%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP146^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Wed Feb 25 08:55:55 AM UTC 2026
% Result : Theorem 10.60s 2.92s
% Output : Refutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 29 unt; 0 typ; 6 def)
% Number of atoms : 212 ( 77 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 845 ( 54 ~; 51 |; 0 &; 722 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 25 con; 0-4 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
set_a: $tType ).
thf(type_def_8,type,
set_real: $tType ).
thf(type_def_9,type,
real: $tType ).
thf(func_def_0,type,
set_real: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
real: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
thf(func_def_5,type,
auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
thf(func_def_6,type,
minus_minus_real: real > real > real ).
thf(func_def_7,type,
minus_minus_a: a > a > a ).
thf(func_def_8,type,
plus_plus_real: real > real > real ).
thf(func_def_9,type,
plus_plus_a: a > a > a ).
thf(func_def_10,type,
uminus_uminus_a_a: ( a > a ) > a > a ).
thf(func_def_11,type,
uminus_uminus_real: real > real ).
thf(func_def_12,type,
uminus_uminus_a: a > a ).
thf(func_def_13,type,
zero_zero_real: real ).
thf(func_def_14,type,
zero_zero_a: a ).
thf(func_def_15,type,
initia826609931terval: set_real > $o ).
thf(func_def_16,type,
bot_bot_set_real: set_real ).
thf(func_def_17,type,
ord_less_real: real > real > $o ).
thf(func_def_18,type,
ord_less_a: a > a > $o ).
thf(func_def_19,type,
top_top_set_real: set_real ).
thf(func_def_20,type,
period720806154rbit_a: ( a > a ) > set_a > a > $o ).
thf(func_def_21,type,
period1305449585riod_a: ( a > a ) > set_a > a > real ).
thf(func_def_22,type,
period138238489rbit_a: ( a > a ) > set_a > a > $o ).
thf(func_def_23,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_24,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_25,type,
member_real: real > set_real > $o ).
thf(func_def_26,type,
member_a: a > set_a > $o ).
thf(func_def_27,type,
x: set_a ).
thf(func_def_28,type,
d: real ).
thf(func_def_29,type,
f: a > a ).
thf(func_def_30,type,
i1: real ).
thf(func_def_31,type,
i2: real ).
thf(func_def_32,type,
ss: real ).
thf(func_def_33,type,
t: real ).
thf(func_def_34,type,
tt: real ).
thf(func_def_35,type,
x2: a ).
thf(func_def_36,type,
xx: a ).
thf(func_def_48,type,
sK0: a ).
thf(func_def_49,type,
sK1: a ).
thf(func_def_50,type,
sK2: a ).
thf(func_def_51,type,
sK3: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_52,type,
sK4: a > real ).
thf(func_def_53,type,
sK5: a > real ).
thf(func_def_54,type,
sK6: a ).
thf(func_def_55,type,
sK7: ( real > $o ) > ( real > $o ) > real ).
thf(func_def_57,type,
sK9: a > real ).
thf(func_def_58,type,
sK10: a > real ).
thf(func_def_59,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f2495,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1907,f1950,f1956,f2159,f2189,f2217,f2484]) ).
thf(f2484,plain,
( spl8_2
| ~ spl8_8
| ~ spl8_13
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f2483]) ).
thf(f2483,plain,
( $false
| spl8_2
| ~ spl8_8
| ~ spl8_13
| ~ spl8_15 ),
inference(subsumption_resolution,[status(thm)],[f2482,f1906]) ).
thf(f1906,plain,
( ( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) )
| spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f1904]) ).
thf(f1904,definition,
( spl8_2
<=> ( xx
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f2482,plain,
( ( xx
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_15 ),
inference(forward_demodulation,[status(thm)],[f2481,f2216]) ).
thf(f2216,plain,
( ( xx
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) )
| ~ spl8_15 ),
inference(avatar_component_clause,[status(thm)],[f2214]) ).
thf(f2214,definition,
( spl8_15
<=> ( xx
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_15])],[avatar_definition]) ).
thf(f2481,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) )
| ~ spl8_8
| ~ spl8_13 ),
inference(forward_demodulation,[status(thm)],[f2480,f1374]) ).
thf(f1374,plain,
! [X0: real] :
( ( minus_minus_real @ X0 @ zero_zero_real )
= X0 ),
inference(cnf_transformation,[status(thm)],[f821]) ).
thf(f821,plain,
! [X0: real] :
( ( minus_minus_real @ X0 @ zero_zero_real )
= X0 ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,axiom,
! [X8: real] :
( ( minus_minus_real @ X8 @ zero_zero_real )
= X8 ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_109_diff__zero) ).
thf(f2480,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ ( minus_minus_real @ tt @ zero_zero_real ) ) ) )
| ~ spl8_8
| ~ spl8_13 ),
inference(forward_demodulation,[status(thm)],[f2479,f2010]) ).
thf(f2010,plain,
! [X2: real,X0: real,X1: real] :
( ( plus_plus_real @ X2 @ ( minus_minus_real @ X0 @ X1 ) )
= ( minus_minus_real @ X2 @ ( minus_minus_real @ X1 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f1285,f1266]) ).
thf(f1266,plain,
! [X2: real,X0: real,X1: real] :
( ( minus_minus_real @ ( plus_plus_real @ X1 @ X2 ) @ X0 )
= ( minus_minus_real @ X1 @ ( minus_minus_real @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f842]) ).
thf(f842,plain,
! [X0: real,X1: real,X2: real] :
( ( minus_minus_real @ ( plus_plus_real @ X1 @ X2 ) @ X0 )
= ( minus_minus_real @ X1 @ ( minus_minus_real @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f334]) ).
thf(f334,axiom,
! [X9: real,X8: real,X18: real] :
( ( minus_minus_real @ ( plus_plus_real @ X8 @ X18 ) @ X9 )
= ( minus_minus_real @ X8 @ ( minus_minus_real @ X9 @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_333_diff__diff__eq2) ).
thf(f1285,plain,
! [X2: real,X0: real,X1: real] :
( ( plus_plus_real @ X2 @ ( minus_minus_real @ X0 @ X1 ) )
= ( minus_minus_real @ ( plus_plus_real @ X2 @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f844]) ).
thf(f844,plain,
! [X0: real,X1: real,X2: real] :
( ( plus_plus_real @ X2 @ ( minus_minus_real @ X0 @ X1 ) )
= ( minus_minus_real @ ( plus_plus_real @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f336]) ).
thf(f336,axiom,
! [X9: real,X18: real,X8: real] :
( ( plus_plus_real @ X8 @ ( minus_minus_real @ X9 @ X18 ) )
= ( minus_minus_real @ ( plus_plus_real @ X8 @ X9 ) @ X18 ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_335_add__diff__eq) ).
thf(f2479,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( plus_plus_real @ ss @ ( minus_minus_real @ zero_zero_real @ tt ) ) ) )
| ~ spl8_8
| ~ spl8_13 ),
inference(subsumption_resolution,[status(thm)],[f2473,f1949]) ).
thf(f1949,plain,
( ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
= $true )
| ~ spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f1947]) ).
thf(f1947,definition,
( spl8_8
<=> ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f2473,plain,
( ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= $true )
| ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( plus_plus_real @ ss @ ( minus_minus_real @ zero_zero_real @ tt ) ) ) )
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f2468]) ).
thf(f2468,plain,
( ( $true != $true )
| ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( plus_plus_real @ ss @ ( minus_minus_real @ zero_zero_real @ tt ) ) ) )
| ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= $true )
| ~ spl8_13 ),
inference(superposition,[status(thm)],[f1197,f2188]) ).
thf(f2188,plain,
( ( ( member_real @ ( minus_minus_real @ zero_zero_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) )
= $true )
| ~ spl8_13 ),
inference(avatar_component_clause,[status(thm)],[f2186]) ).
thf(f2186,definition,
( spl8_13
<=> ( ( member_real @ ( minus_minus_real @ zero_zero_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition]) ).
thf(f1197,plain,
! [X2: a,X0: real,X1: real] :
( ( $true
!= ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) ) ) )
| ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X2 ) )
!= $true )
| ( ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( plus_plus_real @ X0 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f908]) ).
thf(f908,plain,
! [X0: real,X1: real,X2: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X2 ) )
!= $true )
| ( $true
!= ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) ) ) )
| ( ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( plus_plus_real @ X0 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) @ X1 ) ) ),
inference(flattening,[status(thm)],[f907]) ).
thf(f907,plain,
! [X0: real,X1: real,X2: a] :
( ( ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( plus_plus_real @ X0 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) @ X1 ) )
| ( $true
!= ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) ) ) )
| ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X2 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f481]) ).
thf(f481,plain,
! [X0: real,X1: real,X2: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X2 ) )
= $true )
=> ( ( $true
= ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( plus_plus_real @ X0 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f480]) ).
thf(f480,plain,
! [X0: real,X1: real,X2: a] :
( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X2 ) )
=> ( ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( plus_plus_real @ X0 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ X0 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f160]) ).
thf(f160,axiom,
! [X15: real,X1: real,X3: a] :
( ( member_real @ X15 @ ( auto_l612940ivl0_a @ f @ x @ X3 ) )
=> ( ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ X15 ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ X3 @ ( plus_plus_real @ X15 @ X1 ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ X15 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_159_local_Oflow__trans) ).
thf(f2217,plain,
( spl8_15
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f2184,f2156,f1953,f2214]) ).
thf(f1953,definition,
( spl8_9
<=> ( ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition]) ).
thf(f2156,definition,
( spl8_10
<=> ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) ),
introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition]) ).
thf(f2184,plain,
( ( xx
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) )
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[status(thm)],[f2181,f2158]) ).
thf(f2158,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[status(thm)],[f2156]) ).
thf(f2181,plain,
( ( xx
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f2179]) ).
thf(f2179,plain,
( ( xx
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( minus_minus_real @ zero_zero_real @ tt ) ) )
| ( $true != $true )
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f1325,f1955]) ).
thf(f1955,plain,
( ( ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) )
= $true )
| ~ spl8_9 ),
inference(avatar_component_clause,[status(thm)],[f1953]) ).
thf(f1325,plain,
! [X0: real,X1: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
!= $true )
| ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) @ ( minus_minus_real @ zero_zero_real @ X0 ) )
= X1 ) ),
inference(cnf_transformation,[status(thm)],[f1083]) ).
thf(f1083,plain,
! [X0: real,X1: a] :
( ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) @ ( minus_minus_real @ zero_zero_real @ X0 ) )
= X1 )
| ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f573]) ).
thf(f573,plain,
! [X0: real,X1: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
= $true )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) @ ( minus_minus_real @ zero_zero_real @ X0 ) )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f572]) ).
thf(f572,plain,
! [X0: real,X1: a] :
( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) @ ( minus_minus_real @ zero_zero_real @ X0 ) )
= X1 ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,axiom,
! [X1: real,X3: a] :
( ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ X3 ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ X1 ) @ ( minus_minus_real @ zero_zero_real @ X1 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_33_local_Oflows__reverse) ).
thf(f2189,plain,
( spl8_13
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f2170,f2156,f1953,f2186]) ).
thf(f2170,plain,
( ( ( member_real @ ( minus_minus_real @ zero_zero_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) )
= $true )
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[status(thm)],[f2168,f2158]) ).
thf(f2168,plain,
( ( ( member_real @ ( minus_minus_real @ zero_zero_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ) )
= $true )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f2167]) ).
thf(f2167,plain,
( ( $true != $true )
| ( ( member_real @ ( minus_minus_real @ zero_zero_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ) )
= $true )
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f1157,f1955]) ).
thf(f1157,plain,
! [X0: real,X1: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
!= $true )
| ( ( member_real @ ( minus_minus_real @ zero_zero_real @ X0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f920]) ).
thf(f920,plain,
! [X0: real,X1: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
!= $true )
| ( ( member_real @ ( minus_minus_real @ zero_zero_real @ X0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f549]) ).
thf(f549,plain,
! [X0: real,X1: a] :
( ( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
= $true )
=> ( ( member_real @ ( minus_minus_real @ zero_zero_real @ X0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f548]) ).
thf(f548,plain,
! [X0: real,X1: a] :
( ( member_real @ X0 @ ( auto_l612940ivl0_a @ f @ x @ X1 ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ X0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,axiom,
! [X1: real,X3: a] :
( ( member_real @ X1 @ ( auto_l612940ivl0_a @ f @ x @ X3 ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ X1 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_34_local_Oexistence__ivl__reverse) ).
thf(f2159,plain,
spl8_10,
inference(avatar_split_clause,[status(thm)],[f1243,f2156]) ).
thf(f1243,plain,
( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_2_eq) ).
thf(f1956,plain,
spl8_9,
inference(avatar_split_clause,[status(thm)],[f1448,f1953]) ).
thf(f1448,plain,
( ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f622]) ).
thf(f622,plain,
( ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) )
= $true ),
inference(fool_elimination,[status(thm)],[f621]) ).
thf(f621,plain,
member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_4_tt__ex) ).
thf(f1950,plain,
spl8_8,
inference(avatar_split_clause,[status(thm)],[f1410,f1947]) ).
thf(f1410,plain,
( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f405]) ).
thf(f405,plain,
( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f404]) ).
thf(f404,plain,
member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_5_ss__ex) ).
thf(f1907,plain,
~ spl8_2,
inference(avatar_split_clause,[status(thm)],[f1261,f1904]) ).
thf(f1261,plain,
( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
inference(cnf_transformation,[status(thm)],[f794]) ).
thf(f794,plain,
( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
inference(flattening,[status(thm)],[f344]) ).
thf(f344,negated_conjecture,
( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
inference(negated_conjecture,[status(cth)],[f343]) ).
thf(f343,conjecture,
( xx
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP146^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 08:27:51 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : ITP146^1 : TPTP v9.2.1. Released v7.5.0.
% 0.17/0.44 % Domain : Interactive Theorem Proving
% 0.17/0.44 % Problem : Sledgehammer Poincare_Bendixson problem prob_1288__19593336_1
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.17/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Des21]
% 0.17/0.44 % Names : Poincare_Bendixson/prob_1288__19593336_1 [Des21]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.17/0.44 % Syntax : Number of formulae : 380 ( 187 unt; 37 typ; 0 def)
% 0.17/0.44 % Number of atoms : 791 ( 396 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 6 ( 2 avg)
% 0.17/0.44 % Number of connectives : 3066 ( 36 ~; 2 |; 30 &;2756 @)
% 0.17/0.44 % ( 0 <=>; 242 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 14 ( 6 avg)
% 0.17/0.44 % Number of types : 5 ( 4 usr)
% 0.17/0.44 % Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 34 ( 33 usr; 13 con; 0-4 aty)
% 0.17/0.44 % Number of variables : 731 ( 14 ^; 715 !; 2 ?; 731 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:46:31.992
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % Could-be-implicit typings (4)
% 0.17/0.44 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.17/0.44 set_real: $tType ).
% 0.17/0.44
% 0.17/0.44 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.17/0.44 set_a: $tType ).
% 0.17/0.44
% 0.17/0.44 thf(ty_n_t__Real__Oreal,type,
% 0.17/0.44 real: $tType ).
% 0.17/0.44
% 0.17/0.44 thf(ty_n_tf__a,type,
% 0.17/0.44 a: $tType ).
% 0.17/0.44
% 0.17/0.44 % Explicit typings (33)
% 0.17/0.44 thf(sy_c_Flow_Oauto__ll__on__open_Oexistence__ivl0_001tf__a,type,
% 0.17/0.44 auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Flow_Oauto__ll__on__open_Oflow0_001tf__a,type,
% 0.17/0.44 auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 0.17/0.44 minus_minus_real: real > real > real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ominus__class_Ominus_001tf__a,type,
% 0.17/0.44 minus_minus_a: a > a > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.17/0.44 plus_plus_real: real > real > real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Oplus__class_Oplus_001tf__a,type,
% 0.17/0.44 plus_plus_a: a > a > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_Itf__a_Mtf__a_J,type,
% 0.17/0.44 uminus_uminus_a_a: ( a > a ) > a > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 0.17/0.44 uminus_uminus_real: real > real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type,
% 0.17/0.44 uminus_uminus_a: a > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.17/0.44 zero_zero_real: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 0.17/0.44 zero_zero_a: a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Initial__Value__Problem_Ointerval,type,
% 0.17/0.44 initia826609931terval: set_real > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.17/0.44 bot_bot_set_real: set_real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.17/0.44 ord_less_real: real > real > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type,
% 0.17/0.44 ord_less_a: a > a > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.17/0.44 top_top_set_real: set_real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Oclosed__orbit_001tf__a,type,
% 0.17/0.44 period720806154rbit_a: ( a > a ) > set_a > a > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiod_001tf__a,type,
% 0.17/0.44 period1305449585riod_a: ( a > a ) > set_a > a > real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiodic__orbit_001tf__a,type,
% 0.17/0.44 period138238489rbit_a: ( a > a ) > set_a > a > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.17/0.44 collect_real: ( real > $o ) > set_real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.17/0.44 collect_a: ( a > $o ) > set_a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_member_001t__Real__Oreal,type,
% 0.17/0.44 member_real: real > set_real > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_c_member_001tf__a,type,
% 0.17/0.44 member_a: a > set_a > $o ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_X,type,
% 0.17/0.44 x: set_a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_d____,type,
% 0.17/0.44 d: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_f,type,
% 0.17/0.44 f: a > a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_i1____,type,
% 0.17/0.44 i1: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_i2____,type,
% 0.17/0.44 i2: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_ss____,type,
% 0.17/0.44 ss: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_t,type,
% 0.17/0.44 t: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_tt____,type,
% 0.17/0.44 tt: real ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_x,type,
% 0.17/0.44 x2: a ).
% 0.17/0.44
% 0.17/0.44 thf(sy_v_xx____,type,
% 0.17/0.44 xx: a ).
% 0.17/0.44
% 0.17/0.44 % Relevant facts (342)
% 0.17/0.44 thf(fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062,axiom,
% 0.17/0.44 member_a @ xx @ x ).
% 0.17/0.44
% 0.17/0.44 % \<open>xx \<in> X\<close>
% 0.17/0.44 thf(fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062,axiom,
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % \<open>flow0 (flow0 xx tt) (- tt) = flow0 (flow0 x ss) (- tt)\<close>
% 0.17/0.44 thf(fact_2_eq,axiom,
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq
% 0.17/0.44 thf(fact_3_assms_I8_J,axiom,
% 0.17/0.44 member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ) ).
% 0.17/0.44
% 0.17/0.44 % assms(8)
% 0.17/0.44 thf(fact_4_tt__ex,axiom,
% 0.17/0.44 member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) ).
% 0.17/0.44
% 0.17/0.44 % tt_ex
% 0.17/0.44 thf(fact_5_ss__ex,axiom,
% 0.17/0.44 member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) ).
% 0.17/0.44
% 0.17/0.44 % ss_ex
% 0.17/0.44 thf(fact_6_fixpoint__sol_I2_J,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ T )
% 0.17/0.44 = X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fixpoint_sol(2)
% 0.17/0.44 thf(fact_7_neg__tt__ex,axiom,
% 0.17/0.44 member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_tt_ex
% 0.17/0.44 thf(fact_8_diff__existence__ivl__trans,axiom,
% 0.17/0.44 ! [T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ T0 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T0 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_existence_ivl_trans
% 0.17/0.44 thf(fact_9_general_Oexistence__ivl__reverse,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T0 @ T ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.existence_ivl_reverse
% 0.17/0.44 thf(fact_10_general_Oflow__in__domain,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flow_in_domain
% 0.17/0.44 thf(fact_11_general_Oflows__reverse,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ ( minus_minus_real @ T0 @ T ) )
% 0.17/0.44 = X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flows_reverse
% 0.17/0.44 thf(fact_12_general_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ X0 @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.mem_existence_ivl_iv_defined(2)
% 0.17/0.44 thf(fact_13_closed__orbit__flow0,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X @ T ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_flow0
% 0.17/0.44 thf(fact_14_closed__orbit__in__domain,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ( member_a @ X @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_in_domain
% 0.17/0.44 thf(fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( period720806154rbit_a @ f @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fixed_point_imp_closed_orbit_period_zero(1)
% 0.17/0.44 thf(fact_16_recurrence__time__flip__sign_I1_J,axiom,
% 0.17/0.44 ! [T2: real,X: a] :
% 0.17/0.44 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 )
% 0.17/0.44 = X )
% 0.17/0.44 => ( member_real @ ( uminus_uminus_real @ T2 ) @ ( auto_l612940ivl0_a @ f @ x @ X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % recurrence_time_flip_sign(1)
% 0.17/0.44 thf(fact_17_recurrence__time__flip__sign_I2_J,axiom,
% 0.17/0.44 ! [T2: real,X: a] :
% 0.17/0.44 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 )
% 0.17/0.44 = X )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( uminus_uminus_real @ T2 ) )
% 0.17/0.44 = X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % recurrence_time_flip_sign(2)
% 0.17/0.44 thf(fact_18_local_Oflow__undefined0,axiom,
% 0.17/0.44 ! [T: real,X: a] :
% 0.17/0.44 ( ~ ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ T )
% 0.17/0.44 = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flow_undefined0
% 0.17/0.44 thf(fact_19_closed__orbitI,axiom,
% 0.17/0.44 ! [T: real,T3: real,Y: a] :
% 0.17/0.44 ( ( T != T3 )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 0.17/0.44 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) )
% 0.17/0.44 => ( period720806154rbit_a @ f @ x @ Y ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbitI
% 0.17/0.44 thf(fact_20_general_Oflow__undefined0,axiom,
% 0.17/0.44 ! [T: real,T0: real,X: a] :
% 0.17/0.44 ( ~ ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ T0 ) )
% 0.17/0.44 = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flow_undefined0
% 0.17/0.44 thf(fact_21_local_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ X0 @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.mem_existence_ivl_iv_defined(2)
% 0.17/0.44 thf(fact_22_local_Oflow__in__domain,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flow_in_domain
% 0.17/0.44 thf(fact_23_flow0__defined,axiom,
% 0.17/0.44 ! [Xa: real,X0: a] :
% 0.17/0.44 ( ( member_real @ Xa @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ Xa ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % flow0_defined
% 0.17/0.44 thf(fact_24_mvar_Ointerval__axioms,axiom,
% 0.17/0.44 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % mvar.interval_axioms
% 0.17/0.44 thf(fact_25_periodic__orbitI,axiom,
% 0.17/0.44 ! [T: real,T3: real,Y: a] :
% 0.17/0.44 ( ( T != T3 )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 0.17/0.44 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) )
% 0.17/0.44 => ( ( ( f @ Y )
% 0.17/0.44 != zero_zero_a )
% 0.17/0.44 => ( period138238489rbit_a @ f @ x @ Y ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % periodic_orbitI
% 0.17/0.44 thf(fact_26_closed__orbit__periodic,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ( ( f @ X )
% 0.17/0.44 != zero_zero_a )
% 0.17/0.44 => ( period138238489rbit_a @ f @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_periodic
% 0.17/0.44 thf(fact_27_periodic__orbit__imp__flow0__regular,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( period138238489rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ X @ T ) )
% 0.17/0.44 != zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % periodic_orbit_imp_flow0_regular
% 0.17/0.44 thf(fact_28_diff__0,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( minus_minus_a @ zero_zero_a @ A )
% 0.17/0.44 = ( uminus_uminus_a @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_0
% 0.17/0.44 thf(fact_29_diff__0,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( minus_minus_real @ zero_zero_real @ A )
% 0.17/0.44 = ( uminus_uminus_real @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_0
% 0.17/0.44 thf(fact_30_verit__minus__simplify_I3_J,axiom,
% 0.17/0.44 ! [B: a] :
% 0.17/0.44 ( ( minus_minus_a @ zero_zero_a @ B )
% 0.17/0.44 = ( uminus_uminus_a @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_minus_simplify(3)
% 0.17/0.44 thf(fact_31_verit__minus__simplify_I3_J,axiom,
% 0.17/0.44 ! [B: real] :
% 0.17/0.44 ( ( minus_minus_real @ zero_zero_real @ B )
% 0.17/0.44 = ( uminus_uminus_real @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_minus_simplify(3)
% 0.17/0.44 thf(fact_32_closed__orbit__def,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 = ( ? [X2: real] :
% 0.17/0.44 ( ( member_real @ X2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 & ( X2 != zero_zero_real )
% 0.17/0.44 & ( ( auto_ll_on_flow0_a @ f @ x @ X @ X2 )
% 0.17/0.44 = X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_def
% 0.17/0.44 thf(fact_33_local_Oflows__reverse,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) @ ( minus_minus_real @ zero_zero_real @ T ) )
% 0.17/0.44 = X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flows_reverse
% 0.17/0.44 thf(fact_34_local_Oexistence__ivl__reverse,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ zero_zero_real @ T ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_reverse
% 0.17/0.44 thf(fact_35_general_Oflow__initial__time__if,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = X0 ) )
% 0.17/0.44 & ( ~ ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flow_initial_time_if
% 0.17/0.44 thf(fact_36_interval__axioms,axiom,
% 0.17/0.44 initia826609931terval @ top_top_set_real ).
% 0.17/0.44
% 0.17/0.44 % interval_axioms
% 0.17/0.44 thf(fact_37_rev_Oclosed__orbit__eq__rev,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = ( period720806154rbit_a @ f @ x @ X ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_eq_rev
% 0.17/0.44 thf(fact_38_rev_Oclosed__orbit__in__domain,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( member_a @ X @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_in_domain
% 0.17/0.44 thf(fact_39_neg__equal__iff__equal,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ( uminus_uminus_a @ A )
% 0.17/0.44 = ( uminus_uminus_a @ B ) )
% 0.17/0.44 = ( A = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_equal_iff_equal
% 0.17/0.44 thf(fact_40_neg__equal__iff__equal,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ( uminus_uminus_real @ A )
% 0.17/0.44 = ( uminus_uminus_real @ B ) )
% 0.17/0.44 = ( A = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_equal_iff_equal
% 0.17/0.44 thf(fact_41_add_Oinverse__inverse,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_inverse
% 0.17/0.44 thf(fact_42_add_Oinverse__inverse,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_inverse
% 0.17/0.44 thf(fact_43_verit__minus__simplify_I4_J,axiom,
% 0.17/0.44 ! [B: a] :
% 0.17/0.44 ( ( uminus_uminus_a @ ( uminus_uminus_a @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % verit_minus_simplify(4)
% 0.17/0.44 thf(fact_44_verit__minus__simplify_I4_J,axiom,
% 0.17/0.44 ! [B: real] :
% 0.17/0.44 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % verit_minus_simplify(4)
% 0.17/0.44 thf(fact_45_rev_Oexistence__ivl__zero,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.existence_ivl_zero
% 0.17/0.44 thf(fact_46_mem__Collect__eq,axiom,
% 0.17/0.44 ! [A: a,P: a > $o] :
% 0.17/0.44 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.17/0.44 = ( P @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % mem_Collect_eq
% 0.17/0.44 thf(fact_47_mem__Collect__eq,axiom,
% 0.17/0.44 ! [A: real,P: real > $o] :
% 0.17/0.44 ( ( member_real @ A @ ( collect_real @ P ) )
% 0.17/0.44 = ( P @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % mem_Collect_eq
% 0.17/0.44 thf(fact_48_Collect__mem__eq,axiom,
% 0.17/0.44 ! [A2: set_a] :
% 0.17/0.44 ( ( collect_a
% 0.17/0.44 @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
% 0.17/0.44 = A2 ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_mem_eq
% 0.17/0.44 thf(fact_49_Collect__mem__eq,axiom,
% 0.17/0.44 ! [A2: set_real] :
% 0.17/0.44 ( ( collect_real
% 0.17/0.44 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 0.17/0.44 = A2 ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_mem_eq
% 0.17/0.44 thf(fact_50_Collect__cong,axiom,
% 0.17/0.44 ! [P: real > $o,Q: real > $o] :
% 0.17/0.44 ( ! [X3: real] :
% 0.17/0.44 ( ( P @ X3 )
% 0.17/0.44 = ( Q @ X3 ) )
% 0.17/0.44 => ( ( collect_real @ P )
% 0.17/0.44 = ( collect_real @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_cong
% 0.17/0.44 thf(fact_51_Collect__cong,axiom,
% 0.17/0.44 ! [P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( P @ X3 )
% 0.17/0.44 = ( Q @ X3 ) )
% 0.17/0.44 => ( ( collect_a @ P )
% 0.17/0.44 = ( collect_a @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_cong
% 0.17/0.44 thf(fact_52_existence__ivl__zero,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % existence_ivl_zero
% 0.17/0.44 thf(fact_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ X0 @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.mem_existence_ivl_iv_defined(2)
% 0.17/0.44 thf(fact_54_local_Orev_Omem__existence__ivl__subset,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.mem_existence_ivl_subset
% 0.17/0.44 thf(fact_55_local_Omem__existence__ivl__subset,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.mem_existence_ivl_subset
% 0.17/0.44 thf(fact_56_rev_Orev__eq__flow,axiom,
% 0.17/0.44 ! [Y: a,T: real] :
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ ( uminus_uminus_real @ T ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.rev_eq_flow
% 0.17/0.44 thf(fact_57_rev__eq__flow,axiom,
% 0.17/0.44 ! [Y: a,T: real] :
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ Y @ ( uminus_uminus_real @ T ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev_eq_flow
% 0.17/0.44 thf(fact_58_rev_Ofixpoint__sol_I2_J,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T )
% 0.17/0.44 = X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.fixpoint_sol(2)
% 0.17/0.44 thf(fact_59_rev_Oclosed__orbit__flow0,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_flow0
% 0.17/0.44 thf(fact_60_rev_Omvar_Ointerval__axioms,axiom,
% 0.17/0.44 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.mvar.interval_axioms
% 0.17/0.44 thf(fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.fixed_point_imp_closed_orbit_period_zero(1)
% 0.17/0.44 thf(fact_62_local_Orev_Oexistence__ivl__initial__time,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_initial_time
% 0.17/0.44 thf(fact_63_local_Oexistence__ivl__initial__time,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_initial_time
% 0.17/0.44 thf(fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T0 @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.mem_existence_ivl_iv_defined(1)
% 0.17/0.44 thf(fact_65_rev_Ogeneral_Oexistence__ivl__initial__time,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.existence_ivl_initial_time
% 0.17/0.44 thf(fact_66_rev_Omem__existence__ivl__shift__autonomous2,axiom,
% 0.17/0.44 ! [T: real,S: real,X: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( member_a @ X @ x )
% 0.17/0.44 => ( ! [S2: real,T4: real,X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ x )
% 0.17/0.44 => ( ( uminus_uminus_a_a @ f @ X3 )
% 0.17/0.44 = ( uminus_uminus_a_a @ f @ X3 ) ) )
% 0.17/0.44 => ( ( top_top_set_real = top_top_set_real )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.mem_existence_ivl_shift_autonomous2
% 0.17/0.44 thf(fact_67_rev_Ogeneral_Omem__existence__ivl__subset,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.mem_existence_ivl_subset
% 0.17/0.44 thf(fact_68_general_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T0 @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.mem_existence_ivl_iv_defined(1)
% 0.17/0.44 thf(fact_69_general_Oexistence__ivl__initial__time,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.existence_ivl_initial_time
% 0.17/0.44 thf(fact_70_mem__existence__ivl__shift__autonomous2,axiom,
% 0.17/0.44 ! [T: real,S: real,X: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( member_a @ X @ x )
% 0.17/0.44 => ( ! [S2: real,T4: real,X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ x )
% 0.17/0.44 => ( ( f @ X3 )
% 0.17/0.44 = ( f @ X3 ) ) )
% 0.17/0.44 => ( ( top_top_set_real = top_top_set_real )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mem_existence_ivl_shift_autonomous2
% 0.17/0.44 thf(fact_71_general_Omem__existence__ivl__subset,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ T @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.mem_existence_ivl_subset
% 0.17/0.44 thf(fact_72_rev_Odiff__existence__ivl__trans,axiom,
% 0.17/0.44 ! [T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ T0 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T0 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.diff_existence_ivl_trans
% 0.17/0.44 thf(fact_73_rev_Ogeneral_Oexistence__ivl__reverse,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ T0 @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.existence_ivl_reverse
% 0.17/0.44 thf(fact_74_rev_Ogeneral_Oflow__in__domain,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flow_in_domain
% 0.17/0.44 thf(fact_75_rev_Ogeneral_Oflows__reverse,axiom,
% 0.17/0.44 ! [T: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ ( minus_minus_real @ T0 @ T ) )
% 0.17/0.44 = X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flows_reverse
% 0.17/0.44 thf(fact_76_rev_Orecurrence__time__flip__sign_I2_J,axiom,
% 0.17/0.44 ! [T2: real,X: a] :
% 0.17/0.44 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 )
% 0.17/0.44 = X )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( uminus_uminus_real @ T2 ) )
% 0.17/0.44 = X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.recurrence_time_flip_sign(2)
% 0.17/0.44 thf(fact_77_rev_Orecurrence__time__flip__sign_I1_J,axiom,
% 0.17/0.44 ! [T2: real,X: a] :
% 0.17/0.44 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 )
% 0.17/0.44 = X )
% 0.17/0.44 => ( member_real @ ( uminus_uminus_real @ T2 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.recurrence_time_flip_sign(1)
% 0.17/0.44 thf(fact_78_rev_Ofixpoint__sol_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = top_top_set_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.fixpoint_sol(1)
% 0.17/0.44 thf(fact_79_fixpoint__sol_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ f @ x @ X )
% 0.17/0.44 = top_top_set_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fixpoint_sol(1)
% 0.17/0.44 thf(fact_80_local_Orev_Oflow__undefined0,axiom,
% 0.17/0.44 ! [T: real,X: a] :
% 0.17/0.44 ( ~ ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T )
% 0.17/0.44 = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flow_undefined0
% 0.17/0.44 thf(fact_81_rev_Oclosed__orbit__global__existence,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_global_existence
% 0.17/0.44 thf(fact_82_closed__orbit__global__existence,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ f @ x @ X )
% 0.17/0.44 = top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_global_existence
% 0.17/0.44 thf(fact_83_rev_Oclosed__orbitI,axiom,
% 0.17/0.44 ! [T: real,T3: real,Y: a] :
% 0.17/0.44 ( ( T != T3 )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 0.17/0.44 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) )
% 0.17/0.44 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbitI
% 0.17/0.44 thf(fact_84_rev_Operiodic__orbit__imp__flow0__regular,axiom,
% 0.17/0.44 ! [X: a,T: real] :
% 0.17/0.44 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T ) )
% 0.17/0.44 != zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.periodic_orbit_imp_flow0_regular
% 0.17/0.44 thf(fact_85_rev_Oclosed__orbit__periodic,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 != zero_zero_a )
% 0.17/0.44 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_periodic
% 0.17/0.44 thf(fact_86_local_Orev_Oexistence__ivl__reverse,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ zero_zero_real @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_reverse
% 0.17/0.44 thf(fact_87_local_Orev_Oflows__reverse,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) @ ( minus_minus_real @ zero_zero_real @ T ) )
% 0.17/0.44 = X0 ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flows_reverse
% 0.17/0.44 thf(fact_88_rev_Oflow__shift__autonomous2,axiom,
% 0.17/0.44 ! [T: real,S: real,X: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( member_a @ X @ x )
% 0.17/0.44 => ( ! [S2: real,T4: real,X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ x )
% 0.17/0.44 => ( ( uminus_uminus_a_a @ f @ X3 )
% 0.17/0.44 = ( uminus_uminus_a_a @ f @ X3 ) ) )
% 0.17/0.44 => ( ( top_top_set_real = top_top_set_real )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ S ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ S ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.flow_shift_autonomous2
% 0.17/0.44 thf(fact_89_flow__shift__autonomous2,axiom,
% 0.17/0.44 ! [T: real,S: real,X: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 0.17/0.44 => ( ( member_a @ X @ x )
% 0.17/0.44 => ( ! [S2: real,T4: real,X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ x )
% 0.17/0.44 => ( ( f @ X3 )
% 0.17/0.44 = ( f @ X3 ) ) )
% 0.17/0.44 => ( ( top_top_set_real = top_top_set_real )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ S ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ S ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % flow_shift_autonomous2
% 0.17/0.44 thf(fact_90_local_Orev_Oflow__initial__time__if,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = X0 ) )
% 0.17/0.44 & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flow_initial_time_if
% 0.17/0.44 thf(fact_91_local_Oflow__initial__time__if,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = X0 ) )
% 0.17/0.44 & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flow_initial_time_if
% 0.17/0.44 thf(fact_92_rev_Oclosed__orbit__def,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = ( ? [X2: real] :
% 0.17/0.44 ( ( member_real @ X2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 & ( X2 != zero_zero_real )
% 0.17/0.44 & ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ X2 )
% 0.17/0.44 = X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_def
% 0.17/0.44 thf(fact_93_rev_Ogeneral_Oflow__undefined0,axiom,
% 0.17/0.44 ! [T: real,T0: real,X: a] :
% 0.17/0.44 ( ~ ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ T0 ) )
% 0.17/0.44 = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flow_undefined0
% 0.17/0.44 thf(fact_94_rev_Ogeneral_Oflow__initial__time__if,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = X0 ) )
% 0.17/0.44 & ( ~ ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flow_initial_time_if
% 0.17/0.44 thf(fact_95_rev_Operiodic__orbitI,axiom,
% 0.17/0.44 ! [T: real,T3: real,Y: a] :
% 0.17/0.44 ( ( T != T3 )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 0.17/0.44 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 0.17/0.44 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ Y )
% 0.17/0.44 != zero_zero_a )
% 0.17/0.44 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.periodic_orbitI
% 0.17/0.44 thf(fact_96_neg__equal__zero,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ( uminus_uminus_real @ A )
% 0.17/0.44 = A )
% 0.17/0.44 = ( A = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_equal_zero
% 0.17/0.44 thf(fact_97_equal__neg__zero,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( uminus_uminus_real @ A ) )
% 0.17/0.44 = ( A = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % equal_neg_zero
% 0.17/0.44 thf(fact_98_neg__equal__0__iff__equal,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( ( uminus_uminus_a @ A )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 = ( A = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_equal_0_iff_equal
% 0.17/0.44 thf(fact_99_neg__equal__0__iff__equal,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ( uminus_uminus_real @ A )
% 0.17/0.44 = zero_zero_real )
% 0.17/0.44 = ( A = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_equal_0_iff_equal
% 0.17/0.44 thf(fact_100_neg__0__equal__iff__equal,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( zero_zero_a
% 0.17/0.44 = ( uminus_uminus_a @ A ) )
% 0.17/0.44 = ( zero_zero_a = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_0_equal_iff_equal
% 0.17/0.44 thf(fact_101_neg__0__equal__iff__equal,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( zero_zero_real
% 0.17/0.44 = ( uminus_uminus_real @ A ) )
% 0.17/0.44 = ( zero_zero_real = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_0_equal_iff_equal
% 0.17/0.44 thf(fact_102_add_Oinverse__neutral,axiom,
% 0.17/0.44 ( ( uminus_uminus_a @ zero_zero_a )
% 0.17/0.44 = zero_zero_a ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_neutral
% 0.17/0.44 thf(fact_103_add_Oinverse__neutral,axiom,
% 0.17/0.44 ( ( uminus_uminus_real @ zero_zero_real )
% 0.17/0.44 = zero_zero_real ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_neutral
% 0.17/0.44 thf(fact_104_diff__self,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ A )
% 0.17/0.44 = zero_zero_a ) ).
% 0.17/0.44
% 0.17/0.44 % diff_self
% 0.17/0.44 thf(fact_105_diff__self,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ A )
% 0.17/0.44 = zero_zero_real ) ).
% 0.17/0.44
% 0.17/0.44 % diff_self
% 0.17/0.44 thf(fact_106_diff__0__right,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ zero_zero_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_0_right
% 0.17/0.44 thf(fact_107_diff__0__right,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_0_right
% 0.17/0.44 thf(fact_108_diff__zero,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ zero_zero_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_zero
% 0.17/0.44 thf(fact_109_diff__zero,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_zero
% 0.17/0.44 thf(fact_110_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ A )
% 0.17/0.44 = zero_zero_a ) ).
% 0.17/0.44
% 0.17/0.44 % cancel_comm_monoid_add_class.diff_cancel
% 0.17/0.44 thf(fact_111_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ A )
% 0.17/0.44 = zero_zero_real ) ).
% 0.17/0.44
% 0.17/0.44 % cancel_comm_monoid_add_class.diff_cancel
% 0.17/0.44 thf(fact_112_minus__diff__eq,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( uminus_uminus_a @ ( minus_minus_a @ A @ B ) )
% 0.17/0.44 = ( minus_minus_a @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_diff_eq
% 0.17/0.44 thf(fact_113_minus__diff__eq,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.17/0.44 = ( minus_minus_real @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_diff_eq
% 0.17/0.44 thf(fact_114_tt_I1_J,axiom,
% 0.17/0.44 ord_less_real @ zero_zero_real @ tt ).
% 0.17/0.44
% 0.17/0.44 % tt(1)
% 0.17/0.44 thf(fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ X0 @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.mem_existence_ivl_iv_defined(2)
% 0.17/0.44 thf(fact_116_rev_Oflow0__defined,axiom,
% 0.17/0.44 ! [Xa: real,X0: a] :
% 0.17/0.44 ( ( member_real @ Xa @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ Xa ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.flow0_defined
% 0.17/0.44 thf(fact_117_local_Orev_Oflow__in__domain,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) @ x ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flow_in_domain
% 0.17/0.44 thf(fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ zero_zero_real @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.mem_existence_ivl_iv_defined(1)
% 0.17/0.44 thf(fact_119_local_Orev_Oexistence__ivl__initial__time__iff,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 = ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_initial_time_iff
% 0.17/0.44 thf(fact_120_local_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 0.17/0.44 ! [T: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ zero_zero_real @ top_top_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.mem_existence_ivl_iv_defined(1)
% 0.17/0.44 thf(fact_121_local_Oexistence__ivl__initial__time__iff,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 = ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_initial_time_iff
% 0.17/0.44 thf(fact_122_local_Orev_Oflow__initial__time,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flow_initial_time
% 0.17/0.44 thf(fact_123_local_Oflow__initial__time,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 0.17/0.44 = X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flow_initial_time
% 0.17/0.44 thf(fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 = ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.existence_ivl_initial_time_iff
% 0.17/0.44 thf(fact_125_general_Oexistence__ivl__initial__time__iff,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 = ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 & ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.existence_ivl_initial_time_iff
% 0.17/0.44 thf(fact_126_rev_Ogeneral_Oflow__initial__time,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flow_initial_time
% 0.17/0.44 thf(fact_127_general_Oflow__initial__time,axiom,
% 0.17/0.44 ! [T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ T0 @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 0.17/0.44 = X0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flow_initial_time
% 0.17/0.44 thf(fact_128_zero__reorient,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( zero_zero_a = X )
% 0.17/0.44 = ( X = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % zero_reorient
% 0.17/0.44 thf(fact_129_zero__reorient,axiom,
% 0.17/0.44 ! [X: real] :
% 0.17/0.44 ( ( zero_zero_real = X )
% 0.17/0.44 = ( X = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % zero_reorient
% 0.17/0.44 thf(fact_130_minus__equation__iff,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ( uminus_uminus_a @ A )
% 0.17/0.44 = B )
% 0.17/0.44 = ( ( uminus_uminus_a @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_equation_iff
% 0.17/0.44 thf(fact_131_minus__equation__iff,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ( uminus_uminus_real @ A )
% 0.17/0.44 = B )
% 0.17/0.44 = ( ( uminus_uminus_real @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_equation_iff
% 0.17/0.44 thf(fact_132_equation__minus__iff,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( uminus_uminus_a @ B ) )
% 0.17/0.44 = ( B
% 0.17/0.44 = ( uminus_uminus_a @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % equation_minus_iff
% 0.17/0.44 thf(fact_133_equation__minus__iff,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( uminus_uminus_real @ B ) )
% 0.17/0.44 = ( B
% 0.17/0.44 = ( uminus_uminus_real @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % equation_minus_iff
% 0.17/0.44 thf(fact_134_verit__negate__coefficient_I3_J,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( uminus_uminus_a @ A )
% 0.17/0.44 = ( uminus_uminus_a @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_negate_coefficient(3)
% 0.17/0.44 thf(fact_135_verit__negate__coefficient_I3_J,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( uminus_uminus_real @ A )
% 0.17/0.44 = ( uminus_uminus_real @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_negate_coefficient(3)
% 0.17/0.44 thf(fact_136_diff__eq__diff__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a,D: a] :
% 0.17/0.44 ( ( ( minus_minus_a @ A @ B )
% 0.17/0.44 = ( minus_minus_a @ C @ D ) )
% 0.17/0.44 => ( ( A = B )
% 0.17/0.44 = ( C = D ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_diff_eq
% 0.17/0.44 thf(fact_137_diff__eq__diff__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real,D: real] :
% 0.17/0.44 ( ( ( minus_minus_real @ A @ B )
% 0.17/0.44 = ( minus_minus_real @ C @ D ) )
% 0.17/0.44 => ( ( A = B )
% 0.17/0.44 = ( C = D ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_diff_eq
% 0.17/0.44 thf(fact_138_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B )
% 0.17/0.44 = ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.17/0.44 thf(fact_139_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.17/0.44 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.17/0.44 thf(fact_140_eq__iff__diff__eq__0,axiom,
% 0.17/0.44 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.17/0.44 = ( ^ [A3: a,B2: a] :
% 0.17/0.44 ( ( minus_minus_a @ A3 @ B2 )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_iff_diff_eq_0
% 0.17/0.44 thf(fact_141_eq__iff__diff__eq__0,axiom,
% 0.17/0.44 ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
% 0.17/0.44 = ( ^ [A3: real,B2: real] :
% 0.17/0.44 ( ( minus_minus_real @ A3 @ B2 )
% 0.17/0.44 = zero_zero_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_iff_diff_eq_0
% 0.17/0.44 thf(fact_142_minus__diff__commute,axiom,
% 0.17/0.44 ! [B: a,A: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( uminus_uminus_a @ B ) @ A )
% 0.17/0.44 = ( minus_minus_a @ ( uminus_uminus_a @ A ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_diff_commute
% 0.17/0.44 thf(fact_143_minus__diff__commute,axiom,
% 0.17/0.44 ! [B: real,A: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.17/0.44 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_diff_commute
% 0.17/0.44 thf(fact_144_rev_Oclosed__orbit__period__zero__fixed__point,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = zero_zero_real )
% 0.17/0.44 => ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbit_period_zero_fixed_point
% 0.17/0.44 thf(fact_145_closed__orbit__period__zero__fixed__point,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ( ( period1305449585riod_a @ f @ x @ X )
% 0.17/0.44 = zero_zero_real )
% 0.17/0.44 => ( ( f @ X )
% 0.17/0.44 = zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbit_period_zero_fixed_point
% 0.17/0.44 thf(fact_146_rev_Operiodic__orbit__period_I2_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 0.17/0.44 = X ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.periodic_orbit_period(2)
% 0.17/0.44 thf(fact_147_periodic__orbit__period_I2_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( period1305449585riod_a @ f @ x @ X ) )
% 0.17/0.44 = X ) ) ).
% 0.17/0.44
% 0.17/0.44 % periodic_orbit_period(2)
% 0.17/0.44 thf(fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( uminus_uminus_a_a @ f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = zero_zero_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.fixed_point_imp_closed_orbit_period_zero(2)
% 0.17/0.44 thf(fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( member_a @ X @ x )
% 0.17/0.44 => ( ( ( f @ X )
% 0.17/0.44 = zero_zero_a )
% 0.17/0.44 => ( ( period1305449585riod_a @ f @ x @ X )
% 0.17/0.44 = zero_zero_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fixed_point_imp_closed_orbit_period_zero(2)
% 0.17/0.44 thf(fact_150_local_Orev_Oexistence__ivl__notempty,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 0.17/0.44 != bot_bot_set_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_notempty
% 0.17/0.44 thf(fact_151_local_Oexistence__ivl__notempty,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 0.17/0.44 != bot_bot_set_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_notempty
% 0.17/0.44 thf(fact_152_rev_Ogeneral_Oexistence__ivl__trans,axiom,
% 0.17/0.44 ! [S: real,T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.existence_ivl_trans
% 0.17/0.44 thf(fact_153_i2_I2_J,axiom,
% 0.17/0.44 ord_less_real @ zero_zero_real @ i1 ).
% 0.17/0.44
% 0.17/0.44 % i2(2)
% 0.17/0.44 thf(fact_154_add__right__cancel,axiom,
% 0.17/0.44 ! [B: a,A: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ B @ A )
% 0.17/0.44 = ( plus_plus_a @ C @ A ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_right_cancel
% 0.17/0.44 thf(fact_155_add__right__cancel,axiom,
% 0.17/0.44 ! [B: real,A: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ B @ A )
% 0.17/0.44 = ( plus_plus_real @ C @ A ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_right_cancel
% 0.17/0.44 thf(fact_156_add__left__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ A @ B )
% 0.17/0.44 = ( plus_plus_a @ A @ C ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_left_cancel
% 0.17/0.44 thf(fact_157_add__left__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ A @ B )
% 0.17/0.44 = ( plus_plus_real @ A @ C ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_left_cancel
% 0.17/0.44 thf(fact_158_d,axiom,
% 0.17/0.44 ord_less_real @ zero_zero_real @ d ).
% 0.17/0.44
% 0.17/0.44 % d
% 0.17/0.44 thf(fact_159_local_Oflow__trans,axiom,
% 0.17/0.44 ! [S: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( plus_plus_real @ S @ T ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.flow_trans
% 0.17/0.44 thf(fact_160_local_Oexistence__ivl__trans_H,axiom,
% 0.17/0.44 ! [T: real,S: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( plus_plus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_trans'
% 0.17/0.44 thf(fact_161_local_Oexistence__ivl__trans,axiom,
% 0.17/0.44 ! [S: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) )
% 0.17/0.44 => ( member_real @ ( plus_plus_real @ S @ T ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_trans
% 0.17/0.44 thf(fact_162_i2_I3_J,axiom,
% 0.17/0.44 ord_less_real @ i1 @ i2 ).
% 0.17/0.44
% 0.17/0.44 % i2(3)
% 0.17/0.44 thf(fact_163_local_Orev_Oflow__trans,axiom,
% 0.17/0.44 ! [S: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( plus_plus_real @ S @ T ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.flow_trans
% 0.17/0.44 thf(fact_164_local_Orev_Oexistence__ivl__trans_H,axiom,
% 0.17/0.44 ! [T: real,S: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( plus_plus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_trans'
% 0.17/0.44 thf(fact_165_local_Orev_Oexistence__ivl__trans,axiom,
% 0.17/0.44 ! [S: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) )
% 0.17/0.44 => ( member_real @ ( plus_plus_real @ S @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_trans
% 0.17/0.44 thf(fact_166_general_Oflow__trans,axiom,
% 0.17/0.44 ! [S: real,T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.flow_trans
% 0.17/0.44 thf(fact_167_general_Oexistence__ivl__trans_H,axiom,
% 0.17/0.44 ! [T: real,S: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ T @ S ) @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.existence_ivl_trans'
% 0.17/0.44 thf(fact_168_general_Oexistence__ivl__trans,axiom,
% 0.17/0.44 ! [S: real,T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 0.17/0.44 => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % general.existence_ivl_trans
% 0.17/0.44 thf(fact_169_periodic__orbit__period_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ f @ x @ X )
% 0.17/0.44 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % periodic_orbit_period(1)
% 0.17/0.44 thf(fact_170_rev_Ogeneral_Oflow__trans,axiom,
% 0.17/0.44 ! [S: real,T0: real,X0: a,T: real] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 0.17/0.44 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) @ T ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.flow_trans
% 0.17/0.44 thf(fact_171_rev_Ogeneral_Oexistence__ivl__trans_H,axiom,
% 0.17/0.44 ! [T: real,S: real,T0: real,X0: a] :
% 0.17/0.44 ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ T @ S ) @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 0.17/0.44 => ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.general.existence_ivl_trans'
% 0.17/0.44 thf(fact_172_add_Oleft__neutral,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ zero_zero_a @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_neutral
% 0.17/0.44 thf(fact_173_add_Oleft__neutral,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_neutral
% 0.17/0.44 thf(fact_174_add_Oright__neutral,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ zero_zero_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_neutral
% 0.17/0.44 thf(fact_175_add_Oright__neutral,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_neutral
% 0.17/0.44 thf(fact_176_linordered__ab__group__add__class_Odouble__zero,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ A @ A )
% 0.17/0.44 = zero_zero_real )
% 0.17/0.44 = ( A = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % linordered_ab_group_add_class.double_zero
% 0.17/0.44 thf(fact_177_double__zero__sym,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( zero_zero_real
% 0.17/0.44 = ( plus_plus_real @ A @ A ) )
% 0.17/0.44 = ( A = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % double_zero_sym
% 0.17/0.44 thf(fact_178_add__cancel__left__left,axiom,
% 0.17/0.44 ! [B: a,A: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ B @ A )
% 0.17/0.44 = A )
% 0.17/0.44 = ( B = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_left_left
% 0.17/0.44 thf(fact_179_add__cancel__left__left,axiom,
% 0.17/0.44 ! [B: real,A: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ B @ A )
% 0.17/0.44 = A )
% 0.17/0.44 = ( B = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_left_left
% 0.17/0.44 thf(fact_180_add__cancel__left__right,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ A @ B )
% 0.17/0.44 = A )
% 0.17/0.44 = ( B = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_left_right
% 0.17/0.44 thf(fact_181_add__cancel__left__right,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ A @ B )
% 0.17/0.44 = A )
% 0.17/0.44 = ( B = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_left_right
% 0.17/0.44 thf(fact_182_add__cancel__right__left,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( plus_plus_a @ B @ A ) )
% 0.17/0.44 = ( B = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_right_left
% 0.17/0.44 thf(fact_183_add__cancel__right__left,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( plus_plus_real @ B @ A ) )
% 0.17/0.44 = ( B = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_right_left
% 0.17/0.44 thf(fact_184_add__cancel__right__right,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( plus_plus_a @ A @ B ) )
% 0.17/0.44 = ( B = zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_right_right
% 0.17/0.44 thf(fact_185_add__cancel__right__right,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( plus_plus_real @ A @ B ) )
% 0.17/0.44 = ( B = zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_cancel_right_right
% 0.17/0.44 thf(fact_186_neg__less__iff__less,axiom,
% 0.17/0.44 ! [B: a,A: a] :
% 0.17/0.44 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) )
% 0.17/0.44 = ( ord_less_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_less_iff_less
% 0.17/0.44 thf(fact_187_neg__less__iff__less,axiom,
% 0.17/0.44 ! [B: real,A: real] :
% 0.17/0.44 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.17/0.44 = ( ord_less_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_less_iff_less
% 0.17/0.44 thf(fact_188_closed__orbitE,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 => ~ ! [T5: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ T5 )
% 0.17/0.44 => ~ ! [T6: real] :
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( plus_plus_real @ T6 @ T5 ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ X @ T6 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % closed_orbitE
% 0.17/0.44 thf(fact_189_add__less__cancel__right,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 0.17/0.44 = ( ord_less_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_cancel_right
% 0.17/0.44 thf(fact_190_add__less__cancel__right,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.17/0.44 = ( ord_less_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_cancel_right
% 0.17/0.44 thf(fact_191_add__less__cancel__left,axiom,
% 0.17/0.44 ! [C: a,A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 0.17/0.44 = ( ord_less_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_cancel_left
% 0.17/0.44 thf(fact_192_add__less__cancel__left,axiom,
% 0.17/0.44 ! [C: real,A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.17/0.44 = ( ord_less_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_cancel_left
% 0.17/0.44 thf(fact_193_add__minus__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ ( plus_plus_a @ ( uminus_uminus_a @ A ) @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % add_minus_cancel
% 0.17/0.44 thf(fact_194_add__minus__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % add_minus_cancel
% 0.17/0.44 thf(fact_195_minus__add__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( plus_plus_a @ A @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % minus_add_cancel
% 0.17/0.44 thf(fact_196_minus__add__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % minus_add_cancel
% 0.17/0.44 thf(fact_197_minus__add__distrib,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( uminus_uminus_a @ ( plus_plus_a @ A @ B ) )
% 0.17/0.44 = ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_add_distrib
% 0.17/0.44 thf(fact_198_minus__add__distrib,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.17/0.44 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_add_distrib
% 0.17/0.44 thf(fact_199_add__diff__cancel__right_H,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_right'
% 0.17/0.44 thf(fact_200_add__diff__cancel__right_H,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_right'
% 0.17/0.44 thf(fact_201_add__diff__cancel__right,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 0.17/0.44 = ( minus_minus_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_right
% 0.17/0.44 thf(fact_202_add__diff__cancel__right,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.17/0.44 = ( minus_minus_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_right
% 0.17/0.44 thf(fact_203_add__diff__cancel__left_H,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ A )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_left'
% 0.17/0.44 thf(fact_204_add__diff__cancel__left_H,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.17/0.44 = B ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_left'
% 0.17/0.44 thf(fact_205_add__diff__cancel__left,axiom,
% 0.17/0.44 ! [C: a,A: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 0.17/0.44 = ( minus_minus_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_left
% 0.17/0.44 thf(fact_206_add__diff__cancel__left,axiom,
% 0.17/0.44 ! [C: real,A: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.17/0.44 = ( minus_minus_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel_left
% 0.17/0.44 thf(fact_207_diff__add__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( minus_minus_a @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_cancel
% 0.17/0.44 thf(fact_208_diff__add__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_cancel
% 0.17/0.44 thf(fact_209_add__diff__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel
% 0.17/0.44 thf(fact_210_add__diff__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_cancel
% 0.17/0.44 thf(fact_211_rev_Operiodic__orbit__period_I1_J,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.periodic_orbit_period(1)
% 0.17/0.44 thf(fact_212_periodic__orbit__def,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ f @ x @ X )
% 0.17/0.44 = ( ( period720806154rbit_a @ f @ x @ X )
% 0.17/0.44 & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % periodic_orbit_def
% 0.17/0.44 thf(fact_213_tt_I2_J,axiom,
% 0.17/0.44 ord_less_real @ tt @ d ).
% 0.17/0.44
% 0.17/0.44 % tt(2)
% 0.17/0.44 thf(fact_214_rev_Oclosed__orbitE,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 => ~ ! [T5: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ T5 )
% 0.17/0.44 => ~ ! [T6: real] :
% 0.17/0.44 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( plus_plus_real @ T6 @ T5 ) )
% 0.17/0.44 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T6 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.closed_orbitE
% 0.17/0.44 thf(fact_215_rev_Operiodic__orbit__def,axiom,
% 0.17/0.44 ! [X: a] :
% 0.17/0.44 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 = ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 0.17/0.44 & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % rev.periodic_orbit_def
% 0.17/0.44 thf(fact_216_less__neg__neg,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.17/0.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_neg_neg
% 0.17/0.44 thf(fact_217_neg__less__pos,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.17/0.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_less_pos
% 0.17/0.44 thf(fact_218_neg__0__less__iff__less,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
% 0.17/0.44 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_0_less_iff_less
% 0.17/0.44 thf(fact_219_neg__0__less__iff__less,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.17/0.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_0_less_iff_less
% 0.17/0.44 thf(fact_220_neg__less__0__iff__less,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
% 0.17/0.44 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_less_0_iff_less
% 0.17/0.44 thf(fact_221_neg__less__0__iff__less,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.17/0.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % neg_less_0_iff_less
% 0.17/0.44 thf(fact_222_add__less__same__cancel1,axiom,
% 0.17/0.44 ! [B: a,A: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ B @ A ) @ B )
% 0.17/0.44 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_same_cancel1
% 0.17/0.44 thf(fact_223_add__less__same__cancel1,axiom,
% 0.17/0.44 ! [B: real,A: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.17/0.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_same_cancel1
% 0.17/0.44 thf(fact_224_add__less__same__cancel2,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ B )
% 0.17/0.44 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_same_cancel2
% 0.17/0.44 thf(fact_225_add__less__same__cancel2,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.17/0.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_same_cancel2
% 0.17/0.44 thf(fact_226_less__add__same__cancel1,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ ( plus_plus_a @ A @ B ) )
% 0.17/0.44 = ( ord_less_a @ zero_zero_a @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_add_same_cancel1
% 0.17/0.44 thf(fact_227_less__add__same__cancel1,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.17/0.44 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_add_same_cancel1
% 0.17/0.44 thf(fact_228_less__add__same__cancel2,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ ( plus_plus_a @ B @ A ) )
% 0.17/0.44 = ( ord_less_a @ zero_zero_a @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_add_same_cancel2
% 0.17/0.44 thf(fact_229_less__add__same__cancel2,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.17/0.44 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_add_same_cancel2
% 0.17/0.44 thf(fact_230_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.17/0.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % double_add_less_zero_iff_single_add_less_zero
% 0.17/0.44 thf(fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.17/0.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % linordered_ab_group_add_class.zero_less_double_add_iff_zero_less_single_add
% 0.17/0.44 thf(fact_232_diff__gt__0__iff__gt,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
% 0.17/0.44 = ( ord_less_a @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_gt_0_iff_gt
% 0.17/0.44 thf(fact_233_diff__gt__0__iff__gt,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.17/0.44 = ( ord_less_real @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_gt_0_iff_gt
% 0.17/0.44 thf(fact_234_add_Oleft__inverse,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ A )
% 0.17/0.44 = zero_zero_a ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_inverse
% 0.17/0.44 thf(fact_235_add_Oleft__inverse,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.17/0.44 = zero_zero_real ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_inverse
% 0.17/0.44 thf(fact_236_add_Oright__inverse,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ ( uminus_uminus_a @ A ) )
% 0.17/0.44 = zero_zero_a ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_inverse
% 0.17/0.44 thf(fact_237_add_Oright__inverse,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.17/0.44 = zero_zero_real ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_inverse
% 0.17/0.44 thf(fact_238_uminus__add__conv__diff,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ B )
% 0.17/0.44 = ( minus_minus_a @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % uminus_add_conv_diff
% 0.17/0.44 thf(fact_239_uminus__add__conv__diff,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.17/0.44 = ( minus_minus_real @ B @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % uminus_add_conv_diff
% 0.17/0.44 thf(fact_240_diff__minus__eq__add,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ ( uminus_uminus_a @ B ) )
% 0.17/0.44 = ( plus_plus_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_minus_eq_add
% 0.17/0.44 thf(fact_241_diff__minus__eq__add,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.17/0.44 = ( plus_plus_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_minus_eq_add
% 0.17/0.44 thf(fact_242_local_Oexistence__ivl__undefined,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ~ ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_undefined
% 0.17/0.44 thf(fact_243_local_Orev_Oexistence__ivl__undefined,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ~ ( member_a @ X0 @ x )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_undefined
% 0.17/0.44 thf(fact_244_local_Oexistence__ivl__empty__iff,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real )
% 0.17/0.44 = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 | ~ ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_empty_iff
% 0.17/0.44 thf(fact_245_local_Oexistence__ivl__empty1,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.existence_ivl_empty1
% 0.17/0.44 thf(fact_246_local_Orev_Oexistence__ivl__empty__iff,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real )
% 0.17/0.44 = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 | ~ ( member_a @ X0 @ x ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_empty_iff
% 0.17/0.44 thf(fact_247_local_Orev_Oexistence__ivl__empty1,axiom,
% 0.17/0.44 ! [X0: a] :
% 0.17/0.44 ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 0.17/0.44 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 0.17/0.44 = bot_bot_set_real ) ) ).
% 0.17/0.44
% 0.17/0.44 % local.rev.existence_ivl_empty1
% 0.17/0.44 thf(fact_248_add__neg__neg,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ zero_zero_a )
% 0.17/0.44 => ( ( ord_less_a @ B @ zero_zero_a )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_neg_neg
% 0.17/0.44 thf(fact_249_add__neg__neg,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ zero_zero_real )
% 0.17/0.44 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_neg_neg
% 0.17/0.44 thf(fact_250_add__pos__pos,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ zero_zero_a @ A )
% 0.17/0.44 => ( ( ord_less_a @ zero_zero_a @ B )
% 0.17/0.44 => ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_pos_pos
% 0.17/0.44 thf(fact_251_add__pos__pos,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ A )
% 0.17/0.44 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.17/0.44 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_pos_pos
% 0.17/0.44 thf(fact_252_pos__add__strict,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ zero_zero_a @ A )
% 0.17/0.44 => ( ( ord_less_a @ B @ C )
% 0.17/0.44 => ( ord_less_a @ B @ ( plus_plus_a @ A @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pos_add_strict
% 0.17/0.44 thf(fact_253_pos__add__strict,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ zero_zero_real @ A )
% 0.17/0.44 => ( ( ord_less_real @ B @ C )
% 0.17/0.44 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pos_add_strict
% 0.17/0.44 thf(fact_254_add__less__imp__less__right,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 0.17/0.44 => ( ord_less_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_imp_less_right
% 0.17/0.44 thf(fact_255_add__less__imp__less__right,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.17/0.44 => ( ord_less_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_imp_less_right
% 0.17/0.44 thf(fact_256_add__less__imp__less__left,axiom,
% 0.17/0.44 ! [C: a,A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 0.17/0.44 => ( ord_less_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_imp_less_left
% 0.17/0.44 thf(fact_257_add__less__imp__less__left,axiom,
% 0.17/0.44 ! [C: real,A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.17/0.44 => ( ord_less_real @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_less_imp_less_left
% 0.17/0.44 thf(fact_258_add__strict__right__mono,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_right_mono
% 0.17/0.44 thf(fact_259_add__strict__right__mono,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_right_mono
% 0.17/0.44 thf(fact_260_add__strict__left__mono,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_left_mono
% 0.17/0.44 thf(fact_261_add__strict__left__mono,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_left_mono
% 0.17/0.44 thf(fact_262_add__strict__mono,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a,D: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_a @ C @ D )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_mono
% 0.17/0.44 thf(fact_263_add__strict__mono,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real,D: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ( ord_less_real @ C @ D )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_strict_mono
% 0.17/0.44 thf(fact_264_add__right__imp__eq,axiom,
% 0.17/0.44 ! [B: a,A: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ B @ A )
% 0.17/0.44 = ( plus_plus_a @ C @ A ) )
% 0.17/0.44 => ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_right_imp_eq
% 0.17/0.44 thf(fact_265_add__right__imp__eq,axiom,
% 0.17/0.44 ! [B: real,A: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ B @ A )
% 0.17/0.44 = ( plus_plus_real @ C @ A ) )
% 0.17/0.44 => ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_right_imp_eq
% 0.17/0.44 thf(fact_266_add__left__imp__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ A @ B )
% 0.17/0.44 = ( plus_plus_a @ A @ C ) )
% 0.17/0.44 => ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_left_imp_eq
% 0.17/0.44 thf(fact_267_add__left__imp__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ A @ B )
% 0.17/0.44 = ( plus_plus_real @ A @ C ) )
% 0.17/0.44 => ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_left_imp_eq
% 0.17/0.44 thf(fact_268_less__diff__eq,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ ( minus_minus_a @ C @ B ) )
% 0.17/0.44 = ( ord_less_a @ ( plus_plus_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_diff_eq
% 0.17/0.44 thf(fact_269_less__diff__eq,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.17/0.44 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_diff_eq
% 0.17/0.44 thf(fact_270_diff__less__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ ( minus_minus_a @ A @ B ) @ C )
% 0.17/0.44 = ( ord_less_a @ A @ ( plus_plus_a @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_less_eq
% 0.17/0.44 thf(fact_271_diff__less__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.17/0.44 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_less_eq
% 0.17/0.44 thf(fact_272_add_Oleft__commute,axiom,
% 0.17/0.44 ! [B: a,A: a,C: a] :
% 0.17/0.44 ( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) )
% 0.17/0.44 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_commute
% 0.17/0.44 thf(fact_273_add_Oleft__commute,axiom,
% 0.17/0.44 ! [B: real,A: real,C: real] :
% 0.17/0.44 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.17/0.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_commute
% 0.17/0.44 thf(fact_274_add_Ocommute,axiom,
% 0.17/0.44 ( plus_plus_a
% 0.17/0.44 = ( ^ [A3: a,B2: a] : ( plus_plus_a @ B2 @ A3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.commute
% 0.17/0.44 thf(fact_275_add_Ocommute,axiom,
% 0.17/0.44 ( plus_plus_real
% 0.17/0.44 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.commute
% 0.17/0.44 thf(fact_276_add_Oright__cancel,axiom,
% 0.17/0.44 ! [B: a,A: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ B @ A )
% 0.17/0.44 = ( plus_plus_a @ C @ A ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_cancel
% 0.17/0.44 thf(fact_277_add_Oright__cancel,axiom,
% 0.17/0.44 ! [B: real,A: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ B @ A )
% 0.17/0.44 = ( plus_plus_real @ C @ A ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.right_cancel
% 0.17/0.44 thf(fact_278_add_Oleft__cancel,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ A @ B )
% 0.17/0.44 = ( plus_plus_a @ A @ C ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_cancel
% 0.17/0.44 thf(fact_279_add_Oleft__cancel,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ A @ B )
% 0.17/0.44 = ( plus_plus_real @ A @ C ) )
% 0.17/0.44 = ( B = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.left_cancel
% 0.17/0.44 thf(fact_280_add_Oassoc,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
% 0.17/0.44 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.assoc
% 0.17/0.44 thf(fact_281_add_Oassoc,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.17/0.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.assoc
% 0.17/0.44 thf(fact_282_group__cancel_Oadd2,axiom,
% 0.17/0.44 ! [B3: a,K: a,B: a,A: a] :
% 0.17/0.44 ( ( B3
% 0.17/0.44 = ( plus_plus_a @ K @ B ) )
% 0.17/0.44 => ( ( plus_plus_a @ A @ B3 )
% 0.17/0.44 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.add2
% 0.17/0.44 thf(fact_283_group__cancel_Oadd2,axiom,
% 0.17/0.44 ! [B3: real,K: real,B: real,A: real] :
% 0.17/0.44 ( ( B3
% 0.17/0.44 = ( plus_plus_real @ K @ B ) )
% 0.17/0.44 => ( ( plus_plus_real @ A @ B3 )
% 0.17/0.44 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.add2
% 0.17/0.44 thf(fact_284_group__cancel_Oadd1,axiom,
% 0.17/0.44 ! [A2: a,K: a,A: a,B: a] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_a @ K @ A ) )
% 0.17/0.44 => ( ( plus_plus_a @ A2 @ B )
% 0.17/0.44 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.add1
% 0.17/0.44 thf(fact_285_group__cancel_Oadd1,axiom,
% 0.17/0.44 ! [A2: real,K: real,A: real,B: real] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_real @ K @ A ) )
% 0.17/0.44 => ( ( plus_plus_real @ A2 @ B )
% 0.17/0.44 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.add1
% 0.17/0.44 thf(fact_286_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.17/0.44 ! [I: a,J: a,K: a,L: a] :
% 0.17/0.44 ( ( ( I = J )
% 0.17/0.44 & ( K = L ) )
% 0.17/0.44 => ( ( plus_plus_a @ I @ K )
% 0.17/0.44 = ( plus_plus_a @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_semiring(4)
% 0.17/0.44 thf(fact_287_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.17/0.44 ! [I: real,J: real,K: real,L: real] :
% 0.17/0.44 ( ( ( I = J )
% 0.17/0.44 & ( K = L ) )
% 0.17/0.44 => ( ( plus_plus_real @ I @ K )
% 0.17/0.44 = ( plus_plus_real @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_semiring(4)
% 0.17/0.44 thf(fact_288_add__mono__thms__linordered__field_I1_J,axiom,
% 0.17/0.44 ! [I: a,J: a,K: a,L: a] :
% 0.17/0.44 ( ( ( ord_less_a @ I @ J )
% 0.17/0.44 & ( K = L ) )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(1)
% 0.17/0.44 thf(fact_289_add__mono__thms__linordered__field_I1_J,axiom,
% 0.17/0.44 ! [I: real,J: real,K: real,L: real] :
% 0.17/0.44 ( ( ( ord_less_real @ I @ J )
% 0.17/0.44 & ( K = L ) )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(1)
% 0.17/0.44 thf(fact_290_add__mono__thms__linordered__field_I2_J,axiom,
% 0.17/0.44 ! [I: a,J: a,K: a,L: a] :
% 0.17/0.44 ( ( ( I = J )
% 0.17/0.44 & ( ord_less_a @ K @ L ) )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(2)
% 0.17/0.44 thf(fact_291_add__mono__thms__linordered__field_I2_J,axiom,
% 0.17/0.44 ! [I: real,J: real,K: real,L: real] :
% 0.17/0.44 ( ( ( I = J )
% 0.17/0.44 & ( ord_less_real @ K @ L ) )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(2)
% 0.17/0.44 thf(fact_292_add__mono__thms__linordered__field_I5_J,axiom,
% 0.17/0.44 ! [I: a,J: a,K: a,L: a] :
% 0.17/0.44 ( ( ( ord_less_a @ I @ J )
% 0.17/0.44 & ( ord_less_a @ K @ L ) )
% 0.17/0.44 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(5)
% 0.17/0.44 thf(fact_293_add__mono__thms__linordered__field_I5_J,axiom,
% 0.17/0.44 ! [I: real,J: real,K: real,L: real] :
% 0.17/0.44 ( ( ( ord_less_real @ I @ J )
% 0.17/0.44 & ( ord_less_real @ K @ L ) )
% 0.17/0.44 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_mono_thms_linordered_field(5)
% 0.17/0.44 thf(fact_294_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
% 0.17/0.44 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ab_semigroup_add_class.add_ac(1)
% 0.17/0.44 thf(fact_295_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.17/0.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ab_semigroup_add_class.add_ac(1)
% 0.17/0.44 thf(fact_296_verit__comp__simplify1_I1_J,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ~ ( ord_less_a @ A @ A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_comp_simplify1(1)
% 0.17/0.44 thf(fact_297_verit__comp__simplify1_I1_J,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ~ ( ord_less_real @ A @ A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_comp_simplify1(1)
% 0.17/0.44 thf(fact_298_verit__sum__simplify,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ zero_zero_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_sum_simplify
% 0.17/0.44 thf(fact_299_verit__sum__simplify,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_sum_simplify
% 0.17/0.44 thf(fact_300_comm__monoid__add__class_Oadd__0,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ zero_zero_a @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % comm_monoid_add_class.add_0
% 0.17/0.44 thf(fact_301_comm__monoid__add__class_Oadd__0,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % comm_monoid_add_class.add_0
% 0.17/0.44 thf(fact_302_add_Ocomm__neutral,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ zero_zero_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.comm_neutral
% 0.17/0.44 thf(fact_303_add_Ocomm__neutral,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.comm_neutral
% 0.17/0.44 thf(fact_304_add_Ogroup__left__neutral,axiom,
% 0.17/0.44 ! [A: a] :
% 0.17/0.44 ( ( plus_plus_a @ zero_zero_a @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.group_left_neutral
% 0.17/0.44 thf(fact_305_add_Ogroup__left__neutral,axiom,
% 0.17/0.44 ! [A: real] :
% 0.17/0.44 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.group_left_neutral
% 0.17/0.44 thf(fact_306_verit__negate__coefficient_I2_J,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_negate_coefficient(2)
% 0.17/0.44 thf(fact_307_verit__negate__coefficient_I2_J,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % verit_negate_coefficient(2)
% 0.17/0.44 thf(fact_308_less__minus__iff,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
% 0.17/0.44 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_minus_iff
% 0.17/0.44 thf(fact_309_less__minus__iff,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.17/0.44 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_minus_iff
% 0.17/0.44 thf(fact_310_minus__less__iff,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
% 0.17/0.44 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_less_iff
% 0.17/0.44 thf(fact_311_minus__less__iff,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.17/0.44 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % minus_less_iff
% 0.17/0.44 thf(fact_312_diff__strict__right__mono,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_right_mono
% 0.17/0.44 thf(fact_313_diff__strict__right__mono,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_right_mono
% 0.17/0.44 thf(fact_314_diff__strict__left__mono,axiom,
% 0.17/0.44 ! [B: a,A: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ B @ A )
% 0.17/0.44 => ( ord_less_a @ ( minus_minus_a @ C @ A ) @ ( minus_minus_a @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_left_mono
% 0.17/0.44 thf(fact_315_diff__strict__left__mono,axiom,
% 0.17/0.44 ! [B: real,A: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ B @ A )
% 0.17/0.44 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_left_mono
% 0.17/0.44 thf(fact_316_diff__eq__diff__less,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a,D: a] :
% 0.17/0.44 ( ( ( minus_minus_a @ A @ B )
% 0.17/0.44 = ( minus_minus_a @ C @ D ) )
% 0.17/0.44 => ( ( ord_less_a @ A @ B )
% 0.17/0.44 = ( ord_less_a @ C @ D ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_diff_less
% 0.17/0.44 thf(fact_317_diff__eq__diff__less,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real,D: real] :
% 0.17/0.44 ( ( ( minus_minus_real @ A @ B )
% 0.17/0.44 = ( minus_minus_real @ C @ D ) )
% 0.17/0.44 => ( ( ord_less_real @ A @ B )
% 0.17/0.44 = ( ord_less_real @ C @ D ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_diff_less
% 0.17/0.44 thf(fact_318_diff__strict__mono,axiom,
% 0.17/0.44 ! [A: a,B: a,D: a,C: a] :
% 0.17/0.44 ( ( ord_less_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_a @ D @ C )
% 0.17/0.44 => ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_mono
% 0.17/0.44 thf(fact_319_diff__strict__mono,axiom,
% 0.17/0.44 ! [A: real,B: real,D: real,C: real] :
% 0.17/0.44 ( ( ord_less_real @ A @ B )
% 0.17/0.44 => ( ( ord_less_real @ D @ C )
% 0.17/0.44 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_strict_mono
% 0.17/0.44 thf(fact_320_group__cancel_Oneg1,axiom,
% 0.17/0.44 ! [A2: a,K: a,A: a] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_a @ K @ A ) )
% 0.17/0.44 => ( ( uminus_uminus_a @ A2 )
% 0.17/0.44 = ( plus_plus_a @ ( uminus_uminus_a @ K ) @ ( uminus_uminus_a @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.neg1
% 0.17/0.44 thf(fact_321_group__cancel_Oneg1,axiom,
% 0.17/0.44 ! [A2: real,K: real,A: real] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_real @ K @ A ) )
% 0.17/0.44 => ( ( uminus_uminus_real @ A2 )
% 0.17/0.44 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.neg1
% 0.17/0.44 thf(fact_322_add_Oinverse__distrib__swap,axiom,
% 0.17/0.44 ! [A: a,B: a] :
% 0.17/0.44 ( ( uminus_uminus_a @ ( plus_plus_a @ A @ B ) )
% 0.17/0.44 = ( plus_plus_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_distrib_swap
% 0.17/0.44 thf(fact_323_add_Oinverse__distrib__swap,axiom,
% 0.17/0.44 ! [A: real,B: real] :
% 0.17/0.44 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.17/0.44 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add.inverse_distrib_swap
% 0.17/0.44 thf(fact_324_add__implies__diff,axiom,
% 0.17/0.44 ! [C: a,B: a,A: a] :
% 0.17/0.44 ( ( ( plus_plus_a @ C @ B )
% 0.17/0.44 = A )
% 0.17/0.44 => ( C
% 0.17/0.44 = ( minus_minus_a @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_implies_diff
% 0.17/0.44 thf(fact_325_add__implies__diff,axiom,
% 0.17/0.44 ! [C: real,B: real,A: real] :
% 0.17/0.44 ( ( ( plus_plus_real @ C @ B )
% 0.17/0.44 = A )
% 0.17/0.44 => ( C
% 0.17/0.44 = ( minus_minus_real @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_implies_diff
% 0.17/0.44 thf(fact_326_diff__diff__add,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C )
% 0.17/0.44 = ( minus_minus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_diff_add
% 0.17/0.44 thf(fact_327_diff__diff__add,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.17/0.44 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_diff_add
% 0.17/0.44 thf(fact_328_diff__add__eq__diff__diff__swap,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ ( plus_plus_a @ B @ C ) )
% 0.17/0.44 = ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_eq_diff_diff_swap
% 0.17/0.44 thf(fact_329_diff__add__eq__diff__diff__swap,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.17/0.44 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_eq_diff_diff_swap
% 0.17/0.44 thf(fact_330_diff__add__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( plus_plus_a @ ( minus_minus_a @ A @ B ) @ C )
% 0.17/0.44 = ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_eq
% 0.17/0.44 thf(fact_331_diff__add__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.17/0.44 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_add_eq
% 0.17/0.44 thf(fact_332_diff__diff__eq2,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( minus_minus_a @ A @ ( minus_minus_a @ B @ C ) )
% 0.17/0.44 = ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_diff_eq2
% 0.17/0.44 thf(fact_333_diff__diff__eq2,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.17/0.44 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_diff_eq2
% 0.17/0.44 thf(fact_334_add__diff__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( plus_plus_a @ A @ ( minus_minus_a @ B @ C ) )
% 0.17/0.44 = ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_eq
% 0.17/0.44 thf(fact_335_add__diff__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.17/0.44 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_diff_eq
% 0.17/0.44 thf(fact_336_eq__diff__eq,axiom,
% 0.17/0.44 ! [A: a,C: a,B: a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( minus_minus_a @ C @ B ) )
% 0.17/0.44 = ( ( plus_plus_a @ A @ B )
% 0.17/0.44 = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_diff_eq
% 0.17/0.44 thf(fact_337_eq__diff__eq,axiom,
% 0.17/0.44 ! [A: real,C: real,B: real] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( minus_minus_real @ C @ B ) )
% 0.17/0.44 = ( ( plus_plus_real @ A @ B )
% 0.17/0.44 = C ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_diff_eq
% 0.17/0.44 thf(fact_338_diff__eq__eq,axiom,
% 0.17/0.44 ! [A: a,B: a,C: a] :
% 0.17/0.44 ( ( ( minus_minus_a @ A @ B )
% 0.17/0.44 = C )
% 0.17/0.44 = ( A
% 0.17/0.44 = ( plus_plus_a @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_eq
% 0.17/0.44 thf(fact_339_diff__eq__eq,axiom,
% 0.17/0.44 ! [A: real,B: real,C: real] :
% 0.17/0.44 ( ( ( minus_minus_real @ A @ B )
% 0.17/0.44 = C )
% 0.17/0.44 = ( A
% 0.17/0.44 = ( plus_plus_real @ C @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_eq_eq
% 0.17/0.44 thf(fact_340_group__cancel_Osub1,axiom,
% 0.17/0.44 ! [A2: a,K: a,A: a,B: a] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_a @ K @ A ) )
% 0.17/0.44 => ( ( minus_minus_a @ A2 @ B )
% 0.17/0.44 = ( plus_plus_a @ K @ ( minus_minus_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.sub1
% 0.17/0.44 thf(fact_341_group__cancel_Osub1,axiom,
% 0.17/0.44 ! [A2: real,K: real,A: real,B: real] :
% 0.17/0.44 ( ( A2
% 0.17/0.44 = ( plus_plus_real @ K @ A ) )
% 0.17/0.44 => ( ( minus_minus_real @ A2 @ B )
% 0.17/0.44 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % group_cancel.sub1
% 0.17/0.44
% 0.17/0.44 % Conjectures (1)
% 0.17/0.44 thf(conj_0,conjecture,
% 0.17/0.44 ( xx
% 0.17/0.44 = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 2.68/1.48 ---- Embedded in THF ---
% 2.68/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.68/1.48 %%% Generated on Tue Feb 24 08:27:52 EST 2026
% 2.68/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.68/1.48 %%% Logic specification used:
% 2.68/1.48 %%% thf(spec, logic, $$dhol).
% 2.68/1.48
% 2.68/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2DTF28498.p
% See solution above
% 2.68/1.49 ------------------------
% 2.80/1.51 ---- Cleaned THF ---
% 2.80/1.51 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 2.80/1.51 set_real: $tType ).
% 2.80/1.51
% 2.80/1.51 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.80/1.51 set_a: $tType ).
% 2.80/1.51
% 2.80/1.51 thf(ty_n_t__Real__Oreal,type,
% 2.80/1.51 real: $tType ).
% 2.80/1.51
% 2.80/1.51 thf(ty_n_tf__a,type,
% 2.80/1.51 a: $tType ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Flow_Oauto__ll__on__open_Oexistence__ivl0_001tf__a,type,
% 2.80/1.51 auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Flow_Oauto__ll__on__open_Oflow0_001tf__a,type,
% 2.80/1.51 auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 2.80/1.51 minus_minus_real: real > real > real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ominus__class_Ominus_001tf__a,type,
% 2.80/1.51 minus_minus_a: a > a > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 2.80/1.51 plus_plus_real: real > real > real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Oplus__class_Oplus_001tf__a,type,
% 2.80/1.51 plus_plus_a: a > a > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_Itf__a_Mtf__a_J,type,
% 2.80/1.51 uminus_uminus_a_a: ( a > a ) > a > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 2.80/1.51 uminus_uminus_real: real > real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type,
% 2.80/1.51 uminus_uminus_a: a > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 2.80/1.51 zero_zero_real: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 2.80/1.51 zero_zero_a: a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Initial__Value__Problem_Ointerval,type,
% 2.80/1.51 initia826609931terval: set_real > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 2.80/1.51 bot_bot_set_real: set_real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 2.80/1.51 ord_less_real: real > real > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type,
% 2.80/1.51 ord_less_a: a > a > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 2.80/1.51 top_top_set_real: set_real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Oclosed__orbit_001tf__a,type,
% 2.80/1.51 period720806154rbit_a: ( a > a ) > set_a > a > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiod_001tf__a,type,
% 2.80/1.51 period1305449585riod_a: ( a > a ) > set_a > a > real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiodic__orbit_001tf__a,type,
% 2.80/1.51 period138238489rbit_a: ( a > a ) > set_a > a > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 2.80/1.51 collect_real: ( real > $o ) > set_real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.80/1.51 collect_a: ( a > $o ) > set_a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_member_001t__Real__Oreal,type,
% 2.80/1.51 member_real: real > set_real > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_c_member_001tf__a,type,
% 2.80/1.51 member_a: a > set_a > $o ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_X,type,
% 2.80/1.51 x: set_a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_d____,type,
% 2.80/1.51 d: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_f,type,
% 2.80/1.51 f: a > a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_i1____,type,
% 2.80/1.51 i1: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_i2____,type,
% 2.80/1.51 i2: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_ss____,type,
% 2.80/1.51 ss: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_t,type,
% 2.80/1.51 t: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_tt____,type,
% 2.80/1.51 tt: real ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_x,type,
% 2.80/1.51 x2: a ).
% 2.80/1.51
% 2.80/1.51 thf(sy_v_xx____,type,
% 2.80/1.51 xx: a ).
% 2.80/1.51
% 2.80/1.51 thf(fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062,axiom,
% 2.80/1.51 member_a @ xx @ x ).
% 2.80/1.51
% 2.80/1.51 thf(fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062,axiom,
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_2_eq,axiom,
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_3_assms_I8_J,axiom,
% 2.80/1.51 member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_4_tt__ex,axiom,
% 2.80/1.51 member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_5_ss__ex,axiom,
% 2.80/1.51 member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_6_fixpoint__sol_I2_J,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ T )
% 2.80/1.51 = X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_7_neg__tt__ex,axiom,
% 2.80/1.51 member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_8_diff__existence__ivl__trans,axiom,
% 2.80/1.51 ! [T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ T0 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T0 ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_9_general_Oexistence__ivl__reverse,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T0 @ T ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_10_general_Oflow__in__domain,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_11_general_Oflows__reverse,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ ( minus_minus_real @ T0 @ T ) )
% 2.80/1.51 = X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_12_general_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ X0 @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_13_closed__orbit__flow0,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X @ T ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_14_closed__orbit__in__domain,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ( member_a @ X @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( period720806154rbit_a @ f @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_16_recurrence__time__flip__sign_I1_J,axiom,
% 2.80/1.51 ! [T2: real,X: a] :
% 2.80/1.51 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 )
% 2.80/1.51 = X )
% 2.80/1.51 => ( member_real @ ( uminus_uminus_real @ T2 ) @ ( auto_l612940ivl0_a @ f @ x @ X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_17_recurrence__time__flip__sign_I2_J,axiom,
% 2.80/1.51 ! [T2: real,X: a] :
% 2.80/1.51 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 )
% 2.80/1.51 = X )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( uminus_uminus_real @ T2 ) )
% 2.80/1.51 = X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_18_local_Oflow__undefined0,axiom,
% 2.80/1.51 ! [T: real,X: a] :
% 2.80/1.51 ( ~ ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ T )
% 2.80/1.51 = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_19_closed__orbitI,axiom,
% 2.80/1.51 ! [T: real,T3: real,Y: a] :
% 2.80/1.51 ( ( T != T3 )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 2.80/1.51 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) )
% 2.80/1.51 => ( period720806154rbit_a @ f @ x @ Y ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_20_general_Oflow__undefined0,axiom,
% 2.80/1.51 ! [T: real,T0: real,X: a] :
% 2.80/1.51 ( ~ ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ T0 ) )
% 2.80/1.51 = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_21_local_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ X0 @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_22_local_Oflow__in__domain,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_23_flow0__defined,axiom,
% 2.80/1.51 ! [Xa: real,X0: a] :
% 2.80/1.51 ( ( member_real @ Xa @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ Xa ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_24_mvar_Ointerval__axioms,axiom,
% 2.80/1.51 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_25_periodic__orbitI,axiom,
% 2.80/1.51 ! [T: real,T3: real,Y: a] :
% 2.80/1.51 ( ( T != T3 )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 2.80/1.51 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) )
% 2.80/1.51 => ( ( ( f @ Y )
% 2.80/1.51 != zero_zero_a )
% 2.80/1.51 => ( period138238489rbit_a @ f @ x @ Y ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_26_closed__orbit__periodic,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ( ( f @ X )
% 2.80/1.51 != zero_zero_a )
% 2.80/1.51 => ( period138238489rbit_a @ f @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_27_periodic__orbit__imp__flow0__regular,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( period138238489rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ X @ T ) )
% 2.80/1.51 != zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_28_diff__0,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( minus_minus_a @ zero_zero_a @ A )
% 2.80/1.51 = ( uminus_uminus_a @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_29_diff__0,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( minus_minus_real @ zero_zero_real @ A )
% 2.80/1.51 = ( uminus_uminus_real @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_30_verit__minus__simplify_I3_J,axiom,
% 2.80/1.51 ! [B: a] :
% 2.80/1.51 ( ( minus_minus_a @ zero_zero_a @ B )
% 2.80/1.51 = ( uminus_uminus_a @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_31_verit__minus__simplify_I3_J,axiom,
% 2.80/1.51 ! [B: real] :
% 2.80/1.51 ( ( minus_minus_real @ zero_zero_real @ B )
% 2.80/1.51 = ( uminus_uminus_real @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_32_closed__orbit__def,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 = ( ? [X2: real] :
% 2.80/1.51 ( ( member_real @ X2 @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 & ( X2 != zero_zero_real )
% 2.80/1.51 & ( ( auto_ll_on_flow0_a @ f @ x @ X @ X2 )
% 2.80/1.51 = X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_33_local_Oflows__reverse,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) @ ( minus_minus_real @ zero_zero_real @ T ) )
% 2.80/1.51 = X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_34_local_Oexistence__ivl__reverse,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ zero_zero_real @ T ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_35_general_Oflow__initial__time__if,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = X0 ) )
% 2.80/1.51 & ( ~ ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_36_interval__axioms,axiom,
% 2.80/1.51 initia826609931terval @ top_top_set_real ).
% 2.80/1.51
% 2.80/1.51 thf(fact_37_rev_Oclosed__orbit__eq__rev,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = ( period720806154rbit_a @ f @ x @ X ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_38_rev_Oclosed__orbit__in__domain,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( member_a @ X @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_39_neg__equal__iff__equal,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ( uminus_uminus_a @ A )
% 2.80/1.51 = ( uminus_uminus_a @ B ) )
% 2.80/1.51 = ( A = B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_40_neg__equal__iff__equal,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ( uminus_uminus_real @ A )
% 2.80/1.51 = ( uminus_uminus_real @ B ) )
% 2.80/1.51 = ( A = B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_41_add_Oinverse__inverse,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_42_add_Oinverse__inverse,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_43_verit__minus__simplify_I4_J,axiom,
% 2.80/1.51 ! [B: a] :
% 2.80/1.51 ( ( uminus_uminus_a @ ( uminus_uminus_a @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_44_verit__minus__simplify_I4_J,axiom,
% 2.80/1.51 ! [B: real] :
% 2.80/1.51 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_45_rev_Oexistence__ivl__zero,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_46_mem__Collect__eq,axiom,
% 2.80/1.51 ! [A: a,P: a > $o] :
% 2.80/1.51 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.80/1.51 = ( P @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_47_mem__Collect__eq,axiom,
% 2.80/1.51 ! [A: real,P: real > $o] :
% 2.80/1.51 ( ( member_real @ A @ ( collect_real @ P ) )
% 2.80/1.51 = ( P @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_48_Collect__mem__eq,axiom,
% 2.80/1.51 ! [A2: set_a] :
% 2.80/1.51 ( ( collect_a
% 2.80/1.51 @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
% 2.80/1.51 = A2 ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_49_Collect__mem__eq,axiom,
% 2.80/1.51 ! [A2: set_real] :
% 2.80/1.51 ( ( collect_real
% 2.80/1.51 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 2.80/1.51 = A2 ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_50_Collect__cong,axiom,
% 2.80/1.51 ! [P: real > $o,Q: real > $o] :
% 2.80/1.51 ( ! [X3: real] :
% 2.80/1.51 ( ( P @ X3 )
% 2.80/1.51 = ( Q @ X3 ) )
% 2.80/1.51 => ( ( collect_real @ P )
% 2.80/1.51 = ( collect_real @ Q ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_51_Collect__cong,axiom,
% 2.80/1.51 ! [P: a > $o,Q: a > $o] :
% 2.80/1.51 ( ! [X3: a] :
% 2.80/1.51 ( ( P @ X3 )
% 2.80/1.51 = ( Q @ X3 ) )
% 2.80/1.51 => ( ( collect_a @ P )
% 2.80/1.51 = ( collect_a @ Q ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_52_existence__ivl__zero,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ X0 @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_54_local_Orev_Omem__existence__ivl__subset,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_55_local_Omem__existence__ivl__subset,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_56_rev_Orev__eq__flow,axiom,
% 2.80/1.51 ! [Y: a,T: real] :
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ ( uminus_uminus_real @ T ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_57_rev__eq__flow,axiom,
% 2.80/1.51 ! [Y: a,T: real] :
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ Y @ ( uminus_uminus_real @ T ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_58_rev_Ofixpoint__sol_I2_J,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T )
% 2.80/1.51 = X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_59_rev_Oclosed__orbit__flow0,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_60_rev_Omvar_Ointerval__axioms,axiom,
% 2.80/1.51 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_62_local_Orev_Oexistence__ivl__initial__time,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_63_local_Oexistence__ivl__initial__time,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T0 @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_65_rev_Ogeneral_Oexistence__ivl__initial__time,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_66_rev_Omem__existence__ivl__shift__autonomous2,axiom,
% 2.80/1.51 ! [T: real,S: real,X: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( member_a @ X @ x )
% 2.80/1.51 => ( ! [S2: real,T4: real,X3: a] :
% 2.80/1.51 ( ( member_a @ X3 @ x )
% 2.80/1.51 => ( ( uminus_uminus_a_a @ f @ X3 )
% 2.80/1.51 = ( uminus_uminus_a_a @ f @ X3 ) ) )
% 2.80/1.51 => ( ( top_top_set_real = top_top_set_real )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_67_rev_Ogeneral_Omem__existence__ivl__subset,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_68_general_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T0 @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_69_general_Oexistence__ivl__initial__time,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_70_mem__existence__ivl__shift__autonomous2,axiom,
% 2.80/1.51 ! [T: real,S: real,X: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( member_a @ X @ x )
% 2.80/1.51 => ( ! [S2: real,T4: real,X3: a] :
% 2.80/1.51 ( ( member_a @ X3 @ x )
% 2.80/1.51 => ( ( f @ X3 )
% 2.80/1.51 = ( f @ X3 ) ) )
% 2.80/1.51 => ( ( top_top_set_real = top_top_set_real )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_71_general_Omem__existence__ivl__subset,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ T @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_72_rev_Odiff__existence__ivl__trans,axiom,
% 2.80/1.51 ! [T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ T0 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T0 ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_73_rev_Ogeneral_Oexistence__ivl__reverse,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ T0 @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_74_rev_Ogeneral_Oflow__in__domain,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_75_rev_Ogeneral_Oflows__reverse,axiom,
% 2.80/1.51 ! [T: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) @ ( minus_minus_real @ T0 @ T ) )
% 2.80/1.51 = X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_76_rev_Orecurrence__time__flip__sign_I2_J,axiom,
% 2.80/1.51 ! [T2: real,X: a] :
% 2.80/1.51 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 )
% 2.80/1.51 = X )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( uminus_uminus_real @ T2 ) )
% 2.80/1.51 = X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_77_rev_Orecurrence__time__flip__sign_I1_J,axiom,
% 2.80/1.51 ! [T2: real,X: a] :
% 2.80/1.51 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 )
% 2.80/1.51 = X )
% 2.80/1.51 => ( member_real @ ( uminus_uminus_real @ T2 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_78_rev_Ofixpoint__sol_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = top_top_set_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_79_fixpoint__sol_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ f @ x @ X )
% 2.80/1.51 = top_top_set_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_80_local_Orev_Oflow__undefined0,axiom,
% 2.80/1.51 ! [T: real,X: a] :
% 2.80/1.51 ( ~ ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T )
% 2.80/1.51 = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_81_rev_Oclosed__orbit__global__existence,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_82_closed__orbit__global__existence,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ f @ x @ X )
% 2.80/1.51 = top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_83_rev_Oclosed__orbitI,axiom,
% 2.80/1.51 ! [T: real,T3: real,Y: a] :
% 2.80/1.51 ( ( T != T3 )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 2.80/1.51 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) )
% 2.80/1.51 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_84_rev_Operiodic__orbit__imp__flow0__regular,axiom,
% 2.80/1.51 ! [X: a,T: real] :
% 2.80/1.51 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T ) )
% 2.80/1.51 != zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_85_rev_Oclosed__orbit__periodic,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 != zero_zero_a )
% 2.80/1.51 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_86_local_Orev_Oexistence__ivl__reverse,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ zero_zero_real @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_87_local_Orev_Oflows__reverse,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) @ ( minus_minus_real @ zero_zero_real @ T ) )
% 2.80/1.51 = X0 ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_88_rev_Oflow__shift__autonomous2,axiom,
% 2.80/1.51 ! [T: real,S: real,X: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( member_a @ X @ x )
% 2.80/1.51 => ( ! [S2: real,T4: real,X3: a] :
% 2.80/1.51 ( ( member_a @ X3 @ x )
% 2.80/1.51 => ( ( uminus_uminus_a_a @ f @ X3 )
% 2.80/1.51 = ( uminus_uminus_a_a @ f @ X3 ) ) )
% 2.80/1.51 => ( ( top_top_set_real = top_top_set_real )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ S ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ S ) ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_89_flow__shift__autonomous2,axiom,
% 2.80/1.51 ! [T: real,S: real,X: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X ) )
% 2.80/1.51 => ( ( member_a @ X @ x )
% 2.80/1.51 => ( ! [S2: real,T4: real,X3: a] :
% 2.80/1.51 ( ( member_a @ X3 @ x )
% 2.80/1.51 => ( ( f @ X3 )
% 2.80/1.51 = ( f @ X3 ) ) )
% 2.80/1.51 => ( ( top_top_set_real = top_top_set_real )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ S ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ X @ ( minus_minus_real @ T @ S ) ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_90_local_Orev_Oflow__initial__time__if,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = X0 ) )
% 2.80/1.51 & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_91_local_Oflow__initial__time__if,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = X0 ) )
% 2.80/1.51 & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_92_rev_Oclosed__orbit__def,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = ( ? [X2: real] :
% 2.80/1.51 ( ( member_real @ X2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 & ( X2 != zero_zero_real )
% 2.80/1.51 & ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ X2 )
% 2.80/1.51 = X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_93_rev_Ogeneral_Oflow__undefined0,axiom,
% 2.80/1.51 ! [T: real,T0: real,X: a] :
% 2.80/1.51 ( ~ ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( minus_minus_real @ T @ T0 ) )
% 2.80/1.51 = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_94_rev_Ogeneral_Oflow__initial__time__if,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = X0 ) )
% 2.80/1.51 & ( ~ ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_95_rev_Operiodic__orbitI,axiom,
% 2.80/1.51 ! [T: real,T3: real,Y: a] :
% 2.80/1.51 ( ( T != T3 )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 2.80/1.51 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) )
% 2.80/1.51 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ Y )
% 2.80/1.51 != zero_zero_a )
% 2.80/1.51 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_96_neg__equal__zero,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ( uminus_uminus_real @ A )
% 2.80/1.51 = A )
% 2.80/1.51 = ( A = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_97_equal__neg__zero,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( uminus_uminus_real @ A ) )
% 2.80/1.51 = ( A = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_98_neg__equal__0__iff__equal,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( ( uminus_uminus_a @ A )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 = ( A = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_99_neg__equal__0__iff__equal,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ( uminus_uminus_real @ A )
% 2.80/1.51 = zero_zero_real )
% 2.80/1.51 = ( A = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_100_neg__0__equal__iff__equal,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( zero_zero_a
% 2.80/1.51 = ( uminus_uminus_a @ A ) )
% 2.80/1.51 = ( zero_zero_a = A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_101_neg__0__equal__iff__equal,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( zero_zero_real
% 2.80/1.51 = ( uminus_uminus_real @ A ) )
% 2.80/1.51 = ( zero_zero_real = A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_102_add_Oinverse__neutral,axiom,
% 2.80/1.51 ( ( uminus_uminus_a @ zero_zero_a )
% 2.80/1.51 = zero_zero_a ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_103_add_Oinverse__neutral,axiom,
% 2.80/1.51 ( ( uminus_uminus_real @ zero_zero_real )
% 2.80/1.51 = zero_zero_real ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_104_diff__self,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ A )
% 2.80/1.51 = zero_zero_a ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_105_diff__self,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ A )
% 2.80/1.51 = zero_zero_real ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_106_diff__0__right,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ zero_zero_a )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_107_diff__0__right,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_108_diff__zero,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ zero_zero_a )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_109_diff__zero,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_110_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ A )
% 2.80/1.51 = zero_zero_a ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_111_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ A )
% 2.80/1.51 = zero_zero_real ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_112_minus__diff__eq,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( uminus_uminus_a @ ( minus_minus_a @ A @ B ) )
% 2.80/1.51 = ( minus_minus_a @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_113_minus__diff__eq,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 2.80/1.51 = ( minus_minus_real @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_114_tt_I1_J,axiom,
% 2.80/1.51 ord_less_real @ zero_zero_real @ tt ).
% 2.80/1.51
% 2.80/1.51 thf(fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ X0 @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_116_rev_Oflow0__defined,axiom,
% 2.80/1.51 ! [Xa: real,X0: a] :
% 2.80/1.51 ( ( member_real @ Xa @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ Xa ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_117_local_Orev_Oflow__in__domain,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) @ x ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ zero_zero_real @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_119_local_Orev_Oexistence__ivl__initial__time__iff,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 = ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_120_local_Omem__existence__ivl__iv__defined_I1_J,axiom,
% 2.80/1.51 ! [T: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ zero_zero_real @ top_top_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_121_local_Oexistence__ivl__initial__time__iff,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 = ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_122_local_Orev_Oflow__initial__time,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_123_local_Oflow__initial__time,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real )
% 2.80/1.51 = X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 = ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_125_general_Oexistence__ivl__initial__time__iff,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ T0 @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 = ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 & ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_126_rev_Ogeneral_Oflow__initial__time,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_127_general_Oflow__initial__time,axiom,
% 2.80/1.51 ! [T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ T0 @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T0 @ T0 ) )
% 2.80/1.51 = X0 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_128_zero__reorient,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( zero_zero_a = X )
% 2.80/1.51 = ( X = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_129_zero__reorient,axiom,
% 2.80/1.51 ! [X: real] :
% 2.80/1.51 ( ( zero_zero_real = X )
% 2.80/1.51 = ( X = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_130_minus__equation__iff,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ( uminus_uminus_a @ A )
% 2.80/1.51 = B )
% 2.80/1.51 = ( ( uminus_uminus_a @ B )
% 2.80/1.51 = A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_131_minus__equation__iff,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ( uminus_uminus_real @ A )
% 2.80/1.51 = B )
% 2.80/1.51 = ( ( uminus_uminus_real @ B )
% 2.80/1.51 = A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_132_equation__minus__iff,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( uminus_uminus_a @ B ) )
% 2.80/1.51 = ( B
% 2.80/1.51 = ( uminus_uminus_a @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_133_equation__minus__iff,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( uminus_uminus_real @ B ) )
% 2.80/1.51 = ( B
% 2.80/1.51 = ( uminus_uminus_real @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_134_verit__negate__coefficient_I3_J,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( A = B )
% 2.80/1.51 => ( ( uminus_uminus_a @ A )
% 2.80/1.51 = ( uminus_uminus_a @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_135_verit__negate__coefficient_I3_J,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( A = B )
% 2.80/1.51 => ( ( uminus_uminus_real @ A )
% 2.80/1.51 = ( uminus_uminus_real @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_136_diff__eq__diff__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a,D: a] :
% 2.80/1.51 ( ( ( minus_minus_a @ A @ B )
% 2.80/1.51 = ( minus_minus_a @ C @ D ) )
% 2.80/1.51 => ( ( A = B )
% 2.80/1.51 = ( C = D ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_137_diff__eq__diff__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real,D: real] :
% 2.80/1.51 ( ( ( minus_minus_real @ A @ B )
% 2.80/1.51 = ( minus_minus_real @ C @ D ) )
% 2.80/1.51 => ( ( A = B )
% 2.80/1.51 = ( C = D ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_138_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B )
% 2.80/1.51 = ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_139_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 2.80/1.51 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_140_eq__iff__diff__eq__0,axiom,
% 2.80/1.51 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.80/1.51 = ( ^ [A3: a,B2: a] :
% 2.80/1.51 ( ( minus_minus_a @ A3 @ B2 )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_141_eq__iff__diff__eq__0,axiom,
% 2.80/1.51 ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
% 2.80/1.51 = ( ^ [A3: real,B2: real] :
% 2.80/1.51 ( ( minus_minus_real @ A3 @ B2 )
% 2.80/1.51 = zero_zero_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_142_minus__diff__commute,axiom,
% 2.80/1.51 ! [B: a,A: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( uminus_uminus_a @ B ) @ A )
% 2.80/1.51 = ( minus_minus_a @ ( uminus_uminus_a @ A ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_143_minus__diff__commute,axiom,
% 2.80/1.51 ! [B: real,A: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 2.80/1.51 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_144_rev_Oclosed__orbit__period__zero__fixed__point,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = zero_zero_real )
% 2.80/1.51 => ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_145_closed__orbit__period__zero__fixed__point,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ( ( period1305449585riod_a @ f @ x @ X )
% 2.80/1.51 = zero_zero_real )
% 2.80/1.51 => ( ( f @ X )
% 2.80/1.51 = zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_146_rev_Operiodic__orbit__period_I2_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) )
% 2.80/1.51 = X ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_147_periodic__orbit__period_I2_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( period1305449585riod_a @ f @ x @ X ) )
% 2.80/1.51 = X ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( uminus_uminus_a_a @ f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = zero_zero_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( member_a @ X @ x )
% 2.80/1.51 => ( ( ( f @ X )
% 2.80/1.51 = zero_zero_a )
% 2.80/1.51 => ( ( period1305449585riod_a @ f @ x @ X )
% 2.80/1.51 = zero_zero_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_150_local_Orev_Oexistence__ivl__notempty,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 2.80/1.51 != bot_bot_set_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_151_local_Oexistence__ivl__notempty,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 2.80/1.51 != bot_bot_set_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_152_rev_Ogeneral_Oexistence__ivl__trans,axiom,
% 2.80/1.51 ! [S: real,T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_153_i2_I2_J,axiom,
% 2.80/1.51 ord_less_real @ zero_zero_real @ i1 ).
% 2.80/1.51
% 2.80/1.51 thf(fact_154_add__right__cancel,axiom,
% 2.80/1.51 ! [B: a,A: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ B @ A )
% 2.80/1.51 = ( plus_plus_a @ C @ A ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_155_add__right__cancel,axiom,
% 2.80/1.51 ! [B: real,A: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ B @ A )
% 2.80/1.51 = ( plus_plus_real @ C @ A ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_156_add__left__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ A @ B )
% 2.80/1.51 = ( plus_plus_a @ A @ C ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_157_add__left__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ A @ B )
% 2.80/1.51 = ( plus_plus_real @ A @ C ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_158_d,axiom,
% 2.80/1.51 ord_less_real @ zero_zero_real @ d ).
% 2.80/1.51
% 2.80/1.51 thf(fact_159_local_Oflow__trans,axiom,
% 2.80/1.51 ! [S: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( plus_plus_real @ S @ T ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_160_local_Oexistence__ivl__trans_H,axiom,
% 2.80/1.51 ! [T: real,S: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( plus_plus_real @ T @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_161_local_Oexistence__ivl__trans,axiom,
% 2.80/1.51 ! [S: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) )
% 2.80/1.51 => ( member_real @ ( plus_plus_real @ S @ T ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_162_i2_I3_J,axiom,
% 2.80/1.51 ord_less_real @ i1 @ i2 ).
% 2.80/1.51
% 2.80/1.51 thf(fact_163_local_Orev_Oflow__trans,axiom,
% 2.80/1.51 ! [S: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( plus_plus_real @ S @ T ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_164_local_Orev_Oexistence__ivl__trans_H,axiom,
% 2.80/1.51 ! [T: real,S: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( plus_plus_real @ T @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_165_local_Orev_Oexistence__ivl__trans,axiom,
% 2.80/1.51 ! [S: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) )
% 2.80/1.51 => ( member_real @ ( plus_plus_real @ S @ T ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_166_general_Oflow__trans,axiom,
% 2.80/1.51 ! [S: real,T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_167_general_Oexistence__ivl__trans_H,axiom,
% 2.80/1.51 ! [T: real,S: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ T @ S ) @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_168_general_Oexistence__ivl__trans,axiom,
% 2.80/1.51 ! [S: real,T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 2.80/1.51 => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_169_periodic__orbit__period_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ f @ x @ X )
% 2.80/1.51 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_170_rev_Ogeneral_Oflow__trans,axiom,
% 2.80/1.51 ! [S: real,T0: real,X0: a,T: real] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ S @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ T @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) ) )
% 2.80/1.51 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ ( plus_plus_real @ S @ T ) @ T0 ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ S @ T0 ) ) @ T ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_171_rev_Ogeneral_Oexistence__ivl__trans_H,axiom,
% 2.80/1.51 ! [T: real,S: real,T0: real,X0: a] :
% 2.80/1.51 ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ T @ S ) @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( ( member_real @ ( minus_minus_real @ T @ T0 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) )
% 2.80/1.51 => ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( minus_minus_real @ T @ T0 ) ) ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_172_add_Oleft__neutral,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ zero_zero_a @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_173_add_Oleft__neutral,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ zero_zero_real @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_174_add_Oright__neutral,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ zero_zero_a )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_175_add_Oright__neutral,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ zero_zero_real )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_176_linordered__ab__group__add__class_Odouble__zero,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ A @ A )
% 2.80/1.51 = zero_zero_real )
% 2.80/1.51 = ( A = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_177_double__zero__sym,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( zero_zero_real
% 2.80/1.51 = ( plus_plus_real @ A @ A ) )
% 2.80/1.51 = ( A = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_178_add__cancel__left__left,axiom,
% 2.80/1.51 ! [B: a,A: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ B @ A )
% 2.80/1.51 = A )
% 2.80/1.51 = ( B = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_179_add__cancel__left__left,axiom,
% 2.80/1.51 ! [B: real,A: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ B @ A )
% 2.80/1.51 = A )
% 2.80/1.51 = ( B = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_180_add__cancel__left__right,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ A @ B )
% 2.80/1.51 = A )
% 2.80/1.51 = ( B = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_181_add__cancel__left__right,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ A @ B )
% 2.80/1.51 = A )
% 2.80/1.51 = ( B = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_182_add__cancel__right__left,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( plus_plus_a @ B @ A ) )
% 2.80/1.51 = ( B = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_183_add__cancel__right__left,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( plus_plus_real @ B @ A ) )
% 2.80/1.51 = ( B = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_184_add__cancel__right__right,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( plus_plus_a @ A @ B ) )
% 2.80/1.51 = ( B = zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_185_add__cancel__right__right,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( plus_plus_real @ A @ B ) )
% 2.80/1.51 = ( B = zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_186_neg__less__iff__less,axiom,
% 2.80/1.51 ! [B: a,A: a] :
% 2.80/1.51 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) )
% 2.80/1.51 = ( ord_less_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_187_neg__less__iff__less,axiom,
% 2.80/1.51 ! [B: real,A: real] :
% 2.80/1.51 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 2.80/1.51 = ( ord_less_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_188_closed__orbitE,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 => ~ ! [T5: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ T5 )
% 2.80/1.51 => ~ ! [T6: real] :
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( plus_plus_real @ T6 @ T5 ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ X @ T6 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_189_add__less__cancel__right,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 2.80/1.51 = ( ord_less_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_190_add__less__cancel__right,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.80/1.51 = ( ord_less_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_191_add__less__cancel__left,axiom,
% 2.80/1.51 ! [C: a,A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 2.80/1.51 = ( ord_less_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_192_add__less__cancel__left,axiom,
% 2.80/1.51 ! [C: real,A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.80/1.51 = ( ord_less_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_193_add__minus__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ ( plus_plus_a @ ( uminus_uminus_a @ A ) @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_194_add__minus__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_195_minus__add__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( plus_plus_a @ A @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_196_minus__add__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_197_minus__add__distrib,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( uminus_uminus_a @ ( plus_plus_a @ A @ B ) )
% 2.80/1.51 = ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_198_minus__add__distrib,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 2.80/1.51 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_199_add__diff__cancel__right_H,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_200_add__diff__cancel__right_H,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_201_add__diff__cancel__right,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 2.80/1.51 = ( minus_minus_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_202_add__diff__cancel__right,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.80/1.51 = ( minus_minus_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_203_add__diff__cancel__left_H,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ A )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_204_add__diff__cancel__left_H,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 2.80/1.51 = B ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_205_add__diff__cancel__left,axiom,
% 2.80/1.51 ! [C: a,A: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 2.80/1.51 = ( minus_minus_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_206_add__diff__cancel__left,axiom,
% 2.80/1.51 ! [C: real,A: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.80/1.51 = ( minus_minus_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_207_diff__add__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( minus_minus_a @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_208_diff__add__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_209_add__diff__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_210_add__diff__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_211_rev_Operiodic__orbit__period_I1_J,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_212_periodic__orbit__def,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ f @ x @ X )
% 2.80/1.51 = ( ( period720806154rbit_a @ f @ x @ X )
% 2.80/1.51 & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_213_tt_I2_J,axiom,
% 2.80/1.51 ord_less_real @ tt @ d ).
% 2.80/1.51
% 2.80/1.51 thf(fact_214_rev_Oclosed__orbitE,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 => ~ ! [T5: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ T5 )
% 2.80/1.51 => ~ ! [T6: real] :
% 2.80/1.51 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( plus_plus_real @ T6 @ T5 ) )
% 2.80/1.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T6 ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_215_rev_Operiodic__orbit__def,axiom,
% 2.80/1.51 ! [X: a] :
% 2.80/1.51 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 = ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X )
% 2.80/1.51 & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_216_less__neg__neg,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 2.80/1.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_217_neg__less__pos,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 2.80/1.51 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_218_neg__0__less__iff__less,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
% 2.80/1.51 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_219_neg__0__less__iff__less,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 2.80/1.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_220_neg__less__0__iff__less,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
% 2.80/1.51 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_221_neg__less__0__iff__less,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 2.80/1.51 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_222_add__less__same__cancel1,axiom,
% 2.80/1.51 ! [B: a,A: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ B @ A ) @ B )
% 2.80/1.51 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_223_add__less__same__cancel1,axiom,
% 2.80/1.51 ! [B: real,A: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 2.80/1.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_224_add__less__same__cancel2,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ B )
% 2.80/1.51 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_225_add__less__same__cancel2,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.80/1.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_226_less__add__same__cancel1,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ ( plus_plus_a @ A @ B ) )
% 2.80/1.51 = ( ord_less_a @ zero_zero_a @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_227_less__add__same__cancel1,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 2.80/1.51 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_228_less__add__same__cancel2,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ ( plus_plus_a @ B @ A ) )
% 2.80/1.51 = ( ord_less_a @ zero_zero_a @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_229_less__add__same__cancel2,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 2.80/1.51 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_230_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 2.80/1.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 2.80/1.51 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_232_diff__gt__0__iff__gt,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
% 2.80/1.51 = ( ord_less_a @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_233_diff__gt__0__iff__gt,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 2.80/1.51 = ( ord_less_real @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_234_add_Oleft__inverse,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ A )
% 2.80/1.51 = zero_zero_a ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_235_add_Oleft__inverse,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 2.80/1.51 = zero_zero_real ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_236_add_Oright__inverse,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ ( uminus_uminus_a @ A ) )
% 2.80/1.51 = zero_zero_a ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_237_add_Oright__inverse,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 2.80/1.51 = zero_zero_real ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_238_uminus__add__conv__diff,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ B )
% 2.80/1.51 = ( minus_minus_a @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_239_uminus__add__conv__diff,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 2.80/1.51 = ( minus_minus_real @ B @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_240_diff__minus__eq__add,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ ( uminus_uminus_a @ B ) )
% 2.80/1.51 = ( plus_plus_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_241_diff__minus__eq__add,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 2.80/1.51 = ( plus_plus_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_242_local_Oexistence__ivl__undefined,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ~ ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_243_local_Orev_Oexistence__ivl__undefined,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ~ ( member_a @ X0 @ x )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_244_local_Oexistence__ivl__empty__iff,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real )
% 2.80/1.51 = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 | ~ ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_245_local_Oexistence__ivl__empty1,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ f @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_246_local_Orev_Oexistence__ivl__empty__iff,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real )
% 2.80/1.51 = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 | ~ ( member_a @ X0 @ x ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_247_local_Orev_Oexistence__ivl__empty1,axiom,
% 2.80/1.51 ! [X0: a] :
% 2.80/1.51 ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
% 2.80/1.51 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 )
% 2.80/1.51 = bot_bot_set_real ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_248_add__neg__neg,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ zero_zero_a )
% 2.80/1.51 => ( ( ord_less_a @ B @ zero_zero_a )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_249_add__neg__neg,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ zero_zero_real )
% 2.80/1.51 => ( ( ord_less_real @ B @ zero_zero_real )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_250_add__pos__pos,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ zero_zero_a @ A )
% 2.80/1.51 => ( ( ord_less_a @ zero_zero_a @ B )
% 2.80/1.51 => ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_251_add__pos__pos,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ A )
% 2.80/1.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 2.80/1.51 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_252_pos__add__strict,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ zero_zero_a @ A )
% 2.80/1.51 => ( ( ord_less_a @ B @ C )
% 2.80/1.51 => ( ord_less_a @ B @ ( plus_plus_a @ A @ C ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_253_pos__add__strict,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ zero_zero_real @ A )
% 2.80/1.51 => ( ( ord_less_real @ B @ C )
% 2.80/1.51 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_254_add__less__imp__less__right,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) )
% 2.80/1.51 => ( ord_less_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_255_add__less__imp__less__right,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.80/1.51 => ( ord_less_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_256_add__less__imp__less__left,axiom,
% 2.80/1.51 ! [C: a,A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) )
% 2.80/1.51 => ( ord_less_a @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_257_add__less__imp__less__left,axiom,
% 2.80/1.51 ! [C: real,A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.80/1.51 => ( ord_less_real @ A @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_258_add__strict__right__mono,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_259_add__strict__right__mono,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_260_add__strict__left__mono,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_261_add__strict__left__mono,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_262_add__strict__mono,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a,D: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ( ord_less_a @ C @ D )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_263_add__strict__mono,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real,D: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ( ord_less_real @ C @ D )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_264_add__right__imp__eq,axiom,
% 2.80/1.51 ! [B: a,A: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ B @ A )
% 2.80/1.51 = ( plus_plus_a @ C @ A ) )
% 2.80/1.51 => ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_265_add__right__imp__eq,axiom,
% 2.80/1.51 ! [B: real,A: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ B @ A )
% 2.80/1.51 = ( plus_plus_real @ C @ A ) )
% 2.80/1.51 => ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_266_add__left__imp__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ A @ B )
% 2.80/1.51 = ( plus_plus_a @ A @ C ) )
% 2.80/1.51 => ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_267_add__left__imp__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ A @ B )
% 2.80/1.51 = ( plus_plus_real @ A @ C ) )
% 2.80/1.51 => ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_268_less__diff__eq,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ ( minus_minus_a @ C @ B ) )
% 2.80/1.51 = ( ord_less_a @ ( plus_plus_a @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_269_less__diff__eq,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 2.80/1.51 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_270_diff__less__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ ( minus_minus_a @ A @ B ) @ C )
% 2.80/1.51 = ( ord_less_a @ A @ ( plus_plus_a @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_271_diff__less__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.80/1.51 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_272_add_Oleft__commute,axiom,
% 2.80/1.51 ! [B: a,A: a,C: a] :
% 2.80/1.51 ( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) )
% 2.80/1.51 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_273_add_Oleft__commute,axiom,
% 2.80/1.51 ! [B: real,A: real,C: real] :
% 2.80/1.51 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 2.80/1.51 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_274_add_Ocommute,axiom,
% 2.80/1.51 ( plus_plus_a
% 2.80/1.51 = ( ^ [A3: a,B2: a] : ( plus_plus_a @ B2 @ A3 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_275_add_Ocommute,axiom,
% 2.80/1.51 ( plus_plus_real
% 2.80/1.51 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_276_add_Oright__cancel,axiom,
% 2.80/1.51 ! [B: a,A: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ B @ A )
% 2.80/1.51 = ( plus_plus_a @ C @ A ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_277_add_Oright__cancel,axiom,
% 2.80/1.51 ! [B: real,A: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ B @ A )
% 2.80/1.51 = ( plus_plus_real @ C @ A ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_278_add_Oleft__cancel,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ A @ B )
% 2.80/1.51 = ( plus_plus_a @ A @ C ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_279_add_Oleft__cancel,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ A @ B )
% 2.80/1.51 = ( plus_plus_real @ A @ C ) )
% 2.80/1.51 = ( B = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_280_add_Oassoc,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
% 2.80/1.51 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_281_add_Oassoc,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.80/1.51 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_282_group__cancel_Oadd2,axiom,
% 2.80/1.51 ! [B3: a,K: a,B: a,A: a] :
% 2.80/1.51 ( ( B3
% 2.80/1.51 = ( plus_plus_a @ K @ B ) )
% 2.80/1.51 => ( ( plus_plus_a @ A @ B3 )
% 2.80/1.51 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_283_group__cancel_Oadd2,axiom,
% 2.80/1.51 ! [B3: real,K: real,B: real,A: real] :
% 2.80/1.51 ( ( B3
% 2.80/1.51 = ( plus_plus_real @ K @ B ) )
% 2.80/1.51 => ( ( plus_plus_real @ A @ B3 )
% 2.80/1.51 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_284_group__cancel_Oadd1,axiom,
% 2.80/1.51 ! [A2: a,K: a,A: a,B: a] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_a @ K @ A ) )
% 2.80/1.51 => ( ( plus_plus_a @ A2 @ B )
% 2.80/1.51 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_285_group__cancel_Oadd1,axiom,
% 2.80/1.51 ! [A2: real,K: real,A: real,B: real] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_real @ K @ A ) )
% 2.80/1.51 => ( ( plus_plus_real @ A2 @ B )
% 2.80/1.51 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_286_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.80/1.51 ! [I: a,J: a,K: a,L: a] :
% 2.80/1.51 ( ( ( I = J )
% 2.80/1.51 & ( K = L ) )
% 2.80/1.51 => ( ( plus_plus_a @ I @ K )
% 2.80/1.51 = ( plus_plus_a @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_287_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.80/1.51 ! [I: real,J: real,K: real,L: real] :
% 2.80/1.51 ( ( ( I = J )
% 2.80/1.51 & ( K = L ) )
% 2.80/1.51 => ( ( plus_plus_real @ I @ K )
% 2.80/1.51 = ( plus_plus_real @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_288_add__mono__thms__linordered__field_I1_J,axiom,
% 2.80/1.51 ! [I: a,J: a,K: a,L: a] :
% 2.80/1.51 ( ( ( ord_less_a @ I @ J )
% 2.80/1.51 & ( K = L ) )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_289_add__mono__thms__linordered__field_I1_J,axiom,
% 2.80/1.51 ! [I: real,J: real,K: real,L: real] :
% 2.80/1.51 ( ( ( ord_less_real @ I @ J )
% 2.80/1.51 & ( K = L ) )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_290_add__mono__thms__linordered__field_I2_J,axiom,
% 2.80/1.51 ! [I: a,J: a,K: a,L: a] :
% 2.80/1.51 ( ( ( I = J )
% 2.80/1.51 & ( ord_less_a @ K @ L ) )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_291_add__mono__thms__linordered__field_I2_J,axiom,
% 2.80/1.51 ! [I: real,J: real,K: real,L: real] :
% 2.80/1.51 ( ( ( I = J )
% 2.80/1.51 & ( ord_less_real @ K @ L ) )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_292_add__mono__thms__linordered__field_I5_J,axiom,
% 2.80/1.51 ! [I: a,J: a,K: a,L: a] :
% 2.80/1.51 ( ( ( ord_less_a @ I @ J )
% 2.80/1.51 & ( ord_less_a @ K @ L ) )
% 2.80/1.51 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_293_add__mono__thms__linordered__field_I5_J,axiom,
% 2.80/1.51 ! [I: real,J: real,K: real,L: real] :
% 2.80/1.51 ( ( ( ord_less_real @ I @ J )
% 2.80/1.51 & ( ord_less_real @ K @ L ) )
% 2.80/1.51 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_294_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
% 2.80/1.51 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_295_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.80/1.51 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_296_verit__comp__simplify1_I1_J,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ~ ( ord_less_a @ A @ A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_297_verit__comp__simplify1_I1_J,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ~ ( ord_less_real @ A @ A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_298_verit__sum__simplify,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ zero_zero_a )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_299_verit__sum__simplify,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ zero_zero_real )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_300_comm__monoid__add__class_Oadd__0,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ zero_zero_a @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_301_comm__monoid__add__class_Oadd__0,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ zero_zero_real @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_302_add_Ocomm__neutral,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ zero_zero_a )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_303_add_Ocomm__neutral,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ zero_zero_real )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_304_add_Ogroup__left__neutral,axiom,
% 2.80/1.51 ! [A: a] :
% 2.80/1.51 ( ( plus_plus_a @ zero_zero_a @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_305_add_Ogroup__left__neutral,axiom,
% 2.80/1.51 ! [A: real] :
% 2.80/1.51 ( ( plus_plus_real @ zero_zero_real @ A )
% 2.80/1.51 = A ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_306_verit__negate__coefficient_I2_J,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_307_verit__negate__coefficient_I2_J,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_308_less__minus__iff,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
% 2.80/1.51 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_309_less__minus__iff,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 2.80/1.51 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_310_minus__less__iff,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
% 2.80/1.51 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_311_minus__less__iff,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 2.80/1.51 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_312_diff__strict__right__mono,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_313_diff__strict__right__mono,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_314_diff__strict__left__mono,axiom,
% 2.80/1.51 ! [B: a,A: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ B @ A )
% 2.80/1.51 => ( ord_less_a @ ( minus_minus_a @ C @ A ) @ ( minus_minus_a @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_315_diff__strict__left__mono,axiom,
% 2.80/1.51 ! [B: real,A: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ B @ A )
% 2.80/1.51 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_316_diff__eq__diff__less,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a,D: a] :
% 2.80/1.51 ( ( ( minus_minus_a @ A @ B )
% 2.80/1.51 = ( minus_minus_a @ C @ D ) )
% 2.80/1.51 => ( ( ord_less_a @ A @ B )
% 2.80/1.51 = ( ord_less_a @ C @ D ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_317_diff__eq__diff__less,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real,D: real] :
% 2.80/1.51 ( ( ( minus_minus_real @ A @ B )
% 2.80/1.51 = ( minus_minus_real @ C @ D ) )
% 2.80/1.51 => ( ( ord_less_real @ A @ B )
% 2.80/1.51 = ( ord_less_real @ C @ D ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_318_diff__strict__mono,axiom,
% 2.80/1.51 ! [A: a,B: a,D: a,C: a] :
% 2.80/1.51 ( ( ord_less_a @ A @ B )
% 2.80/1.51 => ( ( ord_less_a @ D @ C )
% 2.80/1.51 => ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ D ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_319_diff__strict__mono,axiom,
% 2.80/1.51 ! [A: real,B: real,D: real,C: real] :
% 2.80/1.51 ( ( ord_less_real @ A @ B )
% 2.80/1.51 => ( ( ord_less_real @ D @ C )
% 2.80/1.51 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_320_group__cancel_Oneg1,axiom,
% 2.80/1.51 ! [A2: a,K: a,A: a] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_a @ K @ A ) )
% 2.80/1.51 => ( ( uminus_uminus_a @ A2 )
% 2.80/1.51 = ( plus_plus_a @ ( uminus_uminus_a @ K ) @ ( uminus_uminus_a @ A ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_321_group__cancel_Oneg1,axiom,
% 2.80/1.51 ! [A2: real,K: real,A: real] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_real @ K @ A ) )
% 2.80/1.51 => ( ( uminus_uminus_real @ A2 )
% 2.80/1.51 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_322_add_Oinverse__distrib__swap,axiom,
% 2.80/1.51 ! [A: a,B: a] :
% 2.80/1.51 ( ( uminus_uminus_a @ ( plus_plus_a @ A @ B ) )
% 2.80/1.51 = ( plus_plus_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_323_add_Oinverse__distrib__swap,axiom,
% 2.80/1.51 ! [A: real,B: real] :
% 2.80/1.51 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 2.80/1.51 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_324_add__implies__diff,axiom,
% 2.80/1.51 ! [C: a,B: a,A: a] :
% 2.80/1.51 ( ( ( plus_plus_a @ C @ B )
% 2.80/1.51 = A )
% 2.80/1.51 => ( C
% 2.80/1.51 = ( minus_minus_a @ A @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_325_add__implies__diff,axiom,
% 2.80/1.51 ! [C: real,B: real,A: real] :
% 2.80/1.51 ( ( ( plus_plus_real @ C @ B )
% 2.80/1.51 = A )
% 2.80/1.51 => ( C
% 2.80/1.51 = ( minus_minus_real @ A @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_326_diff__diff__add,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C )
% 2.80/1.51 = ( minus_minus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_327_diff__diff__add,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.80/1.51 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_328_diff__add__eq__diff__diff__swap,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ ( plus_plus_a @ B @ C ) )
% 2.80/1.51 = ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_329_diff__add__eq__diff__diff__swap,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 2.80/1.51 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_330_diff__add__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( plus_plus_a @ ( minus_minus_a @ A @ B ) @ C )
% 2.80/1.51 = ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_331_diff__add__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.80/1.51 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_332_diff__diff__eq2,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( minus_minus_a @ A @ ( minus_minus_a @ B @ C ) )
% 2.80/1.51 = ( minus_minus_a @ ( plus_plus_a @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_333_diff__diff__eq2,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.80/1.51 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_334_add__diff__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( plus_plus_a @ A @ ( minus_minus_a @ B @ C ) )
% 2.80/1.51 = ( minus_minus_a @ ( plus_plus_a @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_335_add__diff__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.80/1.51 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_336_eq__diff__eq,axiom,
% 2.80/1.51 ! [A: a,C: a,B: a] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( minus_minus_a @ C @ B ) )
% 2.80/1.51 = ( ( plus_plus_a @ A @ B )
% 2.80/1.51 = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_337_eq__diff__eq,axiom,
% 2.80/1.51 ! [A: real,C: real,B: real] :
% 2.80/1.51 ( ( A
% 2.80/1.51 = ( minus_minus_real @ C @ B ) )
% 2.80/1.51 = ( ( plus_plus_real @ A @ B )
% 2.80/1.51 = C ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_338_diff__eq__eq,axiom,
% 2.80/1.51 ! [A: a,B: a,C: a] :
% 2.80/1.51 ( ( ( minus_minus_a @ A @ B )
% 2.80/1.51 = C )
% 2.80/1.51 = ( A
% 2.80/1.51 = ( plus_plus_a @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_339_diff__eq__eq,axiom,
% 2.80/1.51 ! [A: real,B: real,C: real] :
% 2.80/1.51 ( ( ( minus_minus_real @ A @ B )
% 2.80/1.51 = C )
% 2.80/1.51 = ( A
% 2.80/1.51 = ( plus_plus_real @ C @ B ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_340_group__cancel_Osub1,axiom,
% 2.80/1.51 ! [A2: a,K: a,A: a,B: a] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_a @ K @ A ) )
% 2.80/1.51 => ( ( minus_minus_a @ A2 @ B )
% 2.80/1.51 = ( plus_plus_a @ K @ ( minus_minus_a @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(fact_341_group__cancel_Osub1,axiom,
% 2.80/1.51 ! [A2: real,K: real,A: real,B: real] :
% 2.80/1.51 ( ( A2
% 2.80/1.51 = ( plus_plus_real @ K @ A ) )
% 2.80/1.51 => ( ( minus_minus_real @ A2 @ B )
% 2.80/1.51 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 2.80/1.51
% 2.80/1.51 thf(conj_0,conjecture,
% 2.80/1.51 ( xx
% 2.80/1.51 = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ) ).
% 2.80/1.51 ------------------------
% 2.80/1.54 % (28599)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/183Mi)
% 2.80/1.54 % (28602)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/2Mi)
% 2.80/1.54 % (28601)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/27Mi)
% 2.80/1.54 % (28605)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/18Mi)
% 2.80/1.54 % (28603)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/2Mi)
% 2.80/1.54 % (28600)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/4Mi)
% 2.80/1.54 % (28604)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/275Mi)
% 2.80/1.54 % (28602)Instruction limit reached!
% 2.80/1.54 % (28602)------------------------------
% 2.80/1.54 % (28602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.54 % (28602)Termination reason: Unknown
% 2.80/1.54 % (28602)Termination phase: shuffling
% 2.80/1.54
% 2.80/1.54 % (28602)Memory used [KB]: 1279
% 2.80/1.54 % (28602)Time elapsed: 0.002 s
% 2.80/1.54 % (28602)Instructions burned: 2 (million)
% 2.80/1.54 % (28602)------------------------------
% 2.80/1.54 % (28602)------------------------------
% 2.80/1.54 % (28603)Instruction limit reached!
% 2.80/1.54 % (28603)------------------------------
% 2.80/1.54 % (28603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.54 % (28603)Termination reason: Unknown
% 2.80/1.55 % (28603)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (28603)Memory used [KB]: 1279
% 2.80/1.55 % (28603)Time elapsed: 0.003 s
% 2.80/1.55 % (28603)Instructions burned: 3 (million)
% 2.80/1.55 % (28603)------------------------------
% 2.80/1.55 % (28603)------------------------------
% 2.80/1.55 % (28600)Instruction limit reached!
% 2.80/1.55 % (28600)------------------------------
% 2.80/1.55 % (28600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.55 % (28600)Termination reason: Unknown
% 2.80/1.55 % (28600)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (28600)Memory used [KB]: 1407
% 2.80/1.55 % (28600)Time elapsed: 0.004 s
% 2.80/1.55 % (28600)Instructions burned: 5 (million)
% 2.80/1.55 % (28600)------------------------------
% 2.80/1.55 % (28600)------------------------------
% 2.80/1.55 % (28605)Instruction limit reached!
% 2.80/1.55 % (28605)------------------------------
% 2.80/1.55 % (28605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.55 % (28605)Termination reason: Unknown
% 2.80/1.55 % (28605)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (28605)Memory used [KB]: 1535
% 2.80/1.55 % (28605)Time elapsed: 0.010 s
% 2.80/1.55 % (28605)Instructions burned: 18 (million)
% 2.80/1.55 % (28605)------------------------------
% 2.80/1.55 % (28605)------------------------------
% 2.80/1.56 % (28601)Instruction limit reached!
% 2.80/1.56 % (28601)------------------------------
% 2.80/1.56 % (28601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.56 % (28601)Termination reason: Unknown
% 2.80/1.56 % (28601)Termination phase: Property scanning
% 2.80/1.56
% 2.80/1.56 % (28601)Memory used [KB]: 1535
% 2.80/1.56 % (28601)Time elapsed: 0.015 s
% 2.80/1.56 % (28601)Instructions burned: 29 (million)
% 2.80/1.56 % (28601)------------------------------
% 2.80/1.56 % (28601)------------------------------
% 2.80/1.56 % (28606)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/3Mi)
% 2.80/1.56 % (28607)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/37Mi)
% 2.80/1.56 % (28606)Instruction limit reached!
% 2.80/1.56 % (28606)------------------------------
% 2.80/1.56 % (28606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.56 % (28606)Termination reason: Unknown
% 2.80/1.56 % (28606)Termination phase: shuffling
% 2.80/1.56
% 2.80/1.56 % (28606)Memory used [KB]: 1279
% 2.80/1.56 % (28606)Time elapsed: 0.003 s
% 2.80/1.56 % (28606)Instructions burned: 3 (million)
% 2.80/1.56 % (28606)------------------------------
% 2.80/1.56 % (28606)------------------------------
% 2.80/1.56 % (28608)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/15Mi)
% 2.80/1.57 % (28609)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/3Mi)
% 2.80/1.57 % (28608)Instruction limit reached!
% 2.80/1.57 % (28608)------------------------------
% 2.80/1.57 % (28608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.57 % (28608)Termination reason: Unknown
% 2.80/1.57 % (28608)Termination phase: shuffling
% 2.80/1.57
% 2.80/1.57 % (28608)Memory used [KB]: 1407
% 2.80/1.57 % (28608)Time elapsed: 0.009 s
% 2.80/1.57 % (28608)Instructions burned: 16 (million)
% 2.80/1.57 % (28608)------------------------------
% 2.80/1.57 % (28608)------------------------------
% 2.80/1.57 % (28609)Instruction limit reached!
% 2.80/1.57 % (28609)------------------------------
% 2.80/1.57 % (28609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.57 % (28609)Termination reason: Unknown
% 2.80/1.57 % (28609)Termination phase: shuffling
% 2.80/1.57
% 2.80/1.57 % (28609)Memory used [KB]: 1279
% 2.80/1.57 % (28609)Time elapsed: 0.003 s
% 2.80/1.57 % (28609)Instructions burned: 4 (million)
% 2.80/1.57 % (28609)------------------------------
% 2.80/1.57 % (28609)------------------------------
% 2.80/1.58 % (28607)Instruction limit reached!
% 2.80/1.58 % (28607)------------------------------
% 2.80/1.58 % (28607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (28607)Termination reason: Unknown
% 2.80/1.58 % (28610)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/1041Mi)
% 2.80/1.58 % (28607)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (28607)Memory used [KB]: 2046
% 2.80/1.58 % (28607)Time elapsed: 0.018 s
% 2.80/1.58 % (28607)Instructions burned: 37 (million)
% 2.80/1.58 % (28611)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/7Mi)
% 2.80/1.58 % (28607)------------------------------
% 2.80/1.58 % (28607)------------------------------
% 2.80/1.58 % (28604)Refutation not found, incomplete strategy
% 2.80/1.58 % (28604)------------------------------
% 2.80/1.58 % (28604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (28604)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.58
% 2.80/1.58
% 2.80/1.58 % (28604)Memory used [KB]: 6268
% 2.80/1.58 % (28604)Time elapsed: 0.038 s
% 2.80/1.58 % (28604)Instructions burned: 75 (million)
% 2.80/1.58 % (28604)------------------------------
% 2.80/1.58 % (28604)------------------------------
% 2.80/1.58 % (28611)Instruction limit reached!
% 2.80/1.58 % (28611)------------------------------
% 2.80/1.58 % (28611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (28611)Termination reason: Unknown
% 2.80/1.58 % (28611)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (28611)Memory used [KB]: 1407
% 2.80/1.58 % (28611)Time elapsed: 0.005 s
% 2.80/1.58 % (28611)Instructions burned: 7 (million)
% 2.80/1.58 % (28611)------------------------------
% 2.80/1.58 % (28611)------------------------------
% 2.80/1.59 % (28612)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/16Mi)
% 2.80/1.59 % (28613)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/3Mi)
% 2.80/1.59 % (28613)Instruction limit reached!
% 2.80/1.59 % (28613)------------------------------
% 2.80/1.59 % (28613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (28613)Termination reason: Unknown
% 2.80/1.59 % (28613)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (28613)Memory used [KB]: 1279
% 2.80/1.59 % (28613)Time elapsed: 0.003 s
% 2.80/1.59 % (28613)Instructions burned: 4 (million)
% 2.80/1.59 % (28613)------------------------------
% 2.80/1.59 % (28613)------------------------------
% 2.80/1.59 % (28599)Instruction limit reached!
% 2.80/1.59 % (28599)------------------------------
% 2.80/1.59 % (28599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (28599)Termination reason: Unknown
% 2.80/1.59 % (28599)Termination phase: Saturation
% 2.80/1.59
% 2.80/1.59 % (28599)Memory used [KB]: 6780
% 2.80/1.59 % (28599)Time elapsed: 0.056 s
% 2.80/1.59 % (28599)Instructions burned: 184 (million)
% 2.80/1.59 % (28599)------------------------------
% 2.80/1.59 % (28599)------------------------------
% 2.80/1.59 % (28614)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/3Mi)
% 2.80/1.59 % (28612)Instruction limit reached!
% 2.80/1.59 % (28612)------------------------------
% 2.80/1.59 % (28612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (28612)Termination reason: Unknown
% 2.80/1.59 % (28612)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (28612)Memory used [KB]: 1407
% 2.80/1.59 % (28612)Time elapsed: 0.009 s
% 2.80/1.59 % (28612)Instructions burned: 16 (million)
% 2.80/1.59 % (28612)------------------------------
% 2.80/1.59 % (28612)------------------------------
% 2.80/1.60 % (28614)Instruction limit reached!
% 2.80/1.60 % (28614)------------------------------
% 2.80/1.60 % (28614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (28614)Termination reason: Unknown
% 2.80/1.60 % (28614)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (28614)Memory used [KB]: 1279
% 2.80/1.60 % (28614)Time elapsed: 0.003 s
% 2.80/1.60 % (28614)Instructions burned: 3 (million)
% 2.80/1.60 % (28614)------------------------------
% 2.80/1.60 % (28614)------------------------------
% 2.80/1.60 % (28615)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/7Mi)
% 2.83/1.60 % (28616)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/3Mi)
% 2.83/1.60 % (28615)Instruction limit reached!
% 2.83/1.60 % (28615)------------------------------
% 2.83/1.60 % (28615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.60 % (28615)Termination reason: Unknown
% 2.83/1.60 % (28615)Termination phase: shuffling
% 2.83/1.60
% 2.83/1.60 % (28615)Memory used [KB]: 1407
% 2.83/1.60 % (28615)Time elapsed: 0.005 s
% 2.83/1.60 % (28615)Instructions burned: 8 (million)
% 2.83/1.60 % (28615)------------------------------
% 2.83/1.60 % (28615)------------------------------
% 2.83/1.60 % (28616)Instruction limit reached!
% 2.83/1.60 % (28616)------------------------------
% 2.83/1.60 % (28616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.60 % (28616)Termination reason: Unknown
% 2.83/1.60 % (28616)Termination phase: shuffling
% 2.83/1.60
% 2.83/1.60 % (28616)Memory used [KB]: 1279
% 2.83/1.60 % (28616)Time elapsed: 0.003 s
% 2.83/1.60 % (28616)Instructions burned: 3 (million)
% 2.83/1.60 % (28616)------------------------------
% 2.83/1.60 % (28616)------------------------------
% 2.83/1.60 % (28617)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/4Mi)
% 2.83/1.60 % (28617)Instruction limit reached!
% 2.83/1.60 % (28617)------------------------------
% 2.83/1.60 % (28617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.60 % (28617)Termination reason: Unknown
% 2.83/1.60 % (28617)Termination phase: shuffling
% 2.83/1.60
% 2.83/1.60 % (28617)Memory used [KB]: 1279
% 2.83/1.60 % (28617)Time elapsed: 0.003 s
% 2.83/1.60 % (28617)Instructions burned: 6 (million)
% 2.83/1.60 % (28617)------------------------------
% 2.83/1.60 % (28617)------------------------------
% 2.83/1.61 % (28618)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/18Mi)
% 2.83/1.61 % (28620)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/6Mi)
% 2.83/1.61 % (28619)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/710Mi)
% 2.83/1.61 % (28623)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/5Mi)
% 2.83/1.61 % (28620)Instruction limit reached!
% 2.83/1.61 % (28620)------------------------------
% 2.83/1.61 % (28620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.61 % (28620)Termination reason: Unknown
% 2.83/1.61 % (28620)Termination phase: shuffling
% 2.83/1.61
% 2.83/1.61 % (28620)Memory used [KB]: 1279
% 2.83/1.61 % (28620)Time elapsed: 0.004 s
% 2.83/1.61 % (28620)Instructions burned: 6 (million)
% 2.83/1.61 % (28620)------------------------------
% 2.83/1.61 % (28620)------------------------------
% 2.83/1.61 % (28623)Instruction limit reached!
% 2.83/1.61 % (28623)------------------------------
% 2.83/1.61 % (28623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.61 % (28623)Termination reason: Unknown
% 2.83/1.61 % (28623)Termination phase: shuffling
% 2.83/1.61
% 2.83/1.61 % (28623)Memory used [KB]: 1407
% 2.83/1.61 % (28623)Time elapsed: 0.003 s
% 2.83/1.61 % (28623)Instructions burned: 7 (million)
% 2.83/1.61 % (28623)------------------------------
% 2.83/1.61 % (28623)------------------------------
% 2.83/1.62 % (28622)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/21Mi)
% 2.83/1.62 % (28618)Instruction limit reached!
% 2.83/1.62 % (28618)------------------------------
% 2.83/1.62 % (28618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.62 % (28618)Termination reason: Unknown
% 2.83/1.62 % (28618)Termination phase: shuffling
% 2.83/1.62
% 2.83/1.62 % (28618)Memory used [KB]: 1535
% 2.83/1.62 % (28618)Time elapsed: 0.010 s
% 2.83/1.62 % (28618)Instructions burned: 18 (million)
% 2.83/1.62 % (28618)------------------------------
% 2.83/1.62 % (28618)------------------------------
% 2.83/1.62 % (28621)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/902Mi)
% 2.83/1.62 % (28624)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/6Mi)
% 2.83/1.63 % (28624)Instruction limit reached!
% 2.83/1.63 % (28624)------------------------------
% 2.83/1.63 % (28624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.63 % (28624)Termination reason: Unknown
% 2.83/1.63 % (28624)Termination phase: shuffling
% 2.83/1.63
% 2.83/1.63 % (28624)Memory used [KB]: 1407
% 2.83/1.63 % (28624)Time elapsed: 0.003 s
% 2.83/1.63 % (28624)Instructions burned: 7 (million)
% 2.83/1.63 % (28624)------------------------------
% 2.83/1.63 % (28624)------------------------------
% 2.83/1.63 % (28622)Instruction limit reached!
% 2.83/1.63 % (28622)------------------------------
% 2.83/1.63 % (28622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.63 % (28622)Termination reason: Unknown
% 2.83/1.63 % (28622)Termination phase: shuffling
% 2.83/1.63
% 2.83/1.63 % (28622)Memory used [KB]: 1535
% 2.83/1.63 % (28622)Time elapsed: 0.011 s
% 2.83/1.63 % (28622)Instructions burned: 21 (million)
% 2.83/1.63 % (28622)------------------------------
% 2.83/1.63 % (28622)------------------------------
% 2.83/1.63 % (28625)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28498 for (2999ds/377Mi)
% 2.83/1.63 % (28626)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/779Mi)
% 2.83/1.64 % (28627)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/19Mi)
% 2.83/1.64 % (28627)Instruction limit reached!
% 2.83/1.64 % (28627)------------------------------
% 2.83/1.64 % (28627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.64 % (28627)Termination reason: Unknown
% 2.83/1.64 % (28627)Termination phase: shuffling
% 2.83/1.64
% 2.83/1.64 % (28627)Memory used [KB]: 1663
% 2.83/1.64 % (28627)Time elapsed: 0.006 s
% 2.83/1.64 % (28627)Instructions burned: 19 (million)
% 2.83/1.64 % (28627)------------------------------
% 2.83/1.64 % (28627)------------------------------
% 2.83/1.64 % (28628)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/879Mi)
% 2.83/1.65 % (28629)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/17Mi)
% 2.83/1.66 % (28629)Instruction limit reached!
% 2.83/1.66 % (28629)------------------------------
% 2.83/1.66 % (28629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.66 % (28629)Termination reason: Unknown
% 2.83/1.66 % (28629)Termination phase: shuffling
% 2.83/1.66
% 2.83/1.66 % (28629)Memory used [KB]: 1407
% 2.83/1.66 % (28629)Time elapsed: 0.007 s
% 2.83/1.66 % (28629)Instructions burned: 18 (million)
% 2.83/1.66 % (28629)------------------------------
% 2.83/1.66 % (28629)------------------------------
% 2.83/1.67 % (28630)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/3Mi)
% 2.83/1.67 % (28630)Instruction limit reached!
% 2.83/1.67 % (28630)------------------------------
% 2.83/1.67 % (28630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (28630)Termination reason: Unknown
% 2.83/1.67 % (28630)Termination phase: shuffling
% 2.83/1.67
% 2.83/1.67 % (28630)Memory used [KB]: 1279
% 2.83/1.67 % (28630)Time elapsed: 0.002 s
% 2.83/1.67 % (28630)Instructions burned: 3 (million)
% 2.83/1.67 % (28630)------------------------------
% 2.83/1.67 % (28630)------------------------------
% 2.83/1.67 % (28621)Refutation not found, incomplete strategy
% 2.83/1.67 % (28621)------------------------------
% 2.83/1.67 % (28621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.67 % (28621)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.67
% 2.83/1.67
% 2.83/1.67 % (28621)Memory used [KB]: 6780
% 2.83/1.67 % (28621)Time elapsed: 0.055 s
% 2.83/1.67 % (28621)Instructions burned: 114 (million)
% 2.83/1.67 % (28621)------------------------------
% 2.83/1.67 % (28621)------------------------------
% 2.83/1.68 % (28631)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/30Mi)
% 2.83/1.69 % (28631)Instruction limit reached!
% 2.83/1.69 % (28631)------------------------------
% 2.83/1.69 % (28631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (28631)Termination reason: Unknown
% 2.83/1.69 % (28631)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (28631)Memory used [KB]: 1663
% 2.83/1.69 % (28631)Time elapsed: 0.011 s
% 2.83/1.69 % (28631)Instructions burned: 32 (million)
% 2.83/1.69 % (28631)------------------------------
% 2.83/1.69 % (28631)------------------------------
% 2.83/1.69 % (28632)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/127Mi)
% 2.83/1.69 % (28633)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28498 for (2998ds/100Mi)
% 2.83/1.72 % (28633)Instruction limit reached!
% 2.83/1.72 % (28633)------------------------------
% 2.83/1.72 % (28633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.72 % (28633)Termination reason: Unknown
% 2.83/1.72 % (28633)Termination phase: Property scanning
% 2.83/1.72
% 2.83/1.72 % (28633)Memory used [KB]: 2174
% 2.83/1.72 % (28633)Time elapsed: 0.027 s
% 2.83/1.72 % (28633)Instructions burned: 103 (million)
% 2.83/1.72 % (28633)------------------------------
% 2.83/1.72 % (28633)------------------------------
% 2.83/1.73 % (28634)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/3Mi)
% 2.83/1.74 % (28634)Instruction limit reached!
% 2.83/1.74 % (28634)------------------------------
% 2.83/1.74 % (28634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74 % (28634)Termination reason: Unknown
% 2.83/1.74 % (28634)Termination phase: shuffling
% 2.83/1.74
% 2.83/1.74 % (28634)Memory used [KB]: 1279
% 2.83/1.74 % (28634)Time elapsed: 0.003 s
% 2.83/1.74 % (28634)Instructions burned: 3 (million)
% 2.83/1.74 % (28634)------------------------------
% 2.83/1.74 % (28634)------------------------------
% 2.83/1.74 % (28632)Instruction limit reached!
% 2.83/1.74 % (28632)------------------------------
% 2.83/1.74 % (28632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74 % (28632)Termination reason: Unknown
% 2.83/1.74 % (28632)Termination phase: Saturation
% 2.83/1.74
% 2.83/1.74 % (28632)Memory used [KB]: 6652
% 2.83/1.74 % (28632)Time elapsed: 0.052 s
% 2.83/1.74 % (28632)Instructions burned: 127 (million)
% 2.83/1.74 % (28632)------------------------------
% 2.83/1.74 % (28632)------------------------------
% 2.83/1.75 % (28635)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/20Mi)
% 2.83/1.75 % (28636)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/86Mi)
% 2.83/1.75 % (28635)Instruction limit reached!
% 2.83/1.75 % (28635)------------------------------
% 2.83/1.75 % (28635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.75 % (28635)Termination reason: Unknown
% 2.83/1.75 % (28635)Termination phase: shuffling
% 2.83/1.75
% 2.83/1.75 % (28635)Memory used [KB]: 1535
% 2.83/1.75 % (28635)Time elapsed: 0.008 s
% 2.83/1.75 % (28635)Instructions burned: 22 (million)
% 2.83/1.75 % (28635)------------------------------
% 2.83/1.75 % (28635)------------------------------
% 2.83/1.76 % (28637)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/107Mi)
% 2.83/1.79 % (28636)Instruction limit reached!
% 2.83/1.79 % (28636)------------------------------
% 2.83/1.79 % (28636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.79 % (28636)Termination reason: Unknown
% 2.83/1.79 % (28636)Termination phase: Saturation
% 2.83/1.79
% 2.83/1.79 % (28636)Memory used [KB]: 6268
% 2.83/1.79 % (28636)Time elapsed: 0.040 s
% 2.83/1.79 % (28636)Instructions burned: 86 (million)
% 2.83/1.79 % (28636)------------------------------
% 2.83/1.79 % (28636)------------------------------
% 2.83/1.79 % (28637)Instruction limit reached!
% 2.83/1.79 % (28637)------------------------------
% 2.83/1.79 % (28637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.79 % (28637)Termination reason: Unknown
% 2.83/1.79 % (28637)Termination phase: Saturation
% 2.83/1.79
% 2.83/1.79 % (28637)Memory used [KB]: 6396
% 2.83/1.79 % (28637)Time elapsed: 0.030 s
% 2.83/1.79 % (28637)Instructions burned: 107 (million)
% 2.83/1.79 % (28637)------------------------------
% 2.83/1.79 % (28637)------------------------------
% 2.83/1.81 % (28639)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/448Mi)
% 2.83/1.81 % (28638)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_28498 for (2997ds/39Mi)
% 2.83/1.82 % (28625)Instruction limit reached!
% 2.83/1.82 % (28625)------------------------------
% 2.83/1.82 % (28625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.82 % (28625)Termination reason: Unknown
% 2.83/1.82 % (28625)Termination phase: Saturation
% 2.83/1.82
% 2.83/1.82 % (28625)Memory used [KB]: 7291
% 2.83/1.82 % (28625)Time elapsed: 0.212 s
% 2.83/1.82 % (28625)Instructions burned: 377 (million)
% 2.83/1.82 % (28625)------------------------------
% 2.83/1.82 % (28625)------------------------------
% 2.83/1.83 % (28638)Instruction limit reached!
% 2.83/1.83 % (28638)------------------------------
% 2.83/1.83 % (28638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.83 % (28638)Termination reason: Unknown
% 2.83/1.83 % (28638)Termination phase: shuffling
% 2.83/1.83
% 2.83/1.83 % (28638)Memory used [KB]: 2046
% 2.83/1.83 % (28638)Time elapsed: 0.013 s
% 2.83/1.83 % (28638)Instructions burned: 42 (million)
% 2.83/1.83 % (28638)------------------------------
% 2.83/1.83 % (28638)------------------------------
% 2.83/1.84 % (28640)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_28498 for (2996ds/46Mi)
% 2.83/1.84 % (28641)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_28498 for (2996ds/98Mi)
% 2.83/1.86 % (28640)Instruction limit reached!
% 2.83/1.86 % (28640)------------------------------
% 2.83/1.86 % (28640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.86 % (28640)Termination reason: Unknown
% 2.83/1.86 % (28640)Termination phase: SInE selection
% 2.83/1.86
% 2.83/1.86 % (28640)Memory used [KB]: 1535
% 2.83/1.86 % (28640)Time elapsed: 0.023 s
% 2.83/1.86 % (28640)Instructions burned: 47 (million)
% 2.83/1.86 % (28640)------------------------------
% 2.83/1.86 % (28640)------------------------------
% 2.83/1.86 % (28641)Instruction limit reached!
% 2.83/1.86 % (28641)------------------------------
% 2.83/1.86 % (28641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.86 % (28641)Termination reason: Unknown
% 2.83/1.86 % (28641)Termination phase: Property scanning
% 2.83/1.86
% 2.83/1.86 % (28641)Memory used [KB]: 2174
% 2.83/1.86 % (28641)Time elapsed: 0.026 s
% 2.83/1.86 % (28641)Instructions burned: 101 (million)
% 2.83/1.86 % (28641)------------------------------
% 2.83/1.86 % (28641)------------------------------
% 2.83/1.87 % (28643)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_28498 for (2996ds/149Mi)
% 2.83/1.87 % (28642)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_28498 for (2996ds/507Mi)
% 2.83/1.91 % (28643)Instruction limit reached!
% 2.83/1.91 % (28643)------------------------------
% 2.83/1.91 % (28643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.91 % (28643)Termination reason: Unknown
% 2.83/1.91 % (28643)Termination phase: Saturation
% 2.83/1.91
% 2.83/1.91 % (28643)Memory used [KB]: 6652
% 2.83/1.91 % (28643)Time elapsed: 0.045 s
% 2.83/1.91 % (28643)Instructions burned: 149 (million)
% 2.83/1.91 % (28643)------------------------------
% 2.83/1.91 % (28643)------------------------------
% 2.83/1.93 % (28644)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_28498 for (2996ds/39Mi)
% 2.83/1.93 % (28642)Refutation not found, incomplete strategy
% 2.83/1.93 % (28642)------------------------------
% 2.83/1.93 % (28642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.93 % (28642)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.93
% 2.83/1.93
% 2.83/1.93 % (28642)Memory used [KB]: 6908
% 2.83/1.93 % (28642)Time elapsed: 0.060 s
% 2.83/1.93 % (28642)Instructions burned: 124 (million)
% 2.83/1.93 % (28642)------------------------------
% 2.83/1.93 % (28642)------------------------------
% 2.83/1.95 % (28644)Instruction limit reached!
% 2.83/1.95 % (28644)------------------------------
% 2.83/1.95 % (28644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.95 % (28644)Termination reason: Unknown
% 2.83/1.95 % (28644)Termination phase: Property scanning
% 2.83/1.95
% 2.83/1.95 % (28644)Memory used [KB]: 1535
% 2.83/1.95 % (28644)Time elapsed: 0.020 s
% 2.83/1.95 % (28644)Instructions burned: 40 (million)
% 2.83/1.95 % (28644)------------------------------
% 2.83/1.95 % (28644)------------------------------
% 2.83/1.95 % (28645)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/6Mi)
% 2.83/1.95 % (28645)Instruction limit reached!
% 2.83/1.95 % (28645)------------------------------
% 2.83/1.95 % (28645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.95 % (28645)Termination reason: Unknown
% 2.83/1.95 % (28645)Termination phase: shuffling
% 2.83/1.95
% 2.83/1.95 % (28645)Memory used [KB]: 1407
% 2.83/1.95 % (28645)Time elapsed: 0.004 s
% 2.83/1.95 % (28645)Instructions burned: 6 (million)
% 2.83/1.95 % (28645)------------------------------
% 2.83/1.95 % (28645)------------------------------
% 2.83/1.95 % (28619)Instruction limit reached!
% 2.83/1.95 % (28619)------------------------------
% 2.83/1.95 % (28619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.95 % (28619)Termination reason: Unknown
% 2.83/1.95 % (28619)Termination phase: Saturation
% 2.83/1.95
% 2.83/1.95 % (28619)Memory used [KB]: 7291
% 2.83/1.95 % (28619)Time elapsed: 0.345 s
% 2.83/1.95 % (28619)Instructions burned: 711 (million)
% 2.83/1.95 % (28619)------------------------------
% 2.83/1.95 % (28619)------------------------------
% 2.83/1.96 % (28646)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/1087Mi)
% 2.83/1.97 % (28647)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/47Mi)
% 2.83/1.97 % (28648)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/44Mi)
% 2.83/1.97 % (28626)Instruction limit reached!
% 2.83/1.97 % (28626)------------------------------
% 2.83/1.97 % (28626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.97 % (28626)Termination reason: Unknown
% 2.83/1.97 % (28626)Termination phase: Saturation
% 2.83/1.97
% 2.83/1.97 % (28626)Memory used [KB]: 8187
% 2.83/1.97 % (28626)Time elapsed: 0.341 s
% 2.83/1.97 % (28626)Instructions burned: 780 (million)
% 2.83/1.97 % (28626)------------------------------
% 2.83/1.97 % (28626)------------------------------
% 2.83/1.98 % (28649)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/432Mi)
% 2.83/1.99 % (28647)Instruction limit reached!
% 2.83/1.99 % (28647)------------------------------
% 2.83/1.99 % (28647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.99 % (28647)Termination reason: Unknown
% 2.83/1.99 % (28647)Termination phase: Preprocessing 3
% 2.83/1.99
% 2.83/1.99 % (28647)Memory used [KB]: 1663
% 2.83/1.99 % (28647)Time elapsed: 0.024 s
% 2.83/1.99 % (28647)Instructions burned: 48 (million)
% 2.83/1.99 % (28647)------------------------------
% 2.83/1.99 % (28647)------------------------------
% 2.83/1.99 % (28648)Instruction limit reached!
% 2.83/1.99 % (28648)------------------------------
% 2.83/1.99 % (28648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.99 % (28648)Termination reason: Unknown
% 2.83/1.99 % (28648)Termination phase: shuffling
% 2.83/1.99
% 2.83/1.99 % (28648)Memory used [KB]: 2046
% 2.83/1.99 % (28648)Time elapsed: 0.021 s
% 2.83/1.99 % (28648)Instructions burned: 44 (million)
% 2.83/1.99 % (28648)------------------------------
% 2.83/1.99 % (28648)------------------------------
% 2.83/2.01 % (28651)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/31Mi)
% 2.83/2.01 % (28650)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_28498 for (2995ds/62Mi)
% 6.14/2.02 % (28639)Instruction limit reached!
% 6.14/2.02 % (28639)------------------------------
% 6.14/2.02 % (28639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.02 % (28639)Termination reason: Unknown
% 6.14/2.02 % (28639)Termination phase: Saturation
% 6.14/2.02
% 6.14/2.02 % (28639)Memory used [KB]: 8059
% 6.14/2.02 % (28639)Time elapsed: 0.209 s
% 6.14/2.02 % (28639)Instructions burned: 448 (million)
% 6.14/2.02 % (28639)------------------------------
% 6.14/2.02 % (28639)------------------------------
% 6.14/2.02 % (28651)Instruction limit reached!
% 6.14/2.02 % (28651)------------------------------
% 6.14/2.02 % (28651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.02 % (28651)Termination reason: Unknown
% 6.14/2.02 % (28651)Termination phase: Property scanning
% 6.14/2.02
% 6.14/2.02 % (28651)Memory used [KB]: 1535
% 6.14/2.02 % (28651)Time elapsed: 0.017 s
% 6.14/2.02 % (28651)Instructions burned: 33 (million)
% 6.14/2.02 % (28651)------------------------------
% 6.14/2.02 % (28651)------------------------------
% 6.14/2.04 % (28652)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/96Mi)
% 6.14/2.04 % (28653)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/453Mi)
% 6.14/2.04 % (28650)Instruction limit reached!
% 6.14/2.04 % (28650)------------------------------
% 6.14/2.04 % (28650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.04 % (28650)Termination reason: Unknown
% 6.14/2.04 % (28650)Termination phase: Property scanning
% 6.14/2.04
% 6.14/2.04 % (28650)Memory used [KB]: 2174
% 6.14/2.04 % (28650)Time elapsed: 0.030 s
% 6.14/2.04 % (28650)Instructions burned: 64 (million)
% 6.14/2.04 % (28650)------------------------------
% 6.14/2.04 % (28650)------------------------------
% 6.14/2.06 % (28654)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/71Mi)
% 6.14/2.06 % (28628)Instruction limit reached!
% 6.14/2.06 % (28628)------------------------------
% 6.14/2.06 % (28628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.06 % (28628)Termination reason: Unknown
% 6.14/2.06 % (28628)Termination phase: Saturation
% 6.14/2.06
% 6.14/2.06 % (28628)Memory used [KB]: 7675
% 6.14/2.06 % (28628)Time elapsed: 0.416 s
% 6.14/2.06 % (28628)Instructions burned: 879 (million)
% 6.14/2.06 % (28628)------------------------------
% 6.14/2.06 % (28628)------------------------------
% 6.14/2.08 % (28655)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/83Mi)
% 6.14/2.08 % (28652)Instruction limit reached!
% 6.14/2.08 % (28652)------------------------------
% 6.14/2.08 % (28652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.08 % (28652)Termination reason: Unknown
% 6.14/2.08 % (28652)Termination phase: Saturation
% 6.14/2.08
% 6.14/2.08 % (28652)Memory used [KB]: 6268
% 6.14/2.08 % (28652)Time elapsed: 0.044 s
% 6.14/2.08 % (28652)Instructions burned: 96 (million)
% 6.14/2.08 % (28652)------------------------------
% 6.14/2.08 % (28652)------------------------------
% 6.14/2.08 % (28610)Instruction limit reached!
% 6.14/2.08 % (28610)------------------------------
% 6.14/2.08 % (28610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.08 % (28610)Termination reason: Unknown
% 6.14/2.08 % (28610)Termination phase: Saturation
% 6.14/2.08
% 6.14/2.08 % (28610)Memory used [KB]: 8059
% 6.14/2.08 % (28610)Time elapsed: 0.508 s
% 6.14/2.08 % (28610)Instructions burned: 1041 (million)
% 6.14/2.08 % (28610)------------------------------
% 6.14/2.08 % (28610)------------------------------
% 6.14/2.09 % (28657)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/11Mi)
% 6.14/2.09 % (28654)Instruction limit reached!
% 6.14/2.09 % (28654)------------------------------
% 6.14/2.09 % (28654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.09 % (28654)Termination reason: Unknown
% 6.14/2.09 % (28654)Termination phase: Property scanning
% 6.14/2.09
% 6.14/2.09 % (28654)Memory used [KB]: 1791
% 6.14/2.09 % (28654)Time elapsed: 0.035 s
% 6.14/2.09 % (28654)Instructions burned: 72 (million)
% 6.14/2.09 % (28654)------------------------------
% 6.14/2.09 % (28654)------------------------------
% 6.14/2.09 % (28657)Instruction limit reached!
% 6.14/2.09 % (28657)------------------------------
% 6.14/2.09 % (28657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.09 % (28657)Termination reason: Unknown
% 6.14/2.09 % (28657)Termination phase: shuffling
% 6.14/2.09
% 6.14/2.09 % (28657)Memory used [KB]: 1535
% 6.14/2.09 % (28657)Time elapsed: 0.005 s
% 6.14/2.09 % (28657)Instructions burned: 14 (million)
% 6.14/2.09 % (28657)------------------------------
% 6.14/2.09 % (28657)------------------------------
% 6.14/2.10 % (28658)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/41Mi)
% 6.14/2.10 % (28660)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/150Mi)
% 6.14/2.11 % (28659)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/6Mi)
% 6.14/2.11 % (28659)Instruction limit reached!
% 6.14/2.11 % (28659)------------------------------
% 6.14/2.11 % (28659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.11 % (28659)Termination reason: Unknown
% 6.14/2.11 % (28659)Termination phase: shuffling
% 6.14/2.11
% 6.14/2.11 % (28659)Memory used [KB]: 1279
% 6.14/2.11 % (28659)Time elapsed: 0.004 s
% 6.14/2.11 % (28659)Instructions burned: 6 (million)
% 6.14/2.11 % (28659)------------------------------
% 6.14/2.11 % (28659)------------------------------
% 6.14/2.11 % (28655)Instruction limit reached!
% 6.14/2.11 % (28655)------------------------------
% 6.14/2.11 % (28655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.11 % (28655)Termination reason: Unknown
% 6.14/2.11 % (28655)Termination phase: Saturation
% 6.14/2.11
% 6.14/2.11 % (28655)Memory used [KB]: 6268
% 6.14/2.11 % (28655)Time elapsed: 0.040 s
% 6.14/2.11 % (28655)Instructions burned: 84 (million)
% 6.14/2.11 % (28655)------------------------------
% 6.14/2.11 % (28655)------------------------------
% 6.14/2.12 % (28658)Instruction limit reached!
% 6.14/2.12 % (28658)------------------------------
% 6.14/2.12 % (28658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.12 % (28658)Termination reason: Unknown
% 6.14/2.12 % (28658)Termination phase: shuffling
% 6.14/2.12
% 6.14/2.12 % (28658)Memory used [KB]: 2046
% 6.14/2.12 % (28658)Time elapsed: 0.020 s
% 6.14/2.12 % (28658)Instructions burned: 41 (million)
% 6.14/2.12 % (28658)------------------------------
% 6.14/2.12 % (28658)------------------------------
% 6.70/2.13 % (28661)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/343Mi)
% 6.70/2.13 % (28662)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/109Mi)
% 6.70/2.13 % (28663)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_28498 for (2994ds/253Mi)
% 6.70/2.15 % (28649)Instruction limit reached!
% 6.70/2.15 % (28649)------------------------------
% 6.70/2.15 % (28649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.15 % (28649)Termination reason: Unknown
% 6.70/2.15 % (28649)Termination phase: Saturation
% 6.70/2.15
% 6.70/2.15 % (28649)Memory used [KB]: 3198
% 6.70/2.15 % (28649)Time elapsed: 0.183 s
% 6.70/2.15 % (28649)Instructions burned: 432 (million)
% 6.70/2.15 % (28649)------------------------------
% 6.70/2.15 % (28649)------------------------------
% 6.70/2.16 % (28665)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_28498 for (2993ds/140Mi)
% 6.70/2.18 % (28660)Instruction limit reached!
% 6.70/2.18 % (28660)------------------------------
% 6.70/2.18 % (28660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.18 % (28660)Termination reason: Unknown
% 6.70/2.18 % (28660)Termination phase: Saturation
% 6.70/2.18
% 6.70/2.18 % (28660)Memory used [KB]: 6780
% 6.70/2.18 % (28660)Time elapsed: 0.076 s
% 6.70/2.18 % (28660)Instructions burned: 151 (million)
% 6.70/2.18 % (28660)------------------------------
% 6.70/2.18 % (28660)------------------------------
% 6.70/2.18 % (28662)Instruction limit reached!
% 6.70/2.18 % (28662)------------------------------
% 6.70/2.18 % (28662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.18 % (28662)Termination reason: Unknown
% 6.70/2.18 % (28662)Termination phase: Saturation
% 6.70/2.18
% 6.70/2.18 % (28662)Memory used [KB]: 6396
% 6.70/2.18 % (28662)Time elapsed: 0.051 s
% 6.70/2.18 % (28662)Instructions burned: 109 (million)
% 6.70/2.18 % (28662)------------------------------
% 6.70/2.18 % (28662)------------------------------
% 6.70/2.19 % (28666)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_28498 for (2993ds/614Mi)
% 6.70/2.20 % (28667)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_28498 for (2993ds/202Mi)
% 7.02/2.21 % (28665)Instruction limit reached!
% 7.02/2.21 % (28665)------------------------------
% 7.02/2.21 % (28665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.21 % (28665)Termination reason: Unknown
% 7.02/2.21 % (28665)Termination phase: Saturation
% 7.02/2.21
% 7.02/2.21 % (28665)Memory used [KB]: 6524
% 7.02/2.21 % (28665)Time elapsed: 0.045 s
% 7.02/2.21 % (28665)Instructions burned: 143 (million)
% 7.02/2.21 % (28665)------------------------------
% 7.02/2.21 % (28665)------------------------------
% 7.02/2.22 % (28668)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_28498 for (2993ds/339Mi)
% 7.02/2.24 % (28667)Refutation not found, incomplete strategy
% 7.02/2.24 % (28667)------------------------------
% 7.02/2.24 % (28667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.24 % (28667)Termination reason: Refutation not found, incomplete strategy
% 7.02/2.24
% 7.02/2.24
% 7.02/2.24 % (28667)Memory used [KB]: 6396
% 7.02/2.24 % (28667)Time elapsed: 0.043 s
% 7.02/2.24 % (28667)Instructions burned: 89 (million)
% 7.02/2.24 % (28667)------------------------------
% 7.02/2.24 % (28667)------------------------------
% 7.02/2.25 % (28653)Instruction limit reached!
% 7.02/2.25 % (28653)------------------------------
% 7.02/2.25 % (28653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.25 % (28653)Termination reason: Unknown
% 7.02/2.25 % (28653)Termination phase: Saturation
% 7.02/2.25
% 7.02/2.25 % (28653)Memory used [KB]: 7291
% 7.02/2.25 % (28653)Time elapsed: 0.214 s
% 7.02/2.25 % (28653)Instructions burned: 453 (million)
% 7.02/2.25 % (28653)------------------------------
% 7.02/2.25 % (28653)------------------------------
% 7.02/2.26 % (28669)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_28498 for (2992ds/283Mi)
% 7.02/2.26 % (28663)Instruction limit reached!
% 7.02/2.26 % (28663)------------------------------
% 7.02/2.26 % (28663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.26 % (28663)Termination reason: Unknown
% 7.02/2.26 % (28663)Termination phase: Saturation
% 7.02/2.26
% 7.02/2.26 % (28663)Memory used [KB]: 6908
% 7.02/2.26 % (28663)Time elapsed: 0.124 s
% 7.02/2.26 % (28663)Instructions burned: 253 (million)
% 7.02/2.26 % (28663)------------------------------
% 7.02/2.26 % (28663)------------------------------
% 7.02/2.27 % (28670)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_28498 for (2992ds/134Mi)
% 7.02/2.28 % (28671)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_28498 for (2992ds/298Mi)
% 7.02/2.30 % (28661)Instruction limit reached!
% 7.02/2.30 % (28661)------------------------------
% 7.02/2.30 % (28661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.30 % (28661)Termination reason: Unknown
% 7.02/2.30 % (28661)Termination phase: Saturation
% 7.02/2.30
% 7.02/2.30 % (28661)Memory used [KB]: 7164
% 7.02/2.30 % (28661)Time elapsed: 0.171 s
% 7.02/2.30 % (28661)Instructions burned: 344 (million)
% 7.02/2.30 % (28661)------------------------------
% 7.02/2.30 % (28661)------------------------------
% 7.78/2.31 % (28672)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_28498 for (2992ds/192Mi)
% 7.78/2.32 % (28668)Instruction limit reached!
% 7.78/2.32 % (28668)------------------------------
% 7.78/2.32 % (28668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.32 % (28668)Termination reason: Unknown
% 7.78/2.32 % (28668)Termination phase: Saturation
% 7.78/2.32
% 7.78/2.32 % (28668)Memory used [KB]: 7164
% 7.78/2.32 % (28668)Time elapsed: 0.128 s
% 7.78/2.32 % (28668)Instructions burned: 340 (million)
% 7.78/2.32 % (28668)------------------------------
% 7.78/2.32 % (28668)------------------------------
% 7.78/2.33 % (28670)Instruction limit reached!
% 7.78/2.33 % (28670)------------------------------
% 7.78/2.33 % (28670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.33 % (28670)Termination reason: Unknown
% 7.78/2.33 % (28670)Termination phase: Saturation
% 7.78/2.33
% 7.78/2.33 % (28670)Memory used [KB]: 6652
% 7.78/2.33 % (28670)Time elapsed: 0.087 s
% 7.78/2.33 % (28670)Instructions burned: 135 (million)
% 7.78/2.33 % (28670)------------------------------
% 7.78/2.33 % (28670)------------------------------
% 7.78/2.33 % (28673)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/258Mi)
% 7.78/2.35 % (28674)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/90Mi)
% 7.78/2.36 % (28673)Refutation not found, incomplete strategy
% 7.78/2.36 % (28673)------------------------------
% 7.78/2.36 % (28673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.36 % (28673)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.36
% 7.78/2.36
% 7.78/2.36 % (28673)Memory used [KB]: 6268
% 7.78/2.36 % (28673)Time elapsed: 0.024 s
% 7.78/2.36 % (28673)Instructions burned: 79 (million)
% 7.78/2.36 % (28673)------------------------------
% 7.78/2.36 % (28673)------------------------------
% 7.78/2.37 % (28675)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/231Mi)
% 7.78/2.38 % (28672)Refutation not found, incomplete strategy
% 7.78/2.38 % (28672)------------------------------
% 7.78/2.38 % (28672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.38 % (28672)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.38
% 7.78/2.38
% 7.78/2.38 % (28672)Memory used [KB]: 7036
% 7.78/2.38 % (28672)Time elapsed: 0.065 s
% 7.78/2.38 % (28672)Instructions burned: 127 (million)
% 7.78/2.38 % (28672)------------------------------
% 7.78/2.38 % (28672)------------------------------
% 7.78/2.39 % (28674)Instruction limit reached!
% 7.78/2.39 % (28674)------------------------------
% 7.78/2.39 % (28674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.39 % (28674)Termination reason: Unknown
% 7.78/2.39 % (28674)Termination phase: Saturation
% 7.78/2.39
% 7.78/2.39 % (28674)Memory used [KB]: 6268
% 7.78/2.39 % (28674)Time elapsed: 0.042 s
% 7.78/2.39 % (28674)Instructions burned: 90 (million)
% 7.78/2.39 % (28674)------------------------------
% 7.78/2.39 % (28674)------------------------------
% 7.78/2.39 % (28669)Instruction limit reached!
% 7.78/2.39 % (28669)------------------------------
% 7.78/2.39 % (28669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.78/2.39 % (28669)Termination reason: Unknown
% 7.78/2.39 % (28669)Termination phase: Saturation
% 7.78/2.39
% 7.78/2.39 % (28669)Memory used [KB]: 7164
% 7.78/2.39 % (28669)Time elapsed: 0.163 s
% 7.78/2.39 % (28669)Instructions burned: 283 (million)
% 7.78/2.39 % (28669)------------------------------
% 7.78/2.39 % (28669)------------------------------
% 8.39/2.40 % (28676)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/458Mi)
% 8.39/2.40 % (28677)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/31Mi)
% 8.39/2.41 % (28678)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_28498 for (2991ds/297Mi)
% 8.39/2.41 % (28671)Instruction limit reached!
% 8.39/2.41 % (28671)------------------------------
% 8.39/2.41 % (28671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.39/2.41 % (28671)Termination reason: Unknown
% 8.39/2.41 % (28671)Termination phase: Saturation
% 8.39/2.41
% 8.39/2.41 % (28671)Memory used [KB]: 7931
% 8.39/2.41 % (28671)Time elapsed: 0.140 s
% 8.39/2.41 % (28671)Instructions burned: 298 (million)
% 8.39/2.41 % (28671)------------------------------
% 8.39/2.41 % (28671)------------------------------
% 8.39/2.42 % (28677)Instruction limit reached!
% 8.39/2.42 % (28677)------------------------------
% 8.39/2.42 % (28677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.39/2.42 % (28677)Termination reason: Unknown
% 8.39/2.42 % (28677)Termination phase: Property scanning
% 8.39/2.42
% 8.39/2.42 % (28677)Memory used [KB]: 1535
% 8.39/2.42 % (28677)Time elapsed: 0.016 s
% 8.39/2.42 % (28677)Instructions burned: 31 (million)
% 8.39/2.42 % (28677)------------------------------
% 8.39/2.42 % (28677)------------------------------
% 8.39/2.43 % (28679)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/987Mi)
% 8.39/2.43 % (28680)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/182Mi)
% 8.39/2.44 % (28675)Instruction limit reached!
% 8.39/2.44 % (28675)------------------------------
% 8.39/2.44 % (28675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.39/2.44 % (28675)Termination reason: Unknown
% 8.39/2.44 % (28675)Termination phase: Saturation
% 8.39/2.44
% 8.39/2.44 % (28675)Memory used [KB]: 6908
% 8.39/2.44 % (28675)Time elapsed: 0.065 s
% 8.39/2.44 % (28675)Instructions burned: 232 (million)
% 8.39/2.44 % (28675)------------------------------
% 8.39/2.44 % (28675)------------------------------
% 8.39/2.44 % (28681)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/182Mi)
% 8.39/2.49 % (28646)Instruction limit reached!
% 8.39/2.49 % (28646)------------------------------
% 8.39/2.49 % (28646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.39/2.49 % (28646)Termination reason: Unknown
% 8.39/2.49 % (28646)Termination phase: Saturation
% 8.39/2.49
% 8.39/2.49 % (28646)Memory used [KB]: 7803
% 8.39/2.49 % (28646)Time elapsed: 0.525 s
% 8.39/2.49 % (28646)Instructions burned: 1089 (million)
% 8.39/2.49 % (28646)------------------------------
% 8.39/2.49 % (28646)------------------------------
% 8.75/2.50 % (28666)Instruction limit reached!
% 8.75/2.50 % (28666)------------------------------
% 8.75/2.50 % (28666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.50 % (28666)Termination reason: Unknown
% 8.75/2.50 % (28666)Termination phase: Saturation
% 8.75/2.50
% 8.75/2.50 % (28666)Memory used [KB]: 8059
% 8.75/2.50 % (28666)Time elapsed: 0.327 s
% 8.75/2.50 % (28666)Instructions burned: 614 (million)
% 8.75/2.50 % (28666)------------------------------
% 8.75/2.50 % (28666)------------------------------
% 8.75/2.50 % (28681)Instruction limit reached!
% 8.75/2.50 % (28681)------------------------------
% 8.75/2.50 % (28681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.50 % (28681)Termination reason: Unknown
% 8.75/2.50 % (28681)Termination phase: Saturation
% 8.75/2.50
% 8.75/2.50 % (28681)Memory used [KB]: 6780
% 8.75/2.50 % (28681)Time elapsed: 0.056 s
% 8.75/2.50 % (28681)Instructions burned: 183 (million)
% 8.75/2.50 % (28681)------------------------------
% 8.75/2.50 % (28681)------------------------------
% 8.75/2.51 % (28684)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/216Mi)
% 8.75/2.51 % (28682)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/154Mi)
% 8.75/2.51 % (28683)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_28498 for (2990ds/79Mi)
% 8.75/2.52 % (28680)Instruction limit reached!
% 8.75/2.52 % (28680)------------------------------
% 8.75/2.52 % (28680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.52 % (28680)Termination reason: Unknown
% 8.75/2.52 % (28680)Termination phase: Saturation
% 8.75/2.52
% 8.75/2.52 % (28680)Memory used [KB]: 6780
% 8.75/2.52 % (28680)Time elapsed: 0.088 s
% 8.75/2.52 % (28680)Instructions burned: 183 (million)
% 8.75/2.52 % (28680)------------------------------
% 8.75/2.52 % (28680)------------------------------
% 8.75/2.54 % (28685)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/114Mi)
% 8.75/2.55 % (28678)Instruction limit reached!
% 8.75/2.55 % (28678)------------------------------
% 8.75/2.55 % (28678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.55 % (28678)Termination reason: Unknown
% 8.75/2.55 % (28678)Termination phase: Saturation
% 8.75/2.55
% 8.75/2.55 % (28678)Memory used [KB]: 7164
% 8.75/2.55 % (28678)Time elapsed: 0.138 s
% 8.75/2.55 % (28678)Instructions burned: 297 (million)
% 8.75/2.55 % (28678)------------------------------
% 8.75/2.55 % (28678)------------------------------
% 8.75/2.55 % (28683)Instruction limit reached!
% 8.75/2.55 % (28683)------------------------------
% 8.75/2.55 % (28683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.55 % (28683)Termination reason: Unknown
% 8.75/2.55 % (28683)Termination phase: Property scanning
% 8.75/2.55
% 8.75/2.55 % (28683)Memory used [KB]: 1791
% 8.75/2.55 % (28683)Time elapsed: 0.038 s
% 8.75/2.55 % (28683)Instructions burned: 80 (million)
% 8.75/2.55 % (28683)------------------------------
% 8.75/2.55 % (28683)------------------------------
% 8.75/2.57 % (28684)Instruction limit reached!
% 8.75/2.57 % (28684)------------------------------
% 8.75/2.57 % (28684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.57 % (28684)Termination reason: Unknown
% 8.75/2.57 % (28684)Termination phase: Saturation
% 8.75/2.57
% 8.75/2.57 % (28684)Memory used [KB]: 7291
% 8.75/2.57 % (28684)Time elapsed: 0.058 s
% 8.75/2.57 % (28684)Instructions burned: 218 (million)
% 8.75/2.57 % (28684)------------------------------
% 8.75/2.57 % (28684)------------------------------
% 8.75/2.57 % (28686)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/922Mi)
% 8.75/2.57 % (28687)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/182Mi)
% 8.75/2.58 % (28688)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/164Mi)
% 8.75/2.58 % (28682)Instruction limit reached!
% 8.75/2.58 % (28682)------------------------------
% 8.75/2.58 % (28682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.58 % (28682)Termination reason: Unknown
% 8.75/2.58 % (28682)Termination phase: Saturation
% 8.75/2.58
% 8.75/2.58 % (28682)Memory used [KB]: 7036
% 8.75/2.58 % (28682)Time elapsed: 0.071 s
% 8.75/2.58 % (28682)Instructions burned: 154 (million)
% 8.75/2.58 % (28682)------------------------------
% 8.75/2.58 % (28682)------------------------------
% 8.75/2.59 % (28685)Instruction limit reached!
% 8.75/2.59 % (28685)------------------------------
% 8.75/2.59 % (28685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.59 % (28685)Termination reason: Unknown
% 8.75/2.59 % (28685)Termination phase: Saturation
% 8.75/2.59
% 8.75/2.59 % (28685)Memory used [KB]: 6524
% 8.75/2.59 % (28685)Time elapsed: 0.054 s
% 8.75/2.59 % (28685)Instructions burned: 115 (million)
% 8.75/2.59 % (28685)------------------------------
% 8.75/2.59 % (28685)------------------------------
% 9.67/2.60 % (28689)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/50Mi)
% 9.67/2.61 % (28690)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_28498 for (2989ds/368Mi)
% 9.67/2.62 % (28688)Instruction limit reached!
% 9.67/2.62 % (28688)------------------------------
% 9.67/2.62 % (28688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.62 % (28688)Termination reason: Unknown
% 9.67/2.62 % (28688)Termination phase: Saturation
% 9.67/2.62
% 9.67/2.62 % (28688)Memory used [KB]: 2430
% 9.67/2.62 % (28688)Time elapsed: 0.046 s
% 9.67/2.62 % (28688)Instructions burned: 165 (million)
% 9.67/2.62 % (28688)------------------------------
% 9.67/2.62 % (28688)------------------------------
% 9.67/2.62 % (28689)Instruction limit reached!
% 9.67/2.62 % (28689)------------------------------
% 9.67/2.62 % (28689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.62 % (28689)Termination reason: Unknown
% 9.67/2.62 % (28689)Termination phase: Property scanning
% 9.67/2.62
% 9.67/2.62 % (28689)Memory used [KB]: 2174
% 9.67/2.62 % (28689)Time elapsed: 0.024 s
% 9.67/2.62 % (28689)Instructions burned: 51 (million)
% 9.67/2.62 % (28689)------------------------------
% 9.67/2.62 % (28689)------------------------------
% 9.67/2.63 % (28676)Instruction limit reached!
% 9.67/2.63 % (28676)------------------------------
% 9.67/2.63 % (28676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.63 % (28676)Termination reason: Unknown
% 9.67/2.63 % (28676)Termination phase: Saturation
% 9.67/2.63
% 9.67/2.63 % (28676)Memory used [KB]: 7164
% 9.67/2.63 % (28676)Time elapsed: 0.226 s
% 9.67/2.63 % (28676)Instructions burned: 458 (million)
% 9.67/2.63 % (28676)------------------------------
% 9.67/2.63 % (28676)------------------------------
% 9.67/2.63 % (28692)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_28498 for (2988ds/1021Mi)
% 9.67/2.64 % (28693)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_28498 for (2988ds/267Mi)
% 9.67/2.64 % (28694)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_28498 for (2988ds/204Mi)
% 9.67/2.65 % (28687)Instruction limit reached!
% 9.67/2.65 % (28687)------------------------------
% 9.67/2.65 % (28687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.65 % (28687)Termination reason: Unknown
% 9.67/2.65 % (28687)Termination phase: Saturation
% 9.67/2.65
% 9.67/2.65 % (28687)Memory used [KB]: 6908
% 9.67/2.65 % (28687)Time elapsed: 0.083 s
% 9.67/2.65 % (28687)Instructions burned: 182 (million)
% 9.67/2.65 % (28687)------------------------------
% 9.67/2.65 % (28687)------------------------------
% 9.67/2.67 % (28695)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_28498 for (2988ds/26Mi)
% 9.67/2.69 % (28695)Instruction limit reached!
% 9.67/2.69 % (28695)------------------------------
% 9.67/2.69 % (28695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.69 % (28695)Termination reason: Unknown
% 9.67/2.69 % (28695)Termination phase: shuffling
% 9.67/2.69
% 9.67/2.69 % (28695)Memory used [KB]: 1663
% 9.67/2.69 % (28695)Time elapsed: 0.009 s
% 9.67/2.69 % (28695)Instructions burned: 26 (million)
% 9.67/2.69 % (28695)------------------------------
% 9.67/2.69 % (28695)------------------------------
% 10.11/2.71 % (28696)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_28498 for (2988ds/53Mi)
% 10.11/2.73 % (28696)Instruction limit reached!
% 10.11/2.73 % (28696)------------------------------
% 10.11/2.73 % (28696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.73 % (28696)Termination reason: Unknown
% 10.11/2.73 % (28696)Termination phase: Property scanning
% 10.11/2.73
% 10.11/2.73 % (28696)Memory used [KB]: 2174
% 10.11/2.73 % (28696)Time elapsed: 0.025 s
% 10.11/2.73 % (28696)Instructions burned: 54 (million)
% 10.11/2.73 % (28696)------------------------------
% 10.11/2.73 % (28696)------------------------------
% 10.11/2.74 % (28693)Instruction limit reached!
% 10.11/2.74 % (28693)------------------------------
% 10.11/2.74 % (28693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.74 % (28693)Termination reason: Unknown
% 10.11/2.74 % (28693)Termination phase: Saturation
% 10.11/2.74
% 10.11/2.74 % (28693)Memory used [KB]: 7036
% 10.11/2.74 % (28693)Time elapsed: 0.115 s
% 10.11/2.74 % (28693)Instructions burned: 267 (million)
% 10.11/2.74 % (28693)------------------------------
% 10.11/2.74 % (28693)------------------------------
% 10.11/2.74 % (28694)Instruction limit reached!
% 10.11/2.74 % (28694)------------------------------
% 10.11/2.74 % (28694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.74 % (28694)Termination reason: Unknown
% 10.11/2.74 % (28694)Termination phase: Saturation
% 10.11/2.74
% 10.11/2.74 % (28694)Memory used [KB]: 6780
% 10.11/2.74 % (28694)Time elapsed: 0.099 s
% 10.11/2.74 % (28694)Instructions burned: 204 (million)
% 10.11/2.74 % (28694)------------------------------
% 10.11/2.74 % (28694)------------------------------
% 10.11/2.75 % (28697)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_28498 for (2987ds/4436Mi)
% 10.11/2.75 % (28698)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_28498 for (2987ds/1539Mi)
% 10.11/2.77 % (28699)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_28498 for (2987ds/408Mi)
% 10.11/2.79 % (28690)Instruction limit reached!
% 10.11/2.79 % (28690)------------------------------
% 10.11/2.79 % (28690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.79 % (28690)Termination reason: Unknown
% 10.11/2.79 % (28690)Termination phase: Saturation
% 10.11/2.79
% 10.11/2.79 % (28690)Memory used [KB]: 7291
% 10.11/2.79 % (28690)Time elapsed: 0.184 s
% 10.11/2.79 % (28690)Instructions burned: 369 (million)
% 10.11/2.79 % (28690)------------------------------
% 10.11/2.79 % (28690)------------------------------
% 10.55/2.80 % (28700)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_28498 for (2987ds/5205Mi)
% 10.55/2.84 % (28699)Refutation not found, incomplete strategy
% 10.55/2.84 % (28699)------------------------------
% 10.55/2.84 % (28699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.84 % (28699)Termination reason: Refutation not found, incomplete strategy
% 10.55/2.84
% 10.55/2.84
% 10.55/2.84 % (28699)Memory used [KB]: 6908
% 10.55/2.84 % (28699)Time elapsed: 0.095 s
% 10.55/2.84 % (28699)Instructions burned: 122 (million)
% 10.55/2.84 % (28699)------------------------------
% 10.55/2.84 % (28699)------------------------------
% 10.55/2.85 % (28701)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_28498 for (2986ds/1913Mi)
% 10.60/2.91 % (28679)Instruction limit reached!
% 10.60/2.91 % (28679)------------------------------
% 10.60/2.91 % (28679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.60/2.91 % (28679)Termination reason: Unknown
% 10.60/2.91 % (28679)Termination phase: Saturation
% 10.60/2.91
% 10.60/2.91 % (28679)Memory used [KB]: 8187
% 10.60/2.91 % (28679)Time elapsed: 0.486 s
% 10.60/2.91 % (28679)Instructions burned: 988 (million)
% 10.60/2.91 % (28679)------------------------------
% 10.60/2.91 % (28679)------------------------------
% 10.60/2.92 % (28698)First to succeed.
% 10.60/2.92 % (28698)Refutation found. Thanks to Tanya!
% 10.60/2.92 % SZS status Theorem for DTF2THF_28498
% 10.60/2.92 % SZS output start Proof for DTF2THF_28498
% 10.60/2.92 thf(type_def_5, type, a: $tType).
% 10.60/2.92 thf(type_def_7, type, set_a: $tType).
% 10.60/2.92 thf(type_def_8, type, set_real: $tType).
% 10.60/2.92 thf(type_def_9, type, real: $tType).
% 10.60/2.92 thf(func_def_0, type, set_real: $tType).
% 10.60/2.92 thf(func_def_1, type, set_a: $tType).
% 10.60/2.92 thf(func_def_2, type, real: $tType).
% 10.60/2.92 thf(func_def_3, type, a: $tType).
% 10.60/2.92 thf(func_def_4, type, auto_l612940ivl0_a: (a > a) > set_a > a > set_real).
% 10.60/2.92 thf(func_def_5, type, auto_ll_on_flow0_a: (a > a) > set_a > a > real > a).
% 10.60/2.92 thf(func_def_6, type, minus_minus_real: real > real > real).
% 10.60/2.92 thf(func_def_7, type, minus_minus_a: a > a > a).
% 10.60/2.92 thf(func_def_8, type, plus_plus_real: real > real > real).
% 10.60/2.92 thf(func_def_9, type, plus_plus_a: a > a > a).
% 10.60/2.92 thf(func_def_10, type, uminus_uminus_a_a: (a > a) > a > a).
% 10.60/2.92 thf(func_def_11, type, uminus_uminus_real: real > real).
% 10.60/2.92 thf(func_def_12, type, uminus_uminus_a: a > a).
% 10.60/2.92 thf(func_def_13, type, zero_zero_real: real).
% 10.60/2.92 thf(func_def_14, type, zero_zero_a: a).
% 10.60/2.92 thf(func_def_15, type, initia826609931terval: set_real > $o).
% 10.60/2.92 thf(func_def_16, type, bot_bot_set_real: set_real).
% 10.60/2.92 thf(func_def_17, type, ord_less_real: real > real > $o).
% 10.60/2.92 thf(func_def_18, type, ord_less_a: a > a > $o).
% 10.60/2.92 thf(func_def_19, type, top_top_set_real: set_real).
% 10.60/2.92 thf(func_def_20, type, period720806154rbit_a: (a > a) > set_a > a > $o).
% 10.60/2.92 thf(func_def_21, type, period1305449585riod_a: (a > a) > set_a > a > real).
% 10.60/2.92 thf(func_def_22, type, period138238489rbit_a: (a > a) > set_a > a > $o).
% 10.60/2.92 thf(func_def_23, type, collect_real: (real > $o) > set_real).
% 10.60/2.92 thf(func_def_24, type, collect_a: (a > $o) > set_a).
% 10.60/2.92 thf(func_def_25, type, member_real: real > set_real > $o).
% 10.60/2.92 thf(func_def_26, type, member_a: a > set_a > $o).
% 10.60/2.92 thf(func_def_27, type, x: set_a).
% 10.60/2.92 thf(func_def_28, type, d: real).
% 10.60/2.92 thf(func_def_29, type, f: a > a).
% 10.60/2.92 thf(func_def_30, type, i1: real).
% 10.60/2.92 thf(func_def_31, type, i2: real).
% 10.60/2.92 thf(func_def_32, type, ss: real).
% 10.60/2.92 thf(func_def_33, type, t: real).
% 10.60/2.92 thf(func_def_34, type, tt: real).
% 10.60/2.92 thf(func_def_35, type, x2: a).
% 10.60/2.92 thf(func_def_36, type, xx: a).
% 10.60/2.92 thf(func_def_48, type, sK0: a).
% 10.60/2.92 thf(func_def_49, type, sK1: a).
% 10.60/2.92 thf(func_def_50, type, sK2: a).
% 10.60/2.92 thf(func_def_51, type, sK3: (a > $o) > (a > $o) > a).
% 10.60/2.92 thf(func_def_52, type, sK4: a > real).
% 10.60/2.92 thf(func_def_53, type, sK5: a > real).
% 10.60/2.92 thf(func_def_54, type, sK6: a).
% 10.60/2.92 thf(func_def_55, type, sK7: (real > $o) > (real > $o) > real).
% 10.60/2.92 thf(func_def_57, type, sK9: a > real).
% 10.60/2.92 thf(func_def_58, type, sK10: a > real).
% 10.60/2.92 thf(func_def_59, type, ph11: !>[X0: $tType]:(X0)).
% 10.60/2.92 thf(f2495,plain,(
% 10.60/2.92 $false),
% 10.60/2.92 inference(avatar_sat_refutation,[status(thm)],[f1907,f1950,f1956,f2159,f2189,f2217,f2484])).
% 10.60/2.92 thf(f2484,plain,(
% 10.60/2.92 spl8_2 | ~spl8_8 | ~spl8_13 | ~spl8_15),
% 10.60/2.92 inference(avatar_contradiction_clause,[status(thm)],[f2483])).
% 10.60/2.92 thf(f2483,plain,(
% 10.60/2.92 $false | (spl8_2 | ~spl8_8 | ~spl8_13 | ~spl8_15)),
% 10.60/2.92 inference(subsumption_resolution,[status(thm)],[f2482,f1906])).
% 10.60/2.92 thf(f1906,plain,(
% 10.60/2.92 (xx != (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt))) | spl8_2),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f1904])).
% 10.60/2.92 thf(f1904,definition,(
% 10.60/2.92 spl8_2 <=> (xx = (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)))),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 10.60/2.92 thf(f2482,plain,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt))) | (~spl8_8 | ~spl8_13 | ~spl8_15)),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f2481,f2216])).
% 10.60/2.92 thf(f2216,plain,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt))) | ~spl8_15),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f2214])).
% 10.60/2.92 thf(f2214,definition,(
% 10.60/2.92 spl8_15 <=> (xx = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt)))),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_15])],[avatar_definition])).
% 10.60/2.92 thf(f2481,plain,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt))) | (~spl8_8 | ~spl8_13)),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f2480,f1374])).
% 10.60/2.92 thf(f1374,plain,(
% 10.60/2.92 ( ! [X0 : real] : (((minus_minus_real @ X0 @ zero_zero_real) = X0)) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f821])).
% 10.60/2.92 thf(f821,plain,(
% 10.60/2.92 ! [X0 : real] : ((minus_minus_real @ X0 @ zero_zero_real) = X0)),
% 10.60/2.92 inference(rectify,[status(thm)],[f110])).
% 10.60/2.92 thf(f110,axiom,(
% 10.60/2.92 ! [X8 : real] : ((minus_minus_real @ X8 @ zero_zero_real) = X8)),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_109_diff__zero)).
% 10.60/2.92 thf(f2480,plain,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt)) = (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ (minus_minus_real @ tt @ zero_zero_real)))) | (~spl8_8 | ~spl8_13)),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f2479,f2010])).
% 10.60/2.92 thf(f2010,plain,(
% 10.60/2.92 ( ! [X2 : real,X0 : real,X1 : real] : (((plus_plus_real @ X2 @ (minus_minus_real @ X0 @ X1)) = (minus_minus_real @ X2 @ (minus_minus_real @ X1 @ X0)))) )),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f1285,f1266])).
% 10.60/2.92 thf(f1266,plain,(
% 10.60/2.92 ( ! [X2 : real,X0 : real,X1 : real] : (((minus_minus_real @ (plus_plus_real @ X1 @ X2) @ X0) = (minus_minus_real @ X1 @ (minus_minus_real @ X0 @ X2)))) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f842])).
% 10.60/2.92 thf(f842,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : real] : ((minus_minus_real @ (plus_plus_real @ X1 @ X2) @ X0) = (minus_minus_real @ X1 @ (minus_minus_real @ X0 @ X2)))),
% 10.60/2.92 inference(rectify,[status(thm)],[f334])).
% 10.60/2.92 thf(f334,axiom,(
% 10.60/2.92 ! [X9 : real,X8 : real,X18 : real] : ((minus_minus_real @ (plus_plus_real @ X8 @ X18) @ X9) = (minus_minus_real @ X8 @ (minus_minus_real @ X9 @ X18)))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_333_diff__diff__eq2)).
% 10.60/2.92 thf(f1285,plain,(
% 10.60/2.92 ( ! [X2 : real,X0 : real,X1 : real] : (((plus_plus_real @ X2 @ (minus_minus_real @ X0 @ X1)) = (minus_minus_real @ (plus_plus_real @ X2 @ X0) @ X1))) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f844])).
% 10.60/2.92 thf(f844,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : real] : ((plus_plus_real @ X2 @ (minus_minus_real @ X0 @ X1)) = (minus_minus_real @ (plus_plus_real @ X2 @ X0) @ X1))),
% 10.60/2.92 inference(rectify,[status(thm)],[f336])).
% 10.60/2.92 thf(f336,axiom,(
% 10.60/2.92 ! [X9 : real,X18 : real,X8 : real] : ((plus_plus_real @ X8 @ (minus_minus_real @ X9 @ X18)) = (minus_minus_real @ (plus_plus_real @ X8 @ X9) @ X18))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_335_add__diff__eq)).
% 10.60/2.92 thf(f2479,plain,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt)) = (auto_ll_on_flow0_a @ f @ x @ x2 @ (plus_plus_real @ ss @ (minus_minus_real @ zero_zero_real @ tt)))) | (~spl8_8 | ~spl8_13)),
% 10.60/2.92 inference(subsumption_resolution,[status(thm)],[f2473,f1949])).
% 10.60/2.92 thf(f1949,plain,(
% 10.60/2.92 ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) = $true) | ~spl8_8),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f1947])).
% 10.60/2.92 thf(f1947,definition,(
% 10.60/2.92 spl8_8 <=> ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) = $true)),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 10.60/2.92 thf(f2473,plain,(
% 10.60/2.92 ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) != $true) | ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt)) = (auto_ll_on_flow0_a @ f @ x @ x2 @ (plus_plus_real @ ss @ (minus_minus_real @ zero_zero_real @ tt)))) | ~spl8_13),
% 10.60/2.92 inference(trivial_inequality_removal,[status(thm)],[f2468])).
% 10.60/2.92 thf(f2468,plain,(
% 10.60/2.92 ($true != $true) | ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt)) = (auto_ll_on_flow0_a @ f @ x @ x2 @ (plus_plus_real @ ss @ (minus_minus_real @ zero_zero_real @ tt)))) | ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) != $true) | ~spl8_13),
% 10.60/2.92 inference(superposition,[status(thm)],[f1197,f2188])).
% 10.60/2.92 thf(f2188,plain,(
% 10.60/2.92 ((member_real @ (minus_minus_real @ zero_zero_real @ tt) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))) = $true) | ~spl8_13),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f2186])).
% 10.60/2.92 thf(f2186,definition,(
% 10.60/2.92 spl8_13 <=> ((member_real @ (minus_minus_real @ zero_zero_real @ tt) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))) = $true)),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition])).
% 10.60/2.92 thf(f1197,plain,(
% 10.60/2.92 ( ! [X2 : a,X0 : real,X1 : real] : (($true != (member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0)))) | ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X2)) != $true) | ((auto_ll_on_flow0_a @ f @ x @ X2 @ (plus_plus_real @ X0 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0) @ X1))) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f908])).
% 10.60/2.92 thf(f908,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X2)) != $true) | ($true != (member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0)))) | ((auto_ll_on_flow0_a @ f @ x @ X2 @ (plus_plus_real @ X0 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0) @ X1)))),
% 10.60/2.92 inference(flattening,[status(thm)],[f907])).
% 10.60/2.92 thf(f907,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : a] : ((((auto_ll_on_flow0_a @ f @ x @ X2 @ (plus_plus_real @ X0 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0) @ X1)) | ($true != (member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0))))) | ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X2)) != $true))),
% 10.60/2.92 inference(ennf_transformation,[status(thm)],[f481])).
% 10.60/2.92 thf(f481,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X2)) = $true) => (($true = (member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0)))) => ((auto_ll_on_flow0_a @ f @ x @ X2 @ (plus_plus_real @ X0 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0) @ X1))))),
% 10.60/2.92 inference(fool_elimination,[status(thm)],[f480])).
% 10.60/2.92 thf(f480,plain,(
% 10.60/2.92 ! [X0 : real,X1 : real,X2 : a] : ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X2)) => ((member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0))) => ((auto_ll_on_flow0_a @ f @ x @ X2 @ (plus_plus_real @ X0 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X2 @ X0) @ X1))))),
% 10.60/2.92 inference(rectify,[status(thm)],[f160])).
% 10.60/2.92 thf(f160,axiom,(
% 10.60/2.92 ! [X15 : real,X1 : real,X3 : a] : ((member_real @ X15 @ (auto_l612940ivl0_a @ f @ x @ X3)) => ((member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X3 @ X15))) => ((auto_ll_on_flow0_a @ f @ x @ X3 @ (plus_plus_real @ X15 @ X1)) = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X3 @ X15) @ X1))))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_159_local_Oflow__trans)).
% 10.60/2.92 thf(f2217,plain,(
% 10.60/2.92 spl8_15 | ~spl8_9 | ~spl8_10),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f2184,f2156,f1953,f2214])).
% 10.60/2.92 thf(f1953,definition,(
% 10.60/2.92 spl8_9 <=> ((member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx)) = $true)),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition])).
% 10.60/2.92 thf(f2156,definition,(
% 10.60/2.92 spl8_10 <=> ((auto_ll_on_flow0_a @ f @ x @ xx @ tt) = (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))),
% 10.60/2.92 introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition])).
% 10.60/2.92 thf(f2184,plain,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss) @ (minus_minus_real @ zero_zero_real @ tt))) | (~spl8_9 | ~spl8_10)),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f2181,f2158])).
% 10.60/2.92 thf(f2158,plain,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ xx @ tt) = (auto_ll_on_flow0_a @ f @ x @ x2 @ ss)) | ~spl8_10),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f2156])).
% 10.60/2.92 thf(f2181,plain,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ xx @ tt) @ (minus_minus_real @ zero_zero_real @ tt))) | ~spl8_9),
% 10.60/2.92 inference(trivial_inequality_removal,[status(thm)],[f2179])).
% 10.60/2.92 thf(f2179,plain,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ xx @ tt) @ (minus_minus_real @ zero_zero_real @ tt))) | ($true != $true) | ~spl8_9),
% 10.60/2.92 inference(superposition,[status(thm)],[f1325,f1955])).
% 10.60/2.92 thf(f1955,plain,(
% 10.60/2.92 ((member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx)) = $true) | ~spl8_9),
% 10.60/2.92 inference(avatar_component_clause,[status(thm)],[f1953])).
% 10.60/2.92 thf(f1325,plain,(
% 10.60/2.92 ( ! [X0 : real,X1 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) != $true) | ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0) @ (minus_minus_real @ zero_zero_real @ X0)) = X1)) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f1083])).
% 10.60/2.92 thf(f1083,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : (((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0) @ (minus_minus_real @ zero_zero_real @ X0)) = X1) | ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) != $true))),
% 10.60/2.92 inference(ennf_transformation,[status(thm)],[f573])).
% 10.60/2.92 thf(f573,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) = $true) => ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0) @ (minus_minus_real @ zero_zero_real @ X0)) = X1))),
% 10.60/2.92 inference(fool_elimination,[status(thm)],[f572])).
% 10.60/2.92 thf(f572,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) => ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0) @ (minus_minus_real @ zero_zero_real @ X0)) = X1))),
% 10.60/2.92 inference(rectify,[status(thm)],[f34])).
% 10.60/2.92 thf(f34,axiom,(
% 10.60/2.92 ! [X1 : real,X3 : a] : ((member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ X3)) => ((auto_ll_on_flow0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X3 @ X1) @ (minus_minus_real @ zero_zero_real @ X1)) = X3))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_33_local_Oflows__reverse)).
% 10.60/2.92 thf(f2189,plain,(
% 10.60/2.92 spl8_13 | ~spl8_9 | ~spl8_10),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f2170,f2156,f1953,f2186])).
% 10.60/2.92 thf(f2170,plain,(
% 10.60/2.92 ((member_real @ (minus_minus_real @ zero_zero_real @ tt) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))) = $true) | (~spl8_9 | ~spl8_10)),
% 10.60/2.92 inference(forward_demodulation,[status(thm)],[f2168,f2158])).
% 10.60/2.92 thf(f2168,plain,(
% 10.60/2.92 ((member_real @ (minus_minus_real @ zero_zero_real @ tt) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ xx @ tt))) = $true) | ~spl8_9),
% 10.60/2.92 inference(trivial_inequality_removal,[status(thm)],[f2167])).
% 10.60/2.92 thf(f2167,plain,(
% 10.60/2.92 ($true != $true) | ((member_real @ (minus_minus_real @ zero_zero_real @ tt) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ xx @ tt))) = $true) | ~spl8_9),
% 10.60/2.92 inference(superposition,[status(thm)],[f1157,f1955])).
% 10.60/2.92 thf(f1157,plain,(
% 10.60/2.92 ( ! [X0 : real,X1 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) != $true) | ((member_real @ (minus_minus_real @ zero_zero_real @ X0) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0))) = $true)) )),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f920])).
% 10.60/2.92 thf(f920,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) != $true) | ((member_real @ (minus_minus_real @ zero_zero_real @ X0) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0))) = $true))),
% 10.60/2.92 inference(ennf_transformation,[status(thm)],[f549])).
% 10.60/2.92 thf(f549,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : (((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) = $true) => ((member_real @ (minus_minus_real @ zero_zero_real @ X0) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0))) = $true))),
% 10.60/2.92 inference(fool_elimination,[status(thm)],[f548])).
% 10.60/2.92 thf(f548,plain,(
% 10.60/2.92 ! [X0 : real,X1 : a] : ((member_real @ X0 @ (auto_l612940ivl0_a @ f @ x @ X1)) => (member_real @ (minus_minus_real @ zero_zero_real @ X0) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X1 @ X0))))),
% 10.60/2.92 inference(rectify,[status(thm)],[f35])).
% 10.60/2.92 thf(f35,axiom,(
% 10.60/2.92 ! [X1 : real,X3 : a] : ((member_real @ X1 @ (auto_l612940ivl0_a @ f @ x @ X3)) => (member_real @ (minus_minus_real @ zero_zero_real @ X1) @ (auto_l612940ivl0_a @ f @ x @ (auto_ll_on_flow0_a @ f @ x @ X3 @ X1))))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_34_local_Oexistence__ivl__reverse)).
% 10.60/2.92 thf(f2159,plain,(
% 10.60/2.92 spl8_10),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f1243,f2156])).
% 10.60/2.92 thf(f1243,plain,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ xx @ tt) = (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f3])).
% 10.60/2.92 thf(f3,axiom,(
% 10.60/2.92 ((auto_ll_on_flow0_a @ f @ x @ xx @ tt) = (auto_ll_on_flow0_a @ f @ x @ x2 @ ss))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_2_eq)).
% 10.60/2.92 thf(f1956,plain,(
% 10.60/2.92 spl8_9),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f1448,f1953])).
% 10.60/2.92 thf(f1448,plain,(
% 10.60/2.92 ((member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx)) = $true)),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f622])).
% 10.60/2.92 thf(f622,plain,(
% 10.60/2.92 ((member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx)) = $true)),
% 10.60/2.92 inference(fool_elimination,[status(thm)],[f621])).
% 10.60/2.92 thf(f621,plain,(
% 10.60/2.92 (member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx))),
% 10.60/2.92 inference(rectify,[status(thm)],[f5])).
% 10.60/2.92 thf(f5,axiom,(
% 10.60/2.92 (member_real @ tt @ (auto_l612940ivl0_a @ f @ x @ xx))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_4_tt__ex)).
% 10.60/2.92 thf(f1950,plain,(
% 10.60/2.92 spl8_8),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f1410,f1947])).
% 10.60/2.92 thf(f1410,plain,(
% 10.60/2.92 ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) = $true)),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f405])).
% 10.60/2.92 thf(f405,plain,(
% 10.60/2.92 ((member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2)) = $true)),
% 10.60/2.92 inference(fool_elimination,[status(thm)],[f404])).
% 10.60/2.92 thf(f404,plain,(
% 10.60/2.92 (member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2))),
% 10.60/2.92 inference(rectify,[status(thm)],[f6])).
% 10.60/2.92 thf(f6,axiom,(
% 10.60/2.92 (member_real @ ss @ (auto_l612940ivl0_a @ f @ x @ x2))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',fact_5_ss__ex)).
% 10.60/2.92 thf(f1907,plain,(
% 10.60/2.92 ~spl8_2),
% 10.60/2.92 inference(avatar_split_clause,[status(thm)],[f1261,f1904])).
% 10.60/2.92 thf(f1261,plain,(
% 10.60/2.92 (xx != (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)))),
% 10.60/2.92 inference(cnf_transformation,[status(thm)],[f794])).
% 10.60/2.92 thf(f794,plain,(
% 10.60/2.92 (xx != (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)))),
% 10.60/2.92 inference(flattening,[status(thm)],[f344])).
% 10.60/2.92 thf(f344,negated_conjecture,(
% 10.60/2.92 ~(xx = (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)))),
% 10.60/2.92 inference(negated_conjecture,[status(cth)],[f343])).
% 10.60/2.92 thf(f343,conjecture,(
% 10.60/2.92 (xx = (auto_ll_on_flow0_a @ f @ x @ x2 @ (minus_minus_real @ ss @ tt)))),
% 10.60/2.92 file('/export/starexec/sandbox/tmp/tmp.qfqK6NSD51/DTF2THF_28498.p',conj_0)).
% 10.60/2.92 % SZS output end Proof for DTF2THF_28498
% 10.60/2.92 % (28698)------------------------------
% 10.60/2.92 % (28698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.60/2.92 % (28698)Termination reason: Refutation
% 10.60/2.92
% 10.60/2.92 % (28698)Memory used [KB]: 7419
% 10.60/2.92 % (28698)Time elapsed: 0.182 s
% 10.60/2.92 % (28698)Instructions burned: 332 (million)
% 10.60/2.92 % (28698)------------------------------
% 10.60/2.92 % (28698)------------------------------
% 10.60/2.92 % (28598)Success in time 1.395 s
%------------------------------------------------------------------------------