_nat: poly_nat ).
thf(tp_zero_zero_poly_real,type,
zero_zero_poly_real: poly_real ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(5,axiom,
! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ A3 ) )
=> ( ( ord_less_real @ ( poly_real2 @ P @ B2 ) @ zero_zero_real )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_poly__IVT__neg) ).
thf(6,axiom,
! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ ( poly_real2 @ P @ A3 ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ B2 ) )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_poly__IVT__pos) ).
thf(106,axiom,
algebraic_int_real @ zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_algebraic__int__0) ).
thf(132,axiom,
! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
=> ( A3 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_dvd__0__left) ).
thf(137,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_zero__neq__one) ).
thf(155,axiom,
! [A3: real] : ( dvd_dvd_real @ A3 @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_dvd__0__right) ).
thf(160,axiom,
! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
= ( A3 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_dvd__0__left__iff) ).
thf(191,axiom,
~ ( finite_finite_real @ field_1537545994s_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Rats__infinite) ).
thf(219,axiom,
! [P2: real > $o,Q: real > $o] :
( ! [X3: real] :
( ( P2 @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_real @ P2 )
= ( collect_real @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Collect__cong) ).
thf(222,axiom,
! [A2: set_real] :
( ( collect_real
@ ^ [X: real] : ( member_real @ X @ A2 ) )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Collect__mem__eq) ).
thf(225,axiom,
! [A3: real,P2: real > $o] :
( ( member_real @ A3 @ ( collect_real @ P2 ) )
= ( P2 @ A3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_mem__Collect__eq) ).
thf(297,axiom,
! [X2: real] :
( ( zero_zero_real = X2 )
= ( X2 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__reorient) ).
thf(303,axiom,
( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_pderiv__0) ).
thf(311,axiom,
! [P: poly_real,Q2: poly_real] :
( ( ( poly_real2 @ P )
= ( poly_real2 @ Q2 ) )
= ( P = Q2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_poly__eq__poly__eq__iff) ).
thf(320,axiom,
! [A2: set_real,B: set_real,R: real > real > $o] :
( ~ ( finite_finite_real @ A2 )
=> ( ( finite_finite_real @ B )
=> ( ! [X3: real] :
( ( member_real @ X3 @ A2 )
=> ? [Xa: real] :
( ( member_real @ Xa @ B )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: real] :
( ( member_real @ X3 @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( member_real @ A @ A2 )
& ( R @ A @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_pigeonhole__infinite__rel) ).
thf(323,axiom,
! [P2: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ P2 ) )
=> ? [X_1: real] : ( P2 @ X_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_not__finite__existsD) ).
thf(324,axiom,
( rsquarefree_real
= ( ^ [P3: poly_real] :
! [A: real] :
~ ( ( ( poly_real2 @ P3 @ A )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ P3 ) @ A )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rsquarefree__roots) ).
thf(326,axiom,
! [P: poly_real] :
( ( ! [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) )
= ( P = zero_zero_poly_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_poly__all__0__iff__0) ).
thf(329,axiom,
! [P2: real > $o,Q: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
| ( Q @ X ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ P2 ) )
& ( finite_finite_real @ ( collect_real @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__Collect__disjI) ).
thf(332,axiom,
! [P2: real > $o,Q: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ P2 ) )
| ( finite_finite_real @ ( collect_real @ Q ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
& ( Q @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__conjI) ).
thf(334,axiom,
! [X2: real] :
( ( poly_real2 @ zero_zero_poly_real @ X2 )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_poly__0) ).
thf(339,axiom,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_p_I3_J) ).
thf(340,axiom,
( ( pderiv_real @ p )
!= zero_zero_poly_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062) ).
thf(341,axiom,
p != zero_zero_poly_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_p_I2_J) ).
thf(342,axiom,
! [P: poly_real] :
( ( P != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_poly__roots__finite) ).
thf(345,conjecture,
( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(346,negated_conjecture,
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[345]) ).
thf(347,plain,
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) )
= $false ),
inference(unfold_def,[status(thm)],[346]) ).
thf(348,plain,
( ( ! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ A3 ) )
=> ( ( ord_less_real @ ( poly_real2 @ P @ B2 ) @ zero_zero_real )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(349,plain,
( ( ! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ ( poly_real2 @ P @ A3 ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ B2 ) )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(350,plain,
( ( algebraic_int_real @ zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(351,plain,
( ( ! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
=> ( A3 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(352,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(353,plain,
( ( ! [A3: real] : ( dvd_dvd_real @ A3 @ zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(354,plain,
( ( ! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
= ( A3 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(355,plain,
( ( ~ ( finite_finite_real @ field_1537545994s_real ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(356,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ! [X3: real] :
( ( P2 @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_real @ P2 )
= ( collect_real @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(357,plain,
( ( ! [A2: set_real] :
( ( collect_real
@ ^ [X: real] : ( member_real @ X @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(358,plain,
( ( ! [A3: real,P2: real > $o] :
( ( member_real @ A3 @ ( collect_real @ P2 ) )
= ( P2 @ A3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(359,plain,
( ( ! [X2: real] :
( ( zero_zero_real = X2 )
= ( X2 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(360,plain,
( ( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(361,plain,
( ( ! [P: poly_real,Q2: poly_real] :
( ( ( poly_real2 @ P )
= ( poly_real2 @ Q2 ) )
= ( P = Q2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(362,plain,
( ( ! [A2: set_real,B: set_real,R: real > real > $o] :
( ~ ( finite_finite_real @ A2 )
=> ( ( finite_finite_real @ B )
=> ( ! [X3: real] :
( ( member_real @ X3 @ A2 )
=> ? [Xa: real] :
( ( member_real @ Xa @ B )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: real] :
( ( member_real @ X3 @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( member_real @ A @ A2 )
& ( R @ A @ X3 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(363,plain,
( ( ! [P2: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ P2 ) )
=> ? [X_1: real] : ( P2 @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(364,plain,
( ( rsquarefree_real
= ( ^ [P3: poly_real] :
! [A: real] :
~ ( ( ( poly_real2 @ P3 @ A )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ P3 ) @ A )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(365,plain,
( ( ! [P: poly_real] :
( ( ! [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) )
= ( P = zero_zero_poly_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(366,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
| ( Q @ X ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ P2 ) )
& ( finite_finite_real @ ( collect_real @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(367,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ P2 ) )
| ( finite_finite_real @ ( collect_real @ Q ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
& ( Q @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(368,plain,
( ( ! [X2: real] :
( ( poly_real2 @ zero_zero_poly_real @ X2 )
= zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(369,plain,
( ( ( poly_real2 @ p @ x )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(370,plain,
( ( ( pderiv_real @ p )
!= zero_zero_poly_real )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(371,plain,
( ( p != zero_zero_poly_real )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(372,plain,
( ( ! [P: poly_real] :
( ( P != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(373,plain,
( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[347]) ).
thf(374,plain,
( ( ! [P: poly_real] :
( ( P != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(375,plain,
( ( p != zero_zero_poly_real )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(376,plain,
( ( ( pderiv_real @ p )
!= zero_zero_poly_real )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(377,plain,
( ( ( poly_real2 @ p @ x )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(378,plain,
( ( ! [X2: real] :
( ( poly_real2 @ zero_zero_poly_real @ X2 )
= zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(379,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ P2 ) )
| ( finite_finite_real @ ( collect_real @ Q ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
& ( Q @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(380,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( P2 @ X )
| ( Q @ X ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ P2 ) )
& ( finite_finite_real @ ( collect_real @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(381,plain,
( ( ! [P: poly_real] :
( ( ! [X: real] :
( ( poly_real2 @ P @ X )
= zero_zero_real ) )
= ( P = zero_zero_poly_real ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(382,plain,
( ( rsquarefree_real
= ( ^ [P3: poly_real] :
! [A: real] :
~ ( ( ( poly_real2 @ P3 @ A )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ P3 ) @ A )
= zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(383,plain,
( ( ! [P2: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ P2 ) )
=> ? [X_1: real] : ( P2 @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(384,plain,
( ( ! [A2: set_real,B: set_real,R: real > real > $o] :
( ~ ( finite_finite_real @ A2 )
=> ( ( finite_finite_real @ B )
=> ( ! [X3: real] :
( ( member_real @ X3 @ A2 )
=> ? [Xa: real] :
( ( member_real @ Xa @ B )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: real] :
( ( member_real @ X3 @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( member_real @ A @ A2 )
& ( R @ A @ X3 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(385,plain,
( ( ! [P: poly_real,Q2: poly_real] :
( ( ( poly_real2 @ P )
= ( poly_real2 @ Q2 ) )
= ( P = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(386,plain,
( ( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(387,plain,
( ( ! [X2: real] :
( ( zero_zero_real = X2 )
= ( X2 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(388,plain,
( ( ! [A3: real,P2: real > $o] :
( ( member_real @ A3 @ ( collect_real @ P2 ) )
= ( P2 @ A3 ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(389,plain,
( ( ! [A2: set_real] :
( ( collect_real
@ ^ [X: real] : ( member_real @ X @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(390,plain,
( ( ! [P2: real > $o,Q: real > $o] :
( ! [X3: real] :
( ( P2 @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_real @ P2 )
= ( collect_real @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(391,plain,
( ( ~ ( finite_finite_real @ field_1537545994s_real ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(392,plain,
( ( ! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
= ( A3 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(393,plain,
( ( ! [A3: real] : ( dvd_dvd_real @ A3 @ zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(394,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(395,plain,
( ( ! [A3: real] :
( ( dvd_dvd_real @ zero_zero_real @ A3 )
=> ( A3 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(396,plain,
( ( algebraic_int_real @ zero_zero_real )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(397,plain,
( ( ! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ ( poly_real2 @ P @ A3 ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ B2 ) )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(398,plain,
( ( ! [A3: real,B2: real,P: poly_real] :
( ( ord_less_real @ A3 @ B2 )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P @ A3 ) )
=> ( ( ord_less_real @ ( poly_real2 @ P @ B2 ) @ zero_zero_real )
=> ? [X3: real] :
( ( ord_less_real @ A3 @ X3 )
& ( ord_less_real @ X3 @ B2 )
& ( ( poly_real2 @ P @ X3 )
= zero_zero_real ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(399,plain,
( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(400,plain,
( ( ! [SX0: real > $o] :
( ~ ~ ( finite_finite_real @ ( collect_real @ SX0 ) )
| ~ ! [SX1: real] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(401,plain,
( ( ( pderiv_real @ p )
!= zero_zero_poly_real )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(402,plain,
( ( ! [SX0: real,SX1: real,SX2: poly_real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ ( poly_real2 @ SX2 @ SX0 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SX2 @ SX1 ) )
| ~ ! [SX3: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SX0 @ SX3 )
| ~ ( ord_less_real @ SX3 @ SX1 ) )
| ( ( poly_real2 @ SX2 @ SX3 )
!= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(403,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(404,plain,
( ( ! [SX0: real > $o,SX1: real > $o] :
( ~ ( ( finite_finite_real @ ( collect_real @ SX0 ) )
| ( finite_finite_real @ ( collect_real @ SX1 ) ) )
| ( finite_finite_real
@ ( collect_real
@ ^ [SX2: real] :
~ ( ~ ( SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(405,plain,
( ( rsquarefree_real
= ( ^ [SX0: poly_real] :
! [SX1: real] :
~ ~ ( ( ( poly_real2 @ SX0 @ SX1 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SX0 ) @ SX1 )
!= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(406,plain,
( ( ! [SX0: real > $o,SX1: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [SX2: real] :
( ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SX0 ) )
| ~ ( finite_finite_real @ ( collect_real @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(407,plain,
( ( ! [SX0: poly_real] :
( ~ ( ( SX0 != zero_zero_poly_real ) )
| ( finite_finite_real
@ ( collect_real
@ ^ [SX1: real] :
( ( poly_real2 @ SX0 @ SX1 )
= zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(408,plain,
( ( ! [SX0: set_real,SX1: set_real,SX2: real > real > $o] :
( ~ ~ ( finite_finite_real @ SX0 )
| ~ ( finite_finite_real @ SX1 )
| ~ ! [SX3: real] :
( ~ ( member_real @ SX3 @ SX0 )
| ~ ! [SX4: real] :
~ ~ ( ~ ( member_real @ SX4 @ SX1 )
| ~ ( SX2 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: real] :
~ ~ ( ~ ( member_real @ SX3 @ SX1 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SX4: real] :
~ ( ~ ( member_real @ SX4 @ SX0 )
| ~ ( SX2 @ SX4 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(409,plain,
( ( ! [SX0: real > $o,SX1: real > $o] :
( ~ ! [SX2: real] :
( ( SX0 @ SX2 )
= ( SX1 @ SX2 ) )
| ( ( collect_real @ SX0 )
= ( collect_real @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(410,plain,
( ( p != zero_zero_poly_real )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(411,plain,
( ( ! [SX0: real,SX1: real,SX2: poly_real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SX2 @ SX0 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SX2 @ SX1 ) @ zero_zero_real )
| ~ ! [SX3: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SX0 @ SX3 )
| ~ ( ord_less_real @ SX3 @ SX1 ) )
| ( ( poly_real2 @ SX2 @ SX3 )
!= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(412,plain,
( ( ! [SX0: real] :
( ~ ( dvd_dvd_real @ zero_zero_real @ SX0 )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(413,plain,
! [SV1: real] :
( ( ( poly_real2 @ zero_zero_poly_real @ SV1 )
= zero_zero_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(414,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= ( SV2 = zero_zero_poly_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(415,plain,
! [SV3: poly_real] :
( ( ! [SY45: poly_real] :
( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SY45 ) )
= ( SV3 = SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(416,plain,
! [SV4: real] :
( ( ( zero_zero_real = SV4 )
= ( SV4 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(417,plain,
! [SV5: real] :
( ( ! [SY46: real > $o] :
( ( member_real @ SV5 @ ( collect_real @ SY46 ) )
= ( SY46 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(418,plain,
! [SV6: set_real] :
( ( ( collect_real
@ ^ [SY47: real] : ( member_real @ SY47 @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(419,plain,
( ( finite_finite_real @ field_1537545994s_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(420,plain,
! [SV7: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= ( SV7 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(421,plain,
! [SV8: real] :
( ( dvd_dvd_real @ SV8 @ zero_zero_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(422,plain,
( ( finite_finite_real
@ ( collect_real
@ ^ [X: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ X )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV9: real > $o] :
( ( ~ ~ ( finite_finite_real @ ( collect_real @ SV9 ) )
| ~ ! [SY48: real] :
~ ( SV9 @ SY48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(424,plain,
( ( ( pderiv_real @ p )
= zero_zero_poly_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV10: real] :
( ( ! [SY49: real,SY50: poly_real] :
( ~ ( ord_less_real @ SV10 @ SY49 )
| ~ ( ord_less_real @ ( poly_real2 @ SY50 @ SV10 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SY50 @ SY49 ) )
| ~ ! [SY51: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY51 )
| ~ ( ord_less_real @ SY51 @ SY49 ) )
| ( ( poly_real2 @ SY50 @ SY51 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(426,plain,
( ( zero_zero_real = one_one_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV11: real > $o] :
( ( ! [SY52: real > $o] :
( ~ ( ( finite_finite_real @ ( collect_real @ SV11 ) )
| ( finite_finite_real @ ( collect_real @ SY52 ) ) )
| ( finite_finite_real
@ ( collect_real
@ ^ [SY53: real] :
~ ( ~ ( SV11 @ SY53 )
| ~ ( SY52 @ SY53 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(428,plain,
( ( ! [SV12: poly_real] :
( ( rsquarefree_real @ SV12 )
= ( ! [SY54: real] :
~ ~ ( ( ( poly_real2 @ SV12 @ SY54 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV12 ) @ SY54 )
!= zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[405]) ).
thf(429,plain,
( ( rsquarefree_real
= ( ^ [SX0: poly_real] :
! [SX1: real] :
~ ~ ( ( ( poly_real2 @ SX0 @ SX1 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SX0 ) @ SX1 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[405]) ).
thf(430,plain,
! [SV13: real > $o] :
( ( ! [SY55: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [SY56: real] :
( ( SV13 @ SY56 )
| ( SY55 @ SY56 ) ) ) )
= ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SY55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(431,plain,
! [SV14: poly_real] :
( ( ~ ( ( SV14 != zero_zero_poly_real ) )
| ( finite_finite_real
@ ( collect_real
@ ^ [SY57: real] :
( ( poly_real2 @ SV14 @ SY57 )
= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(432,plain,
! [SV15: set_real] :
( ( ! [SY58: set_real,SY59: real > real > $o] :
( ~ ~ ( finite_finite_real @ SV15 )
| ~ ( finite_finite_real @ SY58 )
| ~ ! [SY60: real] :
( ~ ( member_real @ SY60 @ SV15 )
| ~ ! [SX4: real] :
~ ~ ( ~ ( member_real @ SX4 @ SY58 )
| ~ ( SY59 @ SY60 @ SX4 ) ) )
| ~ ! [SY62: real] :
~ ~ ( ~ ( member_real @ SY62 @ SY58 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY63: real] :
~ ( ~ ( member_real @ SY63 @ SV15 )
| ~ ( SY59 @ SY63 @ SY62 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(433,plain,
! [SV16: real > $o] :
( ( ! [SY64: real > $o] :
( ~ ! [SY65: real] :
( ( SV16 @ SY65 )
= ( SY64 @ SY65 ) )
| ( ( collect_real @ SV16 )
= ( collect_real @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(434,plain,
( ( p = zero_zero_poly_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(435,plain,
! [SV17: real] :
( ( ! [SY66: real,SY67: poly_real] :
( ~ ( ord_less_real @ SV17 @ SY66 )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SY67 @ SV17 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SY67 @ SY66 ) @ zero_zero_real )
| ~ ! [SY68: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY68 )
| ~ ( ord_less_real @ SY68 @ SY66 ) )
| ( ( poly_real2 @ SY67 @ SY68 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(436,plain,
! [SV18: real] :
( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV18 )
| ( SV18 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(437,plain,
! [SV2: poly_real] :
( ( ~ ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 = zero_zero_poly_real ) )
| ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[414]) ).
thf(438,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= ( SV2 = zero_zero_poly_real ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[414]) ).
thf(439,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= ( SV3 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(440,plain,
! [SV4: real] :
( ( ~ ( ( zero_zero_real = SV4 )
| ( SV4 = zero_zero_real ) )
| ~ ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[416]) ).
thf(441,plain,
! [SV4: real] :
( ( ( zero_zero_real = SV4 )
= ( SV4 = zero_zero_real ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[416]) ).
thf(442,plain,
! [SV20: real > $o,SV5: real] :
( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= ( SV20 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(443,plain,
! [SV7: real] :
( ( ~ ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 = zero_zero_real ) )
| ~ ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(444,plain,
! [SV7: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= ( SV7 = zero_zero_real ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(445,plain,
! [SV9: real > $o] :
( ( ( ~ ~ ( finite_finite_real @ ( collect_real @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY48: real] :
~ ( SV9 @ SY48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(446,plain,
! [SV21: real,SV10: real] :
( ( ! [SY69: poly_real] :
( ~ ( ord_less_real @ SV10 @ SV21 )
| ~ ( ord_less_real @ ( poly_real2 @ SY69 @ SV10 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SY69 @ SV21 ) )
| ~ ! [SY70: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY70 )
| ~ ( ord_less_real @ SY70 @ SV21 ) )
| ( ( poly_real2 @ SY69 @ SY70 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(447,plain,
! [SV22: real > $o,SV11: real > $o] :
( ( ~ ( ( finite_finite_real @ ( collect_real @ SV11 ) )
| ( finite_finite_real @ ( collect_real @ SV22 ) ) )
| ( finite_finite_real
@ ( collect_real
@ ^ [SY71: real] :
~ ( ~ ( SV11 @ SY71 )
| ~ ( SV22 @ SY71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(448,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(449,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(450,plain,
! [SV14: poly_real] :
( ( ( ~ ( ( SV14 != zero_zero_poly_real ) ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY57: real] :
( ( poly_real2 @ SV14 @ SY57 )
= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(451,plain,
! [SV25: set_real,SV15: set_real] :
( ( ! [SY74: real > real > $o] :
( ~ ~ ( finite_finite_real @ SV15 )
| ~ ( finite_finite_real @ SV25 )
| ~ ! [SY75: real] :
( ~ ( member_real @ SY75 @ SV15 )
| ~ ! [SY76: real] :
~ ~ ( ~ ( member_real @ SY76 @ SV25 )
| ~ ( SY74 @ SY75 @ SY76 ) ) )
| ~ ! [SY77: real] :
~ ~ ( ~ ( member_real @ SY77 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY63: real] :
~ ( ~ ( member_real @ SY63 @ SV15 )
| ~ ( SY74 @ SY63 @ SY77 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(452,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ~ ! [SY79: real] :
( ( SV16 @ SY79 )
= ( SV26 @ SY79 ) )
| ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(453,plain,
! [SV27: real,SV17: real] :
( ( ! [SY80: poly_real] :
( ~ ( ord_less_real @ SV17 @ SV27 )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SY80 @ SV17 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SY80 @ SV27 ) @ zero_zero_real )
| ~ ! [SY81: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY81 )
| ~ ( ord_less_real @ SY81 @ SV27 ) )
| ( ( poly_real2 @ SY80 @ SY81 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(454,plain,
! [SV18: real] :
( ( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV18 ) )
= $true )
| ( ( SV18 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(455,plain,
! [SV2: poly_real] :
( ( ( ~ ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 = zero_zero_poly_real ) ) )
= $true )
| ( ( ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(456,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ~ ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
| ( SV3 = SV19 ) )
| ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= ( SV3 = SV19 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[439]) ).
thf(458,plain,
! [SV4: real] :
( ( ( ~ ( ( zero_zero_real = SV4 )
| ( SV4 = zero_zero_real ) ) )
= $true )
| ( ( ~ ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(459,plain,
! [SV20: real > $o,SV5: real] :
( ( ~ ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ( SV20 @ SV5 ) )
| ~ ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[442]) ).
thf(460,plain,
! [SV20: real > $o,SV5: real] :
( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= ( SV20 @ SV5 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[442]) ).
thf(461,plain,
! [SV7: real] :
( ( ( ~ ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 = zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(462,plain,
! [SV9: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY48: real] :
~ ( SV9 @ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(463,plain,
! [SV28: poly_real,SV21: real,SV10: real] :
( ( ~ ( ord_less_real @ SV10 @ SV21 )
| ~ ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
| ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(464,plain,
! [SV22: real > $o,SV11: real > $o] :
( ( ( ~ ( ( finite_finite_real @ ( collect_real @ SV11 ) )
| ( finite_finite_real @ ( collect_real @ SV22 ) ) ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY71: real] :
~ ( ~ ( SV11 @ SY71 )
| ~ ( SV22 @ SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(465,plain,
! [SV23: poly_real] :
( ( ~ ( ( rsquarefree_real @ SV23 )
| ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
| ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[448]) ).
thf(466,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[448]) ).
thf(467,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ~ ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
| ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[449]) ).
thf(468,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[449]) ).
thf(469,plain,
! [SV14: poly_real] :
( ( ( SV14 != zero_zero_poly_real )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY57: real] :
( ( poly_real2 @ SV14 @ SY57 )
= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(470,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ~ ~ ( finite_finite_real @ SV15 )
| ~ ( finite_finite_real @ SV25 )
| ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(471,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ! [SY79: real] :
( ( SV16 @ SY79 )
= ( SV26 @ SY79 ) ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(472,plain,
! [SV30: poly_real,SV27: real,SV17: real] :
( ( ~ ( ord_less_real @ SV17 @ SV27 )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
| ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(473,plain,
! [SV18: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV18 )
= $false )
| ( ( SV18 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(474,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 = zero_zero_poly_real ) )
= $false )
| ( ( ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(475,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ~ ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
| ( SV3 = SV19 ) ) )
= $true )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(476,plain,
! [SV4: real] :
( ( ( ( zero_zero_real = SV4 )
| ( SV4 = zero_zero_real ) )
= $false )
| ( ( ~ ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(477,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ~ ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ( SV20 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(478,plain,
! [SV7: real] :
( ( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 = zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(479,plain,
! [SV9: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV9 ) )
= $true )
| ( ( ~ ! [SY48: real] :
~ ( SV9 @ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(480,plain,
! [SV28: poly_real,SV21: real,SV10: real] :
( ( ( ~ ( ord_less_real @ SV10 @ SV21 ) )
= $true )
| ( ( ~ ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
| ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(481,plain,
! [SV22: real > $o,SV11: real > $o] :
( ( ( ( finite_finite_real @ ( collect_real @ SV11 ) )
| ( finite_finite_real @ ( collect_real @ SV22 ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY71: real] :
~ ( ~ ( SV11 @ SY71 )
| ~ ( SV22 @ SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(482,plain,
! [SV23: poly_real] :
( ( ( ~ ( ( rsquarefree_real @ SV23 )
| ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(483,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(484,plain,
! [SV14: poly_real] :
( ( ( SV14 = zero_zero_poly_real )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY57: real] :
( ( poly_real2 @ SV14 @ SY57 )
= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(485,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ( ~ ~ ( finite_finite_real @ SV15 ) )
= $true )
| ( ( ~ ( finite_finite_real @ SV25 )
| ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(486,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ! [SY79: real] :
( ( SV16 @ SY79 )
= ( SV26 @ SY79 ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(487,plain,
! [SV30: poly_real,SV27: real,SV17: real] :
( ( ( ~ ( ord_less_real @ SV17 @ SV27 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
| ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(488,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(489,plain,
! [SV2: poly_real] :
( ( ( SV2 = zero_zero_poly_real )
= $false )
| ( ( ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(490,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
| ( SV3 = SV19 ) )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(491,plain,
! [SV4: real] :
( ( ( zero_zero_real = SV4 )
= $false )
| ( ( ~ ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(492,plain,
! [SV4: real] :
( ( ( SV4 = zero_zero_real )
= $false )
| ( ( ~ ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(493,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ( SV20 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(494,plain,
! [SV7: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false )
| ( ( ~ ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(495,plain,
! [SV7: real] :
( ( ( SV7 = zero_zero_real )
= $false )
| ( ( ~ ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(496,plain,
! [SV9: real > $o] :
( ( ( ! [SY48: real] :
~ ( SV9 @ SY48 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(497,plain,
! [SV28: poly_real,SV21: real,SV10: real] :
( ( ( ord_less_real @ SV10 @ SV21 )
= $false )
| ( ( ~ ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
| ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(498,plain,
! [SV22: real > $o,SV11: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV11 ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY71: real] :
~ ( ~ ( SV11 @ SY71 )
| ~ ( SV22 @ SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(499,plain,
! [SV11: real > $o,SV22: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV22 ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY71: real] :
~ ( ~ ( SV11 @ SY71 )
| ~ ( SV22 @ SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(500,plain,
! [SV23: poly_real] :
( ( ( ( rsquarefree_real @ SV23 )
| ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(501,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(502,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ( ~ ( finite_finite_real @ SV15 ) )
= $false )
| ( ( ~ ( finite_finite_real @ SV25 )
| ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(503,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[486]) ).
thf(504,plain,
! [SV30: poly_real,SV27: real,SV17: real] :
( ( ( ord_less_real @ SV17 @ SV27 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
| ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
| ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(505,plain,
! [SV2: poly_real] :
( ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false )
| ( ( ~ ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[488]) ).
thf(506,plain,
! [SV2: poly_real] :
( ( ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) )
= $false )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(507,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(508,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 = SV19 )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(509,plain,
! [SV4: real] :
( ( ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) )
= $false )
| ( ( zero_zero_real = SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(510,plain,
! [SV4: real] :
( ( ( ( zero_zero_real != SV4 )
| ( SV4 != zero_zero_real ) )
= $false )
| ( ( SV4 = zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(511,plain,
! [SV20: real > $o,SV5: real] :
( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false )
| ( ( ~ ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(512,plain,
! [SV5: real,SV20: real > $o] :
( ( ( SV20 @ SV5 )
= $false )
| ( ( ~ ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(513,plain,
! [SV7: real] :
( ( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) )
= $false )
| ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(514,plain,
! [SV7: real] :
( ( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 )
| ( SV7 != zero_zero_real ) )
= $false )
| ( ( SV7 = zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(515,plain,
! [SV9: real > $o] :
( ( ( ~ ( SV9 @ ( sK3_SY48 @ SV9 ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[496]) ).
thf(516,plain,
! [SV21: real,SV10: real,SV28: poly_real] :
( ( ( ~ ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
| ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(517,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(518,plain,
! [SV23: poly_real] :
( ( ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(519,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(520,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(521,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ( finite_finite_real @ SV15 )
= $true )
| ( ( ~ ( finite_finite_real @ SV25 )
| ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(522,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
| ~ ( ~ ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ~ ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[503]) ).
thf(523,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[503]) ).
thf(524,plain,
! [SV27: real,SV17: real,SV30: poly_real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) ) )
= $true )
| ( ( ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
| ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(525,plain,
! [SV2: poly_real] :
( ( ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real )
| ( SV2 != zero_zero_poly_real ) )
= $false )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(526,plain,
! [SV2: poly_real] :
( ( ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= $false )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(527,plain,
! [SV2: poly_real] :
( ( ( SV2 != zero_zero_poly_real )
= $false )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(528,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ! [SV31: real] :
( ( poly_real2 @ SV3 @ SV31 )
= ( poly_real2 @ SV19 @ SV31 ) ) )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[507]) ).
thf(529,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[507]) ).
thf(530,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) )
= $false )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(531,plain,
! [SV4: real] :
( ( ( zero_zero_real != SV4 )
= $false )
| ( ( zero_zero_real = SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(532,plain,
! [SV4: real] :
( ( ( SV4 != zero_zero_real )
= $false )
| ( ( zero_zero_real = SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(533,plain,
! [SV4: real] :
( ( ( zero_zero_real != SV4 )
= $false )
| ( ( SV4 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(534,plain,
! [SV4: real] :
( ( ( SV4 != zero_zero_real )
= $false )
| ( ( SV4 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(535,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) )
= $false )
| ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(536,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) )
| ~ ( SV20 @ SV5 ) )
= $false )
| ( ( SV20 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(537,plain,
! [SV7: real] :
( ( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 ) )
= $false )
| ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(538,plain,
! [SV7: real] :
( ( ( SV7 != zero_zero_real )
= $false )
| ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(539,plain,
! [SV7: real] :
( ( ( ~ ( dvd_dvd_real @ zero_zero_real @ SV7 ) )
= $false )
| ( ( SV7 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(540,plain,
! [SV7: real] :
( ( ( SV7 != zero_zero_real )
= $false )
| ( ( SV7 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(541,plain,
! [SV9: real > $o] :
( ( ( SV9 @ ( sK3_SY48 @ SV9 ) )
= $true )
| ( ( finite_finite_real @ ( collect_real @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(542,plain,
! [SV21: real,SV10: real,SV28: poly_real] :
( ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
| ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(543,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(544,plain,
! [SV23: poly_real] :
( ( ( ~ ~ ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[518]) ).
thf(545,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(546,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(547,plain,
! [SV29: real > real > $o,SV15: set_real,SV25: set_real] :
( ( ( ~ ( finite_finite_real @ SV25 ) )
= $true )
| ( ( ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(548,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(549,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ~ ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(550,plain,
! [SV27: real,SV17: real,SV30: poly_real] :
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
| ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(551,plain,
! [SV2: poly_real] :
( ( ( ~ ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= $false )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(552,plain,
! [SV2: poly_real] :
( ( ( SV2 != zero_zero_poly_real )
= $false )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(553,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= $true )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(554,plain,
! [SV2: poly_real] :
( ( ( SV2 = zero_zero_poly_real )
= $true )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(555,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false )
| ( ( ~ ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[528]) ).
thf(556,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) )
= $false )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(557,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
= $false )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(558,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 != SV19 )
= $false )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(559,plain,
! [SV4: real] :
( ( ( zero_zero_real = SV4 )
= $true )
| ( ( zero_zero_real = SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(560,plain,
! [SV4: real] :
( ( ( SV4 = zero_zero_real )
= $true )
| ( ( zero_zero_real = SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(561,plain,
! [SV4: real] :
( ( ( zero_zero_real = SV4 )
= $true )
| ( ( SV4 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(562,plain,
! [SV4: real] :
( ( ( SV4 = zero_zero_real )
= $true )
| ( ( SV4 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(563,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) ) )
= $false )
| ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(564,plain,
! [SV5: real,SV20: real > $o] :
( ( ( ~ ( SV20 @ SV5 ) )
= $false )
| ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(565,plain,
! [SV20: real > $o,SV5: real] :
( ( ( ~ ( member_real @ SV5 @ ( collect_real @ SV20 ) ) )
= $false )
| ( ( SV20 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(566,plain,
! [SV5: real,SV20: real > $o] :
( ( ( ~ ( SV20 @ SV5 ) )
= $false )
| ( ( SV20 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(567,plain,
! [SV7: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $true )
| ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(568,plain,
! [SV7: real] :
( ( ( SV7 = zero_zero_real )
= $true )
| ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(569,plain,
! [SV7: real] :
( ( ( dvd_dvd_real @ zero_zero_real @ SV7 )
= $true )
| ( ( SV7 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(570,plain,
! [SV7: real] :
( ( ( SV7 = zero_zero_real )
= $true )
| ( ( SV7 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(571,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) ) )
= $true )
| ( ( ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(572,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 ) )
= $false )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(573,plain,
! [SV23: poly_real] :
( ( ( ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(574,plain,
! [SV23: poly_real] :
( ( ( ~ ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(575,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(576,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(577,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) ) )
= $true )
| ( ( ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(578,plain,
! [SV29: real > real > $o,SV15: set_real,SV25: set_real] :
( ( ( finite_finite_real @ SV25 )
= $false )
| ( ( ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(579,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(580,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
| ~ ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(581,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ~ ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real ) )
= $true )
| ( ( ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(582,plain,
! [SV2: poly_real] :
( ( ( ! [SY44: real] :
( ( poly_real2 @ SV2 @ SY44 )
= zero_zero_real ) )
= $true )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(583,plain,
! [SV2: poly_real] :
( ( ( SV2 = zero_zero_poly_real )
= $true )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(584,plain,
! [SV32: real,SV2: poly_real] :
( ( ( ( poly_real2 @ SV2 @ SV32 )
= zero_zero_real )
= $true )
| ( ( SV2 = zero_zero_poly_real )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(585,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
| ( SV3 != SV19 ) )
= $false )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(586,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
= $false )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(587,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 != SV19 )
= $false )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(588,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(589,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 = SV19 )
= $true )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(590,plain,
! [SV20: real > $o,SV5: real] :
( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $true )
| ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(591,plain,
! [SV5: real,SV20: real > $o] :
( ( ( SV20 @ SV5 )
= $true )
| ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(592,plain,
! [SV20: real > $o,SV5: real] :
( ( ( member_real @ SV5 @ ( collect_real @ SV20 ) )
= $true )
| ( ( SV20 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(593,plain,
! [SV5: real,SV20: real > $o] :
( ( ( SV20 @ SV5 )
= $true )
| ( ( SV20 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(594,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ~ ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(595,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(596,plain,
! [SV23: poly_real] :
( ( ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(597,plain,
! [SV23: poly_real] :
( ( ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(598,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(599,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(600,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(601,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ( ~ ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(602,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= $true )
| ( ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(603,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( ~ ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $true )
| ( ( ~ ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(604,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ~ ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(605,plain,
! [SV33: real,SV2: poly_real] :
( ( ( ( poly_real2 @ SV2 @ SV33 )
= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ SV2 @ ( sK2_SY44 @ SV2 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(606,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
!= ( poly_real2 @ SV19 ) )
= $false )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(607,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 != SV19 )
= $false )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(608,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(609,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 = SV19 )
= $true )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(610,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ! [SV34: real] :
( ( poly_real2 @ SV3 @ SV34 )
= ( poly_real2 @ SV19 @ SV34 ) ) )
= $true )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(611,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(612,plain,
! [SV28: poly_real,SV21: real,SV10: real] :
( ( ( ! [SY82: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ SY82 )
| ~ ( ord_less_real @ SY82 @ SV21 ) )
| ( ( poly_real2 @ SV28 @ SY82 )
!= zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(613,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ~ ~ ( ( ( poly_real2 @ SV23 @ SV35 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
!= zero_zero_real ) ) )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(614,plain,
! [SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(615,plain,
! [SV23: poly_real] :
( ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
!= zero_zero_real )
= $false )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(616,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(617,plain,
! [SV13: real > $o,SV24: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(618,plain,
! [SV29: real > real > $o,SV25: set_real,SV15: set_real] :
( ( ( ! [SY83: real] :
( ~ ( member_real @ SY83 @ SV15 )
| ~ ! [SY84: real] :
~ ~ ( ~ ( member_real @ SY84 @ SV25 )
| ~ ( SV29 @ SY83 @ SY84 ) ) ) )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(619,plain,
! [SV26: real > $o,SV16: real > $o] :
( ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= $false )
| ( ( ~ ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) ) )
= $true )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(620,plain,
! [SV30: poly_real,SV27: real,SV17: real] :
( ( ( ! [SY87: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ SY87 )
| ~ ( ord_less_real @ SY87 @ SV27 ) )
| ( ( poly_real2 @ SV30 @ SY87 )
!= zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(621,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(622,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( SV3 = SV19 )
= $true )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(623,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ! [SV36: real] :
( ( poly_real2 @ SV3 @ SV36 )
= ( poly_real2 @ SV19 @ SV36 ) ) )
= $true )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[608]) ).
thf(624,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[608]) ).
thf(625,plain,
! [SV19: poly_real,SV37: real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 @ SV37 )
= ( poly_real2 @ SV19 @ SV37 ) )
= $true )
| ( ( SV3 = SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(626,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) )
| ( ( poly_real2 @ SV28 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
!= zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[612]) ).
thf(627,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ~ ( ( ( poly_real2 @ SV23 @ SV35 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
!= zero_zero_real ) ) )
= $false )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(628,plain,
! [SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(629,plain,
! [SV23: poly_real] :
( ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true )
| ( ( ~ ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(630,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(631,plain,
! [SV13: real > $o,SV24: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $false )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(632,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
| ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(633,plain,
! [SV15: set_real,SV25: set_real,SV29: real > real > $o] :
( ( ( ~ ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
| ~ ! [SY88: real] :
~ ~ ( ~ ( member_real @ SY88 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SY88 ) ) )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[618]) ).
thf(634,plain,
! [SV16: real > $o,SV26: real > $o] :
( ( ( SV26 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= $false )
| ( ( SV16 @ ( sK1_SY79 @ SV26 @ SV16 ) )
= $false )
| ( ( ( collect_real @ SV16 )
= ( collect_real @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(635,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) )
| ( ( poly_real2 @ SV30 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
!= zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[620]) ).
thf(636,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ! [SV38: real] :
( ( poly_real2 @ SV3 @ SV38 )
= ( poly_real2 @ SV19 @ SV38 ) ) )
= $true )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(637,plain,
! [SV19: poly_real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $true )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(638,plain,
! [SV19: poly_real,SV39: real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 @ SV39 )
= ( poly_real2 @ SV19 @ SV39 ) )
= $true )
| ( ( ( poly_real2 @ SV3 )
= ( poly_real2 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(639,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ( ~ ~ ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) )
| ( ( poly_real2 @ SV28 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(640,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ( ( poly_real2 @ SV23 @ SV35 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
!= zero_zero_real ) )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(641,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(642,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 )
| ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(643,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(644,plain,
! [SV13: real > $o,SV24: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $true )
| ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(645,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(646,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(647,plain,
! [SV15: set_real,SV25: set_real,SV29: real > real > $o] :
( ( ( ~ ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(648,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real] :
( ( ( ~ ! [SY88: real] :
~ ~ ( ~ ( member_real @ SY88 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SY88 ) ) )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(649,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ( ~ ~ ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) )
| ( ( poly_real2 @ SV30 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
!= zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(650,plain,
! [SV19: poly_real,SV40: real,SV3: poly_real] :
( ( ( ( poly_real2 @ SV3 @ SV40 )
= ( poly_real2 @ SV19 @ SV40 ) )
= $true )
| ( ( ( poly_real2 @ SV3 @ ( sK5_SV31 @ SV19 @ SV3 ) )
= ( poly_real2 @ SV19 @ ( sK5_SV31 @ SV19 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(651,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) )
| ( ( poly_real2 @ SV28 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
!= zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(652,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV35 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
!= zero_zero_real )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(653,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 ) )
= $false )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(654,plain,
! [SV23: poly_real] :
( ( ( ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(655,plain,
! [SV23: poly_real] :
( ( ( ~ ( rsquarefree_real @ SV23 ) )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(656,plain,
! [SV23: poly_real] :
( ( ( ~ ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(657,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY73: real] :
( ( SV13 @ SY73 )
| ( SV24 @ SY73 ) ) ) )
= $true )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(658,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) ) )
= $true )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(659,plain,
! [SV15: set_real,SV25: set_real,SV29: real > real > $o] :
( ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(660,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real] :
( ( ( ! [SY88: real] :
~ ~ ( ~ ( member_real @ SY88 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SY88 ) ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(661,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) )
| ( ( poly_real2 @ SV30 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
!= zero_zero_real ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(662,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(663,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ( poly_real2 @ SV28 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
!= zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(664,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV35 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
!= zero_zero_real )
= $true )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(665,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(666,plain,
! [SV23: poly_real] :
( ( ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(667,plain,
! [SV23: poly_real] :
( ( ( rsquarefree_real @ SV23 )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(668,plain,
! [SV23: poly_real] :
( ( ( ! [SY72: real] :
~ ~ ( ( ( poly_real2 @ SV23 @ SY72 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SY72 )
!= zero_zero_real ) ) )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(669,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) )
| ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(670,plain,
! [SV29: real > real > $o,SV15: set_real,SV25: set_real] :
( ( ( ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(671,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real,SV41: real] :
( ( ( ~ ~ ( ~ ( member_real @ SV41 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 ) ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(672,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(673,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ( poly_real2 @ SV30 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
!= zero_zero_real )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(674,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(675,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ( poly_real2 @ SV28 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
= zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(676,plain,
! [SV35: real,SV23: poly_real] :
( ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV35 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ SV23 @ SV35 )
= zero_zero_real )
= $false )
| ( ( rsquarefree_real @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(677,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ~ ~ ( ( ( poly_real2 @ SV23 @ SV42 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
!= zero_zero_real ) ) )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(678,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ~ ~ ( ( ( poly_real2 @ SV23 @ SV43 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
!= zero_zero_real ) ) )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(679,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV13 ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(680,plain,
! [SV13: real > $o,SV24: real > $o] :
( ( ( ~ ( finite_finite_real @ ( collect_real @ SV24 ) ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(681,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o] :
( ( ( ~ ~ ( ~ ( member_real @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) ) ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[670]) ).
thf(682,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real,SV41: real] :
( ( ( ~ ( ~ ( member_real @ SV41 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 ) ) )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(683,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) ) )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(684,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ( poly_real2 @ SV30 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
= zero_zero_real )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(685,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
| ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(686,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ~ ( ( ( poly_real2 @ SV23 @ SV42 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(687,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ~ ( ( ( poly_real2 @ SV23 @ SV43 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
!= zero_zero_real ) ) )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(688,plain,
! [SV24: real > $o,SV13: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $true )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(689,plain,
! [SV13: real > $o,SV24: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $true )
| ( ( finite_finite_real @ ( collect_real @ SV13 ) )
= $false )
| ( ( finite_finite_real @ ( collect_real @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(690,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o] :
( ( ( ~ ( ~ ( member_real @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) ) ) )
= $true )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(691,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real,SV41: real] :
( ( ( ~ ( member_real @ SV41 @ SV25 )
| ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(692,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
| ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(693,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ~ ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(694,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ~ ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(695,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ( ( poly_real2 @ SV23 @ SV42 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
!= zero_zero_real ) )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(696,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ( ( poly_real2 @ SV23 @ SV43 )
!= zero_zero_real )
| ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
!= zero_zero_real ) )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(697,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o] :
( ( ( ~ ( member_real @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(698,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real,SV41: real] :
( ( ( ~ ( member_real @ SV41 @ SV25 ) )
= $true )
| ( ( ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(699,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ~ ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(700,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ~ ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(701,plain,
! [SV21: real,SV28: poly_real,SV10: real] :
( ( ( ord_less_real @ SV10 @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(702,plain,
! [SV10: real,SV21: real,SV28: poly_real] :
( ( ( ord_less_real @ ( sK6_SY82 @ SV28 @ SV21 @ SV10 ) @ SV21 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV28 @ SV21 ) )
= $false )
| ( ( ord_less_real @ ( poly_real2 @ SV28 @ SV10 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(703,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV42 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(704,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV43 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(705,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o] :
( ( ( ~ ( member_real @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) @ SV25 ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(706,plain,
! [SV25: set_real,SV29: real > real > $o,SV15: set_real] :
( ( ( ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(707,plain,
! [SV15: set_real,SV29: real > real > $o,SV25: set_real,SV41: real] :
( ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( ~ ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 ) )
= $true )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(708,plain,
! [SV27: real,SV30: poly_real,SV17: real] :
( ( ( ord_less_real @ SV17 @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(709,plain,
! [SV17: real,SV27: real,SV30: poly_real] :
( ( ( ord_less_real @ ( sK8_SY87 @ SV30 @ SV27 @ SV17 ) @ SV27 )
= $true )
| ( ( ord_less_real @ ( poly_real2 @ SV30 @ SV27 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ SV30 @ SV17 ) )
= $false )
| ( ( ord_less_real @ SV17 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[700]) ).
thf(710,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV42 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(711,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ( poly_real2 @ SV23 @ SV43 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
!= zero_zero_real )
= $true )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(712,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o] :
( ( ( member_real @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) @ SV25 )
= $true )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(713,plain,
! [SV25: set_real,SV29: real > real > $o,SV15: set_real] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $true )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(714,plain,
! [SV41: real,SV15: set_real,SV25: set_real,SV29: real > real > $o] :
( ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( ~ ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(715,plain,
! [SV42: real,SV23: poly_real] :
( ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV42 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ SV23 @ SV42 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ SV23 @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(716,plain,
! [SV43: real,SV23: poly_real] :
( ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ SV43 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ SV23 @ SV43 )
= zero_zero_real )
= $false )
| ( ( ( poly_real2 @ ( pderiv_real @ SV23 ) @ ( sK4_SY72 @ SV23 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(717,plain,
! [SV25: set_real,SV29: real > real > $o,SV15: set_real] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY89: real] :
~ ( ~ ( member_real @ SY89 @ SV15 )
| ~ ( SV29 @ SY89 @ ( sK9_SY85 @ SV29 @ SV15 @ SV25 ) ) ) ) )
= $false )
| ( ( member_real @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV15 )
= $true )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(718,plain,
! [SV41: real,SV29: real > real > $o,SV15: set_real,SV25: set_real] :
( ( ( ! [SY85: real] :
~ ~ ( ~ ( member_real @ SY85 @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY86: real] :
~ ( ~ ( member_real @ SY86 @ SV15 )
| ~ ( SV29 @ SY86 @ SY85 ) ) ) ) ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(719,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o,SV41: real] :
( ( ( ~ ~ ( ~ ( member_real @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) ) ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[718]) ).
thf(720,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o,SV41: real] :
( ( ( ~ ( ~ ( member_real @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) ) ) )
= $true )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(721,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o,SV41: real] :
( ( ( ~ ( member_real @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) @ SV25 )
| ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(722,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o,SV41: real] :
( ( ( ~ ( member_real @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) @ SV25 ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(723,plain,
! [SV25: set_real,SV41: real,SV29: real > real > $o,SV15: set_real] :
( ( ( ~ ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(724,plain,
! [SV25: set_real,SV15: set_real,SV29: real > real > $o,SV41: real] :
( ( ( member_real @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) @ SV25 )
= $true )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(725,plain,
! [SV25: set_real,SV41: real,SV29: real > real > $o,SV15: set_real] :
( ( ( ~ ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) ) )
= $true )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(726,plain,
! [SV25: set_real,SV41: real,SV29: real > real > $o,SV15: set_real] :
( ( ( finite_finite_real
@ ( collect_real
@ ^ [SY90: real] :
~ ( ~ ( member_real @ SY90 @ SV15 )
| ~ ( SV29 @ SY90 @ ( sK10_SY85 @ SV41 @ SV29 @ SV15 @ SV25 ) ) ) ) )
= $false )
| ( ( member_real @ SV41 @ SV25 )
= $false )
| ( ( SV29 @ ( sK7_SY83 @ SV29 @ SV25 @ SV15 ) @ SV41 )
= $false )
| ( ( finite_finite_real @ SV25 )
= $false )
| ( ( finite_finite_real @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(727,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[377,726,724,717,716,715,712,709,708,702,701,689,688,684,676,675,667,665,657,650,644,643,638,637,634,625,624,622,611,609,605,602,598,595,593,592,591,590,589,584,583,570,569,568,567,562,561,560,559,554,541,523,499,498,484,473,468,466,460,457,444,441,438,434,429,426,424,422,421,419,418,413,396,386]) ).
thf(728,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[727]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP094^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 11:17:20 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.24/1.02 ..
% 4.24/1.02
% 4.24/1.02 No.of.Axioms: 25
% 4.24/1.02
% 4.24/1.02 Length.of.Defs: 0
% 4.24/1.02
% 4.24/1.02 Contains.Choice.Funs: false
% 4.24/1.02 ............
% 4.24/1.02
% 4.24/1.02 ********************************
% 4.24/1.02 * All subproblems solved! *
% 4.24/1.02 ********************************
% 4.24/1.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:25,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:727,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.24/1.02
% 4.24/1.02 %**** Beginning of derivation protocol ****
% 4.24/1.02 % SZS output start CNFRefutation
% See solution above
% 4.24/1.03
% 4.24/1.03 %**** End of derivation protocol ****
% 4.24/1.03 %**** no. of clauses in derivation: 409 ****
% 4.24/1.03 %**** clause counter: 727 ****
% 4.24/1.03
% 4.24/1.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:25,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:727,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------