TSTP Solution File: ITP040^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP040^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 04:01:41 EDT 2023
% Result : Theorem 0.96s 1.14s
% Output : Proof 0.98s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_real,type,
set_real: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_finite1398487019real_c,type,
finite1398487019real_c: $tType ).
thf(ty_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(ty_set_Pr1389752855real_c,type,
set_Pr1389752855real_c: $tType ).
thf(ty_sum_sum_c_c,type,
sum_sum_c_c: $tType ).
thf(ty_set_c,type,
set_c: $tType ).
thf(ty_formula_a_b_c,type,
formula_a_b_c: $tType ).
thf(ty_set_Fi1407883041real_c,type,
set_Fi1407883041real_c: $tType ).
thf(ty_set_Sum_sum_c_c,type,
set_Sum_sum_c_c: $tType ).
thf(ty_oDE_a_c,type,
oDE_a_c: $tType ).
thf(ty_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(ty_bb,type,
bb: finite1398487019real_c ).
thf(ty_denota1275485728_a_b_c,type,
denota1275485728_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > finite1398487019real_c ).
thf(ty_if_real,type,
if_real: $o > real > real > real ).
thf(ty_t,type,
t: real ).
thf(ty_finite772340578real_c,type,
finite772340578real_c: finite1398487019real_c > c > real ).
thf(ty_static_FVF_a_b_c,type,
static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
thf(ty_denota1896987029_a_b_c,type,
denota1896987029_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_denota161327353_a_b_c,type,
denota161327353_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_i2,type,
i2: c ).
thf(ty_denota256060419gree_c,type,
denota256060419gree_c: finite1398487019real_c > finite1398487019real_c > set_c > $o ).
thf(ty_member_Sum_sum_c_c,type,
member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
thf(ty_denota1293057250_a_b_c,type,
denota1293057250_a_b_c: denota231621370t_unit > oDE_a_c > set_Sum_sum_c_c ).
thf(ty_ba,type,
ba: finite1398487019real_c ).
thf(ty_p,type,
p: formula_a_b_c ).
thf(ty_uminus1381786404um_c_c,type,
uminus1381786404um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(ty_collec230941376real_c,type,
collec230941376real_c: ( finite1398487019real_c > $o ) > set_Fi1407883041real_c ).
thf(ty_x,type,
x: real ).
thf(ty_aa,type,
aa: finite1398487019real_c ).
thf(ty_phi,type,
phi: formula_a_b_c ).
thf(ty_initia1631504802real_c,type,
initia1631504802real_c: ( real > finite1398487019real_c ) > ( real > finite1398487019real_c > finite1398487019real_c ) > set_real > set_Fi1407883041real_c > $o ).
thf(ty_sum_Inl_c_c,type,
sum_Inl_c_c: c > sum_sum_c_c ).
thf(ty_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(ty_collect_c,type,
collect_c: ( c > $o ) > set_c ).
thf(ty_static_FVO_a_c,type,
static_FVO_a_c: oDE_a_c > set_c ).
thf(ty_osafe_a_c,type,
osafe_a_c: oDE_a_c > $o ).
thf(ty_member1895684704real_c,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(ty_member_c,type,
member_c: c > set_c > $o ).
thf(ty_denota968303861_a_b_c,type,
denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
thf(ty_ab,type,
ab: finite1398487019real_c ).
thf(ty_fsafe_a_b_c,type,
fsafe_a_b_c: formula_a_b_c > $o ).
thf(ty_sol,type,
sol: real > finite1398487019real_c ).
thf(ty_static_BVO_a_c,type,
static_BVO_a_c: oDE_a_c > set_Sum_sum_c_c ).
thf(ty_produc2010422875real_c,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(ty_denota540094197_a_b_c,type,
denota540094197_a_b_c: denota231621370t_unit > oDE_a_c > set_c ).
thf(ty_ode,type,
ode: oDE_a_c ).
thf(ty_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(ty_set_or656347191t_real,type,
set_or656347191t_real: real > real > set_real ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_sum_Inr_c_c,type,
sum_Inr_c_c: c > sum_sum_c_c ).
thf(ty_finite557796307c_real,type,
finite557796307c_real: ( c > real ) > finite1398487019real_c ).
thf(ty_oDEa,type,
oDEa: oDE_a_c ).
thf(ty_produc394644079real_c,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_i,type,
i: denota231621370t_unit ).
thf(ty_produc314122909real_c,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(ty_image_c_Sum_sum_c_c,type,
image_c_Sum_sum_c_c: ( c > sum_sum_c_c ) > set_c > set_Sum_sum_c_c ).
thf(sP1,plain,
( sP1
<=> ( member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: oDE_a_c] :
( ( member_c @ i2 @ ( denota540094197_a_b_c @ i @ X1 ) )
=> ( member_c @ i2 @ ( static_FVO_a_c @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: denota231621370t_unit,X2: oDE_a_c] :
( ( member_c @ i2 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
=> ( member_c @ i2 @ ( static_FVO_a_c @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: c,X2: denota231621370t_unit,X3: oDE_a_c] :
( ( member_c @ X1 @ ( denota540094197_a_b_c @ X2 @ X3 ) )
=> ( member_c @ X1 @ ( static_FVO_a_c @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_eq_real @ zero_zero_real @ t ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(conj_11,conjecture,
( ( finite772340578real_c @ ab @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ).
thf(h0,negated_conjecture,
( ( finite772340578real_c @ ab @ i2 )
!= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ),
inference(assume_negation,[status(cth)],[conj_11]) ).
thf(h1,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_0_ode__to__fvo,axiom,
sP5 ).
thf(conj_1,axiom,
sP1 ).
thf(conj_2,axiom,
~ sP7 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h0])],[1,2,3,4,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h5,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ),
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h1,h2,h0])],[6,7,8,9,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h6,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ),
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h4,h4,h1,h2,h0])],[11,12,13,14,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h10,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ),
introduced(assumption,[]) ).
thf(16,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,h6,h7,h4,h4,h1,h2,h0])],[16,17,18,19,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h11,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c
@ ( denota1275485728_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ i2 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c
@ ( denota1275485728_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ i2 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c
@ ( denota1275485728_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ i2 ) ),
introduced(assumption,[]) ).
thf(21,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[21,22,23,24,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(26,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[26,27,28,29,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h14,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ),
introduced(assumption,[]) ).
thf(31,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[31,32,33,34,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h17,assumption,
( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h20,assumption,
( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ),
introduced(assumption,[]) ).
thf(36,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[36,37,38,39,fact_0_ode__to__fvo,conj_1,h19]) ).
thf(h21,assumption,
sP7,
introduced(assumption,[]) ).
thf(h22,assumption,
( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ),
introduced(assumption,[]) ).
thf(41,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h21,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[h21,conj_2]) ).
thf(42,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[42,43,44,45,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(47,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[47,48,49,50,fact_0_ode__to__fvo,conj_1,h19]) ).
thf(52,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h21,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[h21,conj_2]) ).
thf(h23,assumption,
( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ bb @ i2 ) ),
introduced(assumption,[]) ).
thf(53,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[53,54,55,56,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h25,assumption,
( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ bb @ i2 ) ),
introduced(assumption,[]) ).
thf(58,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[58,59,60,61,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h26,assumption,
( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ab @ i2 ) ),
introduced(assumption,[]) ).
thf(63,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[63,64,65,66,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h28,assumption,
~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ),
introduced(assumption,[]) ).
thf(68,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[68,69,70,71,fact_0_ode__to__fvo,conj_1,conj_2]) ).
thf(h29,assumption,
( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ),
introduced(assumption,[]) ).
thf(73,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(77,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[73,74,75,76,fact_0_ode__to__fvo,conj_1,h19]) ).
thf(78,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h21,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[h21,conj_2]) ).
thf(h31,assumption,
~ ( osafe_a_c @ oDEa ),
introduced(assumption,[]) ).
thf(h32,assumption,
( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(79,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[79,80,81,82,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h33,assumption,
~ ( fsafe_a_b_c @ phi ),
introduced(assumption,[]) ).
thf(h34,assumption,
( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(84,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[84,85,86,87,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h35,assumption,
ode != oDEa,
introduced(assumption,[]) ).
thf(h36,assumption,
( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ) ) ),
introduced(assumption,[]) ).
thf(89,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(93,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[89,90,91,92,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h37,assumption,
p != phi,
introduced(assumption,[]) ).
thf(h38,assumption,
( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ) ),
introduced(assumption,[]) ).
thf(94,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(98,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h37,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[94,95,96,97,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h39,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h40,assumption,
( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ),
introduced(assumption,[]) ).
thf(99,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(100,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(101,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(103,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h39,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[99,100,101,102,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h41,assumption,
( ( produc394644079real_c @ aa @ ba )
!= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ),
introduced(assumption,[]) ).
thf(104,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(105,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(107,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(108,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h41,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[104,105,106,107,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h43,assumption,
~ ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ),
introduced(assumption,[]) ).
thf(109,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(111,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(112,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(113,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[109,110,111,112,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h45,assumption,
~ ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
sP6,
introduced(assumption,[]) ).
thf(114,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(116,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(117,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(118,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h45,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[114,115,116,117,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h47,assumption,
( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(119,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(120,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(121,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(122,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(123,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[119,120,121,122,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h48,assumption,
( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(124,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(125,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(126,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(127,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(128,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[124,125,126,127,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h49,assumption,
( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(129,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(130,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(131,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(132,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(133,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[129,130,131,132,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h50,assumption,
( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(134,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(135,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(136,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(137,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(138,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h37,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[134,135,136,137,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h51,assumption,
( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(139,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h39,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[h46,h39]) ).
thf(h52,assumption,
( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(140,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(141,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(142,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(143,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(144,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h41,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[140,141,142,143,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h53,assumption,
( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(145,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(146,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(147,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(148,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(149,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[145,146,147,148,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h54,assumption,
( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(150,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(151,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(152,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(153,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(154,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h45,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[150,151,152,153,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h55,assumption,
( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(155,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(156,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(157,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(158,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(159,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[155,156,157,158,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h56,assumption,
( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(160,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(161,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(162,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(163,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(164,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[160,161,162,163,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h57,assumption,
( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(165,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(166,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(167,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(168,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(169,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[165,166,167,168,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h58,assumption,
( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(170,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(171,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(172,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(173,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(174,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h37,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[170,171,172,173,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(h59,assumption,
( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(175,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h39,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[h46,h39]) ).
thf(h60,assumption,
( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h61,assumption,
denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( produc394644079real_c @ ab @ bb ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ),
introduced(assumption,[]) ).
thf(h62,assumption,
denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( denota1896987029_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ ( denota1293057250_a_b_c @ i @ oDEa ),
introduced(assumption,[]) ).
thf(h63,assumption,
( denota1997846518gree_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ),
introduced(assumption,[]) ).
thf(h64,assumption,
( denota1997846518gree_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( denota1896987029_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( denota1293057250_a_b_c @ i @ oDEa ) ),
introduced(assumption,[]) ).
thf(h65,assumption,
member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ),
introduced(assumption,[]) ).
thf(h66,assumption,
member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ),
introduced(assumption,[]) ).
thf(h67,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ),
introduced(assumption,[]) ).
thf(h68,assumption,
~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ),
introduced(assumption,[]) ).
thf(176,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(177,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(178,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(179,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(180,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h41,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[176,177,178,179,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(181,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(182,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(183,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(184,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(185,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h67,h68,h63,h64,h61,h62,h41,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[181,182,183,184,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,axiom,
( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) )
= ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
thf(186,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h63,h64,h61,h62,h41,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_bq(discharge,[h65,h66]),tab_bq(discharge,[h67,h68])],[fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,180,185,h65,h66,h67,h68]) ).
thf(fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
~ ( ( denota1997846518gree_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
=> ~ ( denota1997846518gree_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( denota1896987029_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
thf(187,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h41,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h63,h64])],[fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,186,h63,h64]) ).
thf(fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
~ ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( produc394644079real_c @ ab @ bb ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
=> ~ ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( denota1896987029_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
thf(188,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,187,h61,h62]) ).
thf(h69,assumption,
( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(189,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(190,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(191,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(192,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(193,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h43,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[189,190,191,192,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(194,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(195,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(196,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(197,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(198,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h67,h68,h63,h64,h61,h62,h43,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[194,195,196,197,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(199,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h63,h64,h61,h62,h43,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_bq(discharge,[h65,h66]),tab_bq(discharge,[h67,h68])],[fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,193,198,h65,h66,h67,h68]) ).
thf(200,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h43,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h63,h64])],[fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,199,h63,h64]) ).
thf(201,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,200,h61,h62]) ).
thf(h70,assumption,
( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(202,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(203,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(204,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(205,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(206,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h45,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[202,203,204,205,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(207,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(208,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(209,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(210,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(211,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h67,h68,h63,h64,h61,h62,h45,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[207,208,209,210,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(212,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h63,h64,h61,h62,h45,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_bq(discharge,[h65,h66]),tab_bq(discharge,[h67,h68])],[fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,206,211,h65,h66,h67,h68]) ).
thf(213,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h45,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h63,h64])],[fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,212,h63,h64]) ).
thf(214,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,213,h61,h62]) ).
thf(215,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(216,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(217,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(218,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(219,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h70,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[215,216,217,218,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(220,plain,
( ~ sP4
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(221,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(222,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(223,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(224,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h67,h68,h63,h64,h61,h62,h70,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0])],[220,221,222,223,conj_2,conj_1,fact_0_ode__to__fvo]) ).
thf(225,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h63,h64,h61,h62,h70,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_bq(discharge,[h65,h66]),tab_bq(discharge,[h67,h68])],[fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,219,224,h65,h66,h67,h68]) ).
thf(226,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h70,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h63,h64])],[fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,225,h63,h64]) ).
thf(227,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h70,h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,226,h61,h62]) ).
thf(228,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h69,h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h45]),tab_imp(discharge,[h70])],[h69,214,227,h45,h70]) ).
thf(229,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h60,h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h69])],[h60,201,228,h43,h69]) ).
thf(230,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h59,h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h41]),tab_imp(discharge,[h60])],[h59,188,229,h41,h60]) ).
thf(231,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h58,h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h39]),tab_imp(discharge,[h59])],[h58,175,230,h39,h59]) ).
thf(232,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h57,h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h37]),tab_imp(discharge,[h58])],[h57,174,231,h37,h58]) ).
thf(233,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h56,h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h35]),tab_imp(discharge,[h57])],[h56,169,232,h35,h57]) ).
thf(234,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h55,h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h33]),tab_imp(discharge,[h56])],[h55,164,233,h33,h56]) ).
thf(fact_112__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Aab_A_061_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
( ( osafe_a_c @ oDEa )
=> ( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ab
= ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(235,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h54,h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h31]),tab_imp(discharge,[h55])],[fact_112__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Aab_A_061_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,159,234,h31,h55]) ).
thf(236,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h53,h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h45]),tab_imp(discharge,[h54])],[h53,154,235,h45,h54]) ).
thf(237,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h52,h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h53])],[h52,149,236,h43,h53]) ).
thf(238,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h51,h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h41]),tab_imp(discharge,[h52])],[h51,144,237,h41,h52]) ).
thf(239,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h50,h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h39]),tab_imp(discharge,[h51])],[h50,139,238,h39,h51]) ).
thf(240,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h49,h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h37]),tab_imp(discharge,[h50])],[h49,138,239,h37,h50]) ).
thf(241,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h48,h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h35]),tab_imp(discharge,[h49])],[h48,133,240,h35,h49]) ).
thf(242,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h47,h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h33]),tab_imp(discharge,[h48])],[h47,128,241,h33,h48]) ).
thf(fact_113__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_A_061_Amk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_At_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
( ( osafe_a_c @ oDEa )
=> ( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
= ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(243,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h46,h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h31]),tab_imp(discharge,[h47])],[fact_113__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_A_061_Amk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_At_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,123,242,h31,h47]) ).
thf(244,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h44,h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h45]),tab_imp(discharge,[h46])],[h44,118,243,h45,h46]) ).
thf(245,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h42,h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h44])],[h42,113,244,h43,h44]) ).
thf(246,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h40,h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h41]),tab_imp(discharge,[h42])],[h40,108,245,h41,h42]) ).
thf(247,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h38,h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h39]),tab_imp(discharge,[h40])],[h38,103,246,h39,h40]) ).
thf(248,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h36,h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h37]),tab_imp(discharge,[h38])],[h36,98,247,h37,h38]) ).
thf(249,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h34,h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h35]),tab_imp(discharge,[h36])],[h34,93,248,h35,h36]) ).
thf(250,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h32,h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h33]),tab_imp(discharge,[h34])],[h32,88,249,h33,h34]) ).
thf(fact_114__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_A0_A_092_060le_062_At_092_060close_062,axiom,
( ( osafe_a_c @ oDEa )
=> ( ( fsafe_a_b_c @ phi )
=> ( ( ode = oDEa )
=> ( ( p = phi )
=> ( sP6
=> ( ( ( produc394644079real_c @ aa @ ba )
= ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
=> ( ( initia1631504802real_c @ sol
@ ^ [X1: real] : ( denota1275485728_a_b_c @ i @ oDEa )
@ ( set_or656347191t_real @ zero_zero_real @ t )
@ ( collec230941376real_c
@ ^ [X1: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X1 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
=> ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
@ ( collect_c
@ ^ [X1: c] :
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_BVO_a_c @ oDEa ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X1 ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
=> sP6 ) ) ) ) ) ) ) ) ).
thf(251,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h31]),tab_imp(discharge,[h32])],[fact_114__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_A0_A_092_060le_062_At_092_060close_062,83,250,h31,h32]) ).
thf(252,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h30,h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h18,78,251,h21,h22]) ).
thf(253,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h29,h18,h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h30])],[h29,77,252,h19,h30]) ).
thf(254,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h18])],[h28,253,h29,h18]) ).
thf(conj_3,axiom,
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
=> ~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ).
thf(255,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h27,h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h28])],[conj_3,72,254,h26,h28]) ).
thf(conj_4,axiom,
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
=> ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ).
thf(256,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[conj_4,67,255,h26,h27]) ).
thf(conj_5,axiom,
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
=> ( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ bb @ i2 ) ) ) ).
thf(257,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h24,h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h25])],[conj_5,62,256,h23,h25]) ).
thf(conj_6,axiom,
( ~ ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
=> ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ bb @ i2 ) ) ) ).
thf(258,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[conj_6,57,257,h23,h24]) ).
thf(259,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h18,52,258,h21,h22]) ).
thf(260,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,51,259,h19,h20]) ).
thf(261,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,260,h17,h18]) ).
thf(262,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h16])],[h15,46,261,h10,h16]) ).
thf(263,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h18,41,262,h21,h22]) ).
thf(264,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,40,263,h19,h20]) ).
thf(265,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,264,h17,h18]) ).
thf(266,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h15,h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h16])],[h14,35,265,h8,h16]) ).
thf(conj_7,axiom,
~ ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ) )
=> ~ ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ~ ( ( sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ~ sP7
=> ( ( finite772340578real_c
@ ( produc2010422875real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ) ).
thf(267,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[conj_7,266,h14,h15]) ).
thf(268,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h13])],[h12,30,267,h5,h13]) ).
thf(269,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h13])],[h11,25,268,h3,h13]) ).
thf(conj_8,axiom,
~ ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c
@ ( denota1275485728_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ i2 ) ) )
=> ~ ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c
@ ( produc314122909real_c
@ ( denota161327353_a_b_c @ i @ oDEa
@ ( produc394644079real_c
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) )
@ bb )
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) ) )
@ i2 )
= ( finite772340578real_c
@ ( denota1275485728_a_b_c @ i @ oDEa
@ ( finite557796307c_real
@ ^ [X1: c] : ( if_real @ ( member_c @ X1 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ X1 ) @ ( finite772340578real_c @ ab @ X1 ) ) ) )
@ i2 ) ) ) ) ).
thf(270,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h9,h6,h7,h4,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[conj_8,269,h11,h12]) ).
thf(271,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h9])],[h7,20,270,h10,h9]) ).
thf(272,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h4,h4,h1,h2,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,15,271,h8,h9]) ).
thf(conj_9,axiom,
~ ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
=> ~ ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ) ) ).
thf(273,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[conj_9,272,h6,h7]) ).
thf(274,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h4])],[h2,10,273,h5,h4]) ).
thf(275,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,5,274,h3,h4]) ).
thf(conj_10,axiom,
~ ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) )
=> ~ ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
=> ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
= ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) ) ) ).
thf(276,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[conj_10,275,h1,h2]) ).
thf(0,theorem,
( ( finite772340578real_c @ ab @ i2 )
= ( finite772340578real_c @ ( sol @ x ) @ i2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[276,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP040^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 14:06:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.96/1.14 % SZS status Theorem
% 0.96/1.14 % Mode: cade22sinegrackle2x6978
% 0.96/1.14 % Steps: 8928
% 0.96/1.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------