%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP111^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 08:55:38 AM UTC 2026
% Result : Theorem 2.38s 1.95s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 233 ( 38 unt; 0 typ; 7 def)
% Number of atoms : 2060 ( 415 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 3856 ( 286 ~; 416 |; 231 &;2405 @)
% ( 7 <=>; 240 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 20 con; 0-2 aty)
% ( 182 !!; 89 ??; 0 @@+; 0 @@-)
% Number of variables : 367 ( 287 ^; 71 !; 9 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
extended_ereal: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(type_def_8,type,
set_a: $tType ).
thf(func_def_0,type,
extended_ereal: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
extend1289208545_ereal: extended_ereal ).
thf(func_def_4,type,
extended_MInfty: extended_ereal ).
thf(func_def_5,type,
extended_PInfty: extended_ereal ).
thf(func_def_6,type,
times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_7,type,
uminus1208298309_ereal: extended_ereal > extended_ereal ).
thf(func_def_8,type,
zero_z163181189_ereal: extended_ereal ).
thf(func_def_9,type,
lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).
thf(func_def_10,type,
ord_le2001149050_ereal: extended_ereal > extended_ereal > $o ).
thf(func_def_11,type,
divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_12,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_13,type,
topolo1276428101open_a: set_a > $o ).
thf(func_def_14,type,
member_a: a > set_a > $o ).
thf(func_def_15,type,
f: a > extended_ereal ).
thf(func_def_16,type,
x0: a ).
thf(func_def_35,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK2: extended_ereal ).
thf(func_def_37,type,
sK3: set_a > a ).
thf(func_def_38,type,
sK4: extended_ereal > set_a ).
thf(func_def_39,type,
sK5: extended_ereal > extended_ereal ).
thf(func_def_40,type,
sK6: extended_ereal > set_a ).
thf(func_def_41,type,
sK7: extended_ereal > extended_ereal ).
thf(func_def_42,type,
sK8: extended_ereal ).
thf(func_def_43,type,
sK9: set_a > a ).
thf(func_def_44,type,
sK10: extended_ereal ).
thf(func_def_45,type,
sK11: extended_ereal > extended_ereal ).
thf(func_def_46,type,
sK12: extended_ereal > set_a ).
thf(func_def_47,type,
sK13: extended_ereal > extended_ereal ).
thf(func_def_48,type,
sK14: extended_ereal ).
thf(func_def_49,type,
sK15: set_a > a ).
thf(func_def_50,type,
sK16: extended_ereal > extended_ereal ).
thf(func_def_51,type,
sK17: extended_ereal > extended_ereal ).
thf(f1418,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f562,f688,f702,f761,f884,f948,f987,f1281,f1402,f1417]) ).
thf(f1417,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f1416]) ).
thf(f1416,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1415]) ).
thf(f1415,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f1406,f692]) ).
thf(f692,plain,
! [X1: extended_ereal] :
( ( ord_le2001149050_ereal @ X1 @ extended_MInfty )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f691]) ).
thf(f691,plain,
! [X1: extended_ereal] :
( $true
= ( ~ ( ord_le2001149050_ereal @ X1 @ extended_MInfty ) ) ),
inference(forward_demodulation,[status(thm)],[f690,f475]) ).
thf(f475,plain,
( extended_MInfty
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ),
inference(definition_unfolding,[status(thm)],[f379,f474]) ).
thf(f474,plain,
( extend1289208545_ereal
= ( uminus1208298309_ereal @ extended_MInfty ) ),
inference(definition_unfolding,[status(thm)],[f429,f469]) ).
thf(f469,plain,
( extended_PInfty
= ( uminus1208298309_ereal @ extended_MInfty ) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
thf(f352,plain,
( extended_PInfty
= ( uminus1208298309_ereal @ extended_MInfty ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,axiom,
( extended_PInfty
= ( uminus1208298309_ereal @ extended_MInfty ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_40_uminus__ereal_Osimps_I3_J) ).
thf(f429,plain,
extend1289208545_ereal = extended_PInfty,
inference(cnf_transformation,[status(thm)],[f235]) ).
thf(f235,plain,
extend1289208545_ereal = extended_PInfty,
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,axiom,
extend1289208545_ereal = extended_PInfty,
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_49_infinity__ereal__def) ).
thf(f379,plain,
( ( uminus1208298309_ereal @ extend1289208545_ereal )
= extended_MInfty ),
inference(cnf_transformation,[status(thm)],[f134]) ).
thf(f134,plain,
( ( uminus1208298309_ereal @ extend1289208545_ereal )
= extended_MInfty ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,axiom,
( ( uminus1208298309_ereal @ extend1289208545_ereal )
= extended_MInfty ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_37_MInfty__eq__minfinity) ).
thf(f690,plain,
! [X1: extended_ereal] :
( ( ~ ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f689]) ).
thf(f689,plain,
! [X1: extended_ereal] :
( $true
= ( ^ [Y0: extended_ereal] :
~ ( ord_le2001149050_ereal @ Y0 @ ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
~ ( ord_le2001149050_ereal @ Y0 @ ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f423,f474]) ).
thf(f423,plain,
( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
~ ( ord_le2001149050_ereal @ Y0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
thf(f322,plain,
( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
~ ( ord_le2001149050_ereal @ Y0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ),
inference(fool_elimination,[status(thm)],[f321]) ).
thf(f321,plain,
! [X0: extended_ereal] :
~ ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,axiom,
! [X18: extended_ereal] :
~ ( ord_le2001149050_ereal @ X18 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_25_less__ereal_Osimps_I3_J) ).
thf(f1406,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK2 @ extended_MInfty ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f1310,f634]) ).
thf(f634,plain,
( ( ( f @ x0 )
= extended_MInfty )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f633]) ).
thf(f633,definition,
( spl0_4
<=> ( ( f @ x0 )
= extended_MInfty ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1310,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1308]) ).
thf(f1308,plain,
( ( ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1307]) ).
thf(f1307,plain,
( ( ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f561]) ).
thf(f561,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f559]) ).
thf(f559,definition,
( spl0_2
<=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f1402,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1401]) ).
thf(f1401,plain,
( $false
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1400]) ).
thf(f1400,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f1310,f1399]) ).
thf(f1399,plain,
( ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1396]) ).
thf(f1396,plain,
( ( $true = $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f1390,f1366]) ).
thf(f1366,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK12 @ X1 ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1364]) ).
thf(f1364,plain,
( ! [X1: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false )
| ( $true
= ( ( member_a @ x0 @ ( sK12 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK12 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1362]) ).
thf(f1362,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ( member_a @ x0 @ ( sK12 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK12 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ ( sK12 @ X1 ) ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1361]) ).
thf(f1361,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1360]) ).
thf(f1360,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1359]) ).
thf(f1359,plain,
( ! [X1: extended_ereal] :
( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1358]) ).
thf(f1358,plain,
( ! [X1: extended_ereal] :
( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f701]) ).
thf(f701,plain,
( ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f699]) ).
thf(f699,definition,
( spl0_7
<=> ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1390,plain,
( ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1389]) ).
thf(f1389,plain,
( ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1388,f1373]) ).
thf(f1373,plain,
( ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1367]) ).
thf(f1367,plain,
( ( $true = $false )
| ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f1363,f1310]) ).
thf(f1363,plain,
( ! [X1: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false )
| ( $true
= ( topolo1276428101open_a @ ( sK12 @ X1 ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1362]) ).
thf(f1388,plain,
( ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( $true = $false )
| ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $false )
| ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1386,f1310]) ).
thf(f1386,plain,
( ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
= $false )
| ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1379]) ).
thf(f1379,plain,
( ( ( topolo1276428101open_a @ ( sK12 @ sK2 ) )
= $false )
| ( $true = $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
= $false )
| ( ( member_a @ x0 @ ( sK12 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f1365,f1322]) ).
thf(f1322,plain,
( ! [X1: set_a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ! [X1: set_a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) )
= $false )
| ( ( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1320]) ).
thf(f1320,plain,
( ! [X1: set_a] :
( $false
= ( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1319]) ).
thf(f1319,plain,
( ! [X1: set_a] :
( ( ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) )
@ X1 )
= $false )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f1309]) ).
thf(f1309,plain,
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1308]) ).
thf(f1365,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK12 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1364]) ).
thf(f1281,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f1280]) ).
thf(f1280,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1279]) ).
thf(f1279,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f1216,f1278]) ).
thf(f1278,plain,
( ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1276]) ).
thf(f1276,plain,
( ( $true = $false )
| ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f995,f1258]) ).
thf(f1258,plain,
( ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1257]) ).
thf(f1257,plain,
( ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ( $true = $false )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f1256,f1216]) ).
thf(f1256,plain,
( ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1255]) ).
thf(f1255,plain,
( ( $true = $false )
| ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f1248,f1230]) ).
thf(f1230,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK6 @ sK14 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1218]) ).
thf(f1218,plain,
( ( $true = $false )
| ( $true
= ( topolo1276428101open_a @ ( sK6 @ sK14 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f1216,f994]) ).
thf(f994,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK6 @ X1 ) ) ) )
| spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f825,f686]) ).
thf(f686,plain,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f685]) ).
thf(f685,definition,
( spl0_6
<=> ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f825,plain,
( ! [X1: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false )
| ( $true
= ( topolo1276428101open_a @ ( sK6 @ X1 ) ) ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f824]) ).
thf(f824,plain,
( ! [X1: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false )
| ( $true
= ( ( member_a @ x0 @ ( sK6 @ X1 ) )
& ( topolo1276428101open_a @ ( sK6 @ X1 ) ) ) ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f822]) ).
thf(f822,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ( member_a @ x0 @ ( sK6 @ X1 ) )
& ( topolo1276428101open_a @ ( sK6 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK6 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f821]) ).
thf(f821,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) )
@ ( sK6 @ X1 ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| spl0_2 ),
inference(sigma_clausification,[status(thm)],[f802]) ).
thf(f802,plain,
( ! [X1: extended_ereal] :
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) )
= $true )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f801]) ).
thf(f801,plain,
( ! [X1: extended_ereal] :
( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f800]) ).
thf(f800,plain,
( ! [X1: extended_ereal] :
( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ X1 ) )
| spl0_2 ),
inference(pi_clausification,[status(thm)],[f560]) ).
thf(f560,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
!= $false )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f559]) ).
thf(f1248,plain,
( ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ( ( topolo1276428101open_a @ ( sK6 @ sK14 ) )
= $false )
| ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1245]) ).
thf(f1245,plain,
( ( ( topolo1276428101open_a @ ( sK6 @ sK14 ) )
= $false )
| ( $false
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $true = $false )
| ( $false
= ( member_a @ x0 @ ( sK6 @ sK14 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f993,f1240]) ).
thf(f1240,plain,
( ! [X1: set_a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y0 ) ) ) )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f1239]) ).
thf(f1239,plain,
( ! [X1: set_a] :
( ( ( member_a @ x0 @ X1 )
= $false )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ X1 ) )
= $false ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f1238]) ).
thf(f1238,plain,
( ! [X1: set_a] :
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f1237]) ).
thf(f1237,plain,
( ! [X1: set_a] :
( ( ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) )
@ X1 )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f1215]) ).
thf(f1215,plain,
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f1214]) ).
thf(f1214,plain,
( ( ( ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f1213,f686]) ).
thf(f1213,plain,
( ( ( ( ord_le2001149050_ereal @ sK14 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK14 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f1212]) ).
thf(f1212,plain,
( ( ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) )
@ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f770,f686]) ).
thf(f770,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f766]) ).
thf(f766,plain,
( ( $true = $false )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f527,f557]) ).
thf(f557,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f555]) ).
thf(f555,definition,
( spl0_1
<=> ( ( lower_191460856_ereal @ x0 @ f )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f527,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f526]) ).
thf(f526,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f525]) ).
thf(f525,plain,
( ( $true
= ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) ) )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f524]) ).
thf(f524,plain,
( ( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ( $true
= ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f503]) ).
thf(f503,plain,
( $true
= ( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f441,f474]) ).
thf(f441,plain,
( $true
= ( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
thf(f142,plain,
( $true
= ( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062) ).
thf(f993,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK6 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f823,f686]) ).
thf(f823,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK6 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f822]) ).
thf(f995,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK6 @ X1 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f826,f686]) ).
thf(f826,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK6 @ X1 ) ) )
| ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
= $false ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f824]) ).
thf(f1216,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK14 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f1214]) ).
thf(f987,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f986]) ).
thf(f986,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f985]) ).
thf(f985,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f984]) ).
thf(f984,plain,
( ( ( $false
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK10 @ ( f @ Y1 ) ) ) )
& ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f983,f692]) ).
thf(f983,plain,
( ( $false
= ( ( ord_le2001149050_ereal @ sK10 @ extended_MInfty )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK10 @ ( f @ Y1 ) ) ) )
& ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f982,f634]) ).
thf(f982,plain,
( ( $false
= ( ( ord_le2001149050_ereal @ sK10 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK10 @ ( f @ Y1 ) ) ) )
& ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f981]) ).
thf(f981,plain,
( ( ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) )
@ sK10 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f975]) ).
thf(f975,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f974]) ).
thf(f974,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( extended_MInfty != extended_MInfty )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f953,f634]) ).
thf(f953,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
!= extended_MInfty )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f952]) ).
thf(f952,plain,
( ( $true = $false )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
!= extended_MInfty )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f544,f557]) ).
thf(f544,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_MInfty )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f543]) ).
thf(f543,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
!= extended_MInfty ) ),
inference(equality_proxy_clausification,[status(thm)],[f542]) ).
thf(f542,plain,
( ( ( f @ x0 )
!= extended_MInfty )
| ( $true
= ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f541]) ).
thf(f541,plain,
( ( ( ( f @ x0 )
= extended_MInfty )
= $false )
| ( $true
= ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f540]) ).
thf(f540,plain,
( $true
= ( ( ( f @ x0 )
= extended_MInfty )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(forward_demodulation,[status(thm)],[f480,f475]) ).
thf(f480,plain,
( $true
= ( ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(definition_unfolding,[status(thm)],[f370,f474]) ).
thf(f370,plain,
( $true
= ( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
thf(f188,plain,
( $true
= ( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(fool_elimination,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062) ).
thf(f948,plain,
( spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f947]) ).
thf(f947,plain,
( $false
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f946]) ).
thf(f946,plain,
( ( $true = $false )
| spl0_2
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f890,f945]) ).
thf(f945,plain,
( ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f943]) ).
thf(f943,plain,
( ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| ( $true = $false )
| spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f826,f929]) ).
thf(f929,plain,
( ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f928]) ).
thf(f928,plain,
( ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| ( $true = $false )
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f927,f890]) ).
thf(f927,plain,
( ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f926]) ).
thf(f926,plain,
( ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| ( $true = $false )
| ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f922,f905]) ).
thf(f905,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK6 @ sK8 ) ) )
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f891]) ).
thf(f891,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK6 @ sK8 ) ) )
| ( $true = $false )
| spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f890,f825]) ).
thf(f922,plain,
( ( ( topolo1276428101open_a @ ( sK6 @ sK8 ) )
= $false )
| ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f917]) ).
thf(f917,plain,
( ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
= $false )
| ( ( topolo1276428101open_a @ ( sK6 @ sK8 ) )
= $false )
| ( ( member_a @ x0 @ ( sK6 @ sK8 ) )
= $false )
| ( $true = $false )
| spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f823,f913]) ).
thf(f913,plain,
( ! [X1: set_a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y0 ) ) ) )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f912]) ).
thf(f912,plain,
( ! [X1: set_a] :
( ( ( ( member_a @ x0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y0 ) ) ) ) )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f911]) ).
thf(f911,plain,
( ! [X1: set_a] :
( ( ( member_a @ x0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ X1 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f910]) ).
thf(f910,plain,
( ! [X1: set_a] :
( ( ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) )
@ X1 )
= $false )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f889]) ).
thf(f889,plain,
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f888]) ).
thf(f888,plain,
( ( ( ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK8 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f887]) ).
thf(f887,plain,
( ( ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f883]) ).
thf(f883,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f881]) ).
thf(f881,definition,
( spl0_8
<=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f890,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK8 @ ( f @ x0 ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f888]) ).
thf(f884,plain,
( spl0_8
| spl0_6
| ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f768,f633,f555,f685,f881]) ).
thf(f768,plain,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f765]) ).
thf(f765,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( $true = $false )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_1
| spl0_4 ),
inference(backward_demodulation,[status(thm)],[f764,f557]) ).
thf(f764,plain,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f531,f635]) ).
thf(f635,plain,
( ( ( f @ x0 )
!= extended_MInfty )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f633]) ).
thf(f531,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
= extended_MInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f522,f475]) ).
thf(f522,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f520]) ).
thf(f520,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= $false )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f519]) ).
thf(f519,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f518]) ).
thf(f518,plain,
( ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f517]) ).
thf(f517,plain,
( ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f516]) ).
thf(f516,plain,
( ( $true
= ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) )
| ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f515]) ).
thf(f515,plain,
( ( $true
= ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f514]) ).
thf(f514,plain,
( ( $false
= ( ( f @ x0 )
!= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ( $true
= ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f489]) ).
thf(f489,plain,
( $true
= ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
=> ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f391,f474,f474]) ).
thf(f391,plain,
( $true
= ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
thf(f184,plain,
( $true
= ( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( topolo1276428101open_a @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ( topolo1276428101open_a @ X1 )
& ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062) ).
thf(f761,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f760]) ).
thf(f760,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f759]) ).
thf(f759,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f703,f758]) ).
thf(f758,plain,
( ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f755]) ).
thf(f755,plain,
( ( $true = $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f753,f723]) ).
thf(f723,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK4 @ X1 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f722]) ).
thf(f722,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK4 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ ( sK4 @ X1 ) )
& ( member_a @ x0 @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f721]) ).
thf(f721,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $true
= ( ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) )
@ ( sK4 @ X1 ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f720]) ).
thf(f720,plain,
( ! [X1: extended_ereal] :
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f719]) ).
thf(f719,plain,
( ! [X1: extended_ereal] :
( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f718,f686]) ).
thf(f718,plain,
( ! [X1: extended_ereal] :
( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) )
& ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f717]) ).
thf(f717,plain,
( ! [X1: extended_ereal] :
( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f683]) ).
thf(f683,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f681]) ).
thf(f681,definition,
( spl0_5
<=> ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f753,plain,
( ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f752]) ).
thf(f752,plain,
( ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f751,f703]) ).
thf(f751,plain,
( ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f750]) ).
thf(f750,plain,
( ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f749,f737]) ).
thf(f737,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK4 @ sK2 ) ) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f729]) ).
thf(f729,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK4 @ sK2 ) ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f725,f703]) ).
thf(f725,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( ( topolo1276428101open_a @ ( sK4 @ X1 ) )
= $true ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f724]) ).
thf(f724,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK4 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) )
& ( topolo1276428101open_a @ ( sK4 @ X1 ) ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f722]) ).
thf(f749,plain,
( ( ( topolo1276428101open_a @ ( sK4 @ sK2 ) )
= $false )
| ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f745]) ).
thf(f745,plain,
( ( $true = $false )
| ( ( topolo1276428101open_a @ ( sK4 @ sK2 ) )
= $false )
| ( ( member_a @ x0 @ ( sK4 @ sK2 ) )
= $false )
| ( ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) )
= $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f726,f578]) ).
thf(f578,plain,
( ! [X1: set_a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f577]) ).
thf(f577,plain,
( ! [X1: set_a] :
( ( ( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f576]) ).
thf(f576,plain,
( ! [X1: set_a] :
( $false
= ( ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f575]) ).
thf(f575,plain,
( ! [X1: set_a] :
( ( ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) )
@ X1 )
= $false )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f573]) ).
thf(f573,plain,
( ( ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f572]) ).
thf(f572,plain,
( ( ( ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( member_a @ x0 @ Y0 )
& ( topolo1276428101open_a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK2 @ ( f @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f571]) ).
thf(f571,plain,
( ( ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f561]) ).
thf(f726,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK4 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f724]) ).
thf(f703,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK2 @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f574,f686]) ).
thf(f574,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK2 @ ( f @ x0 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f572]) ).
thf(f702,plain,
( spl0_7
| spl0_6
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f570,f559,f633,f685,f699]) ).
thf(f570,plain,
( ( ( f @ x0 )
= extended_MInfty )
| ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f566]) ).
thf(f566,plain,
( ( $true = $false )
| ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( f @ x0 )
= extended_MInfty )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f530,f564]) ).
thf(f564,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f563]) ).
thf(f563,plain,
( ( $true = $false )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f539,f561]) ).
thf(f539,plain,
( ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f536]) ).
thf(f536,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f535]) ).
thf(f535,plain,
( ( lower_191460856_ereal @ x0 @ f )
= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f513]) ).
thf(f513,plain,
( $true
= ( ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
= ( lower_191460856_ereal @ x0 @ f ) ) ),
inference(boolean_simplification,[status(thm)],[f428]) ).
thf(f428,plain,
( $true
= ( ~ ( ( ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
!= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
thf(f156,plain,
( $true
= ( ~ ( ( ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
!= ( lower_191460856_ereal @ x0 @ f ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f155]) ).
thf(f155,plain,
~ ~ ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) )
!= ( lower_191460856_ereal @ x0 @ f ) ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,negated_conjecture,
~ ~ ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) )
!= ( lower_191460856_ereal @ x0 @ f ) ),
inference(negated_conjecture,[status(cth)],[f121]) ).
thf(f121,conjecture,
~ ! [X0: extended_ereal] :
( ( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) )
!= ( lower_191460856_ereal @ x0 @ f ) ),
file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',conj_0) ).
thf(f530,plain,
( ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( ( f @ x0 )
= extended_MInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false ) ),
inference(backward_demodulation,[status(thm)],[f523,f475]) ).
thf(f523,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f521]) ).
thf(f521,plain,
( ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( $true
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 ) ) ) ) ) )
| ( $true
= ( ( f @ x0 )
= ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ extended_MInfty ) ) ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f519]) ).
thf(f688,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f568,f559,f685,f681]) ).
thf(f568,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $true )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f565]) ).
thf(f565,plain,
( ( $true = $false )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $true )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f528,f564]) ).
thf(f528,plain,
( ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) )
& ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 ) ) ) ) )
= $true )
| ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extended_MInfty ) )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f526]) ).
thf(f562,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f538,f559,f555]) ).
thf(f538,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f537]) ).
thf(f537,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $true
= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( member_a @ x0 @ Y1 )
& ( topolo1276428101open_a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP111^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:24:56 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.45 ---- Original DTF file ---
% 0.26/0.45 thf(spec,logic,$$dhol).
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % File : ITP111^1 : TPTP v9.2.1. Released v7.5.0.
% 0.26/0.45 % Domain : Interactive Theorem Proving
% 0.26/0.45 % Problem : Sledgehammer Lower_Semicontinuous problem prob_214__6249176_1
% 0.26/0.45 % Version : Especial.
% 0.26/0.45 % English :
% 0.26/0.45
% 0.26/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.45 % Source : [Des21]
% 0.26/0.45 % Names : Lower_Semicontinuous/prob_214__6249176_1 [Des21]
% 0.26/0.45
% 0.26/0.45 % Status : Theorem
% 0.26/0.45 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.45 % Syntax : Number of formulae : 138 ( 59 unt; 17 typ; 0 def)
% 0.26/0.45 % Number of atoms : 359 ( 148 equ; 0 cnn)
% 0.26/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.26/0.45 % Number of connectives : 932 ( 58 ~; 18 |; 35 &; 684 @)
% 0.26/0.45 % ( 0 <=>; 137 =>; 0 <=; 0 <~>)
% 0.26/0.45 % Maximal formula depth : 14 ( 6 avg)
% 0.26/0.45 % Number of types : 4 ( 3 usr)
% 0.26/0.45 % Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% 0.26/0.45 % Number of symbols : 15 ( 14 usr; 5 con; 0-2 aty)
% 0.26/0.45 % Number of variables : 288 ( 3 ^; 255 !; 30 ?; 288 :)
% 0.26/0.45 % SPC : TH0_THM_EQU_NAR
% 0.26/0.45
% 0.26/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:48.195
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % Could-be-implicit typings (3)
% 0.26/0.45 thf(ty_n_t__Extended____Real__Oereal,type,
% 0.26/0.45 extended_ereal: $tType ).
% 0.26/0.45
% 0.26/0.45 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.26/0.45 set_a: $tType ).
% 0.26/0.45
% 0.26/0.45 thf(ty_n_tf__a,type,
% 0.26/0.45 a: $tType ).
% 0.26/0.45
% 0.26/0.45 % Explicit typings (14)
% 0.26/0.45 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity_001t__Extended____Real__Oereal,type,
% 0.26/0.45 extend1289208545_ereal: extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Extended__Real_Oereal_OMInfty,type,
% 0.26/0.45 extended_MInfty: extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Extended__Real_Oereal_OPInfty,type,
% 0.26/0.45 extended_PInfty: extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Real__Oereal,type,
% 0.26/0.45 times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Extended____Real__Oereal,type,
% 0.26/0.45 uminus1208298309_ereal: extended_ereal > extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Real__Oereal,type,
% 0.26/0.45 zero_z163181189_ereal: extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Olsc__at_001tf__a_001t__Extended____Real__Oereal,type,
% 0.26/0.45 lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Real__Oereal,type,
% 0.26/0.45 ord_le2001149050_ereal: extended_ereal > extended_ereal > $o ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Rings_Odivide__class_Odivide_001t__Extended____Real__Oereal,type,
% 0.26/0.45 divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.26/0.45 collect_a: ( a > $o ) > set_a ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001tf__a,type,
% 0.26/0.45 topolo1276428101open_a: set_a > $o ).
% 0.26/0.45
% 0.26/0.45 thf(sy_c_member_001tf__a,type,
% 0.26/0.45 member_a: a > set_a > $o ).
% 0.26/0.45
% 0.26/0.45 thf(sy_v_f,type,
% 0.26/0.45 f: a > extended_ereal ).
% 0.26/0.45
% 0.26/0.45 thf(sy_v_x0,type,
% 0.26/0.45 x0: a ).
% 0.26/0.45
% 0.26/0.45 % Relevant facts (120)
% 0.26/0.45 thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.26/0.45 ( ( ( f @ x0 )
% 0.26/0.45 = extend1289208545_ereal )
% 0.26/0.45 => ( ( lower_191460856_ereal @ x0 @ f )
% 0.26/0.45 = ( ! [C: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 0.26/0.45 => ? [T: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ T )
% 0.26/0.45 & ( member_a @ x0 @ T )
% 0.26/0.45 & ! [X: a] :
% 0.26/0.45 ( ( member_a @ X @ T )
% 0.26/0.45 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % \<open>f x0 = \<infinity> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.26/0.45 thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.26/0.45 ( ( ( f @ x0 )
% 0.26/0.45 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.45 => ( ( lower_191460856_ereal @ x0 @ f )
% 0.26/0.45 = ( ! [C: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 0.26/0.45 => ? [T: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ T )
% 0.26/0.45 & ( member_a @ x0 @ T )
% 0.26/0.45 & ! [X: a] :
% 0.26/0.45 ( ( member_a @ X @ T )
% 0.26/0.45 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % \<open>f x0 = - \<infinity> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.26/0.45 thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 0.26/0.45 ( ( ( f @ x0 )
% 0.26/0.45 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.45 => ( ( ( f @ x0 )
% 0.26/0.45 != extend1289208545_ereal )
% 0.26/0.45 => ( ( lower_191460856_ereal @ x0 @ f )
% 0.26/0.45 = ( ! [C: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 0.26/0.45 => ? [T: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ T )
% 0.26/0.45 & ( member_a @ x0 @ T )
% 0.26/0.45 & ! [X: a] :
% 0.26/0.45 ( ( member_a @ X @ T )
% 0.26/0.45 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % \<open>\<lbrakk>f x0 \<noteq> - \<infinity>; f x0 \<noteq> \<infinity>\<rbrakk> \<Longrightarrow> lsc_at x0 f = (\<forall>C<f x0. \<exists>T. open T \<and> x0 \<in> T \<and> (\<forall>y\<in>T. C < f y))\<close>
% 0.26/0.45 thf(fact_3_lsc__at__MInfty,axiom,
% 0.26/0.45 ! [F: a > extended_ereal,X0: a] :
% 0.26/0.45 ( ( ( F @ X0 )
% 0.26/0.45 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.45 => ( lower_191460856_ereal @ X0 @ F ) ) ).
% 0.26/0.45
% 0.26/0.45 % lsc_at_MInfty
% 0.26/0.45 thf(fact_4_t0__space,axiom,
% 0.26/0.45 ! [X2: a,Y: a] :
% 0.26/0.45 ( ( X2 != Y )
% 0.26/0.45 => ? [U: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ U )
% 0.26/0.45 & ( ( member_a @ X2 @ U )
% 0.26/0.45 != ( member_a @ Y @ U ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % t0_space
% 0.26/0.45 thf(fact_5_t1__space,axiom,
% 0.26/0.45 ! [X2: a,Y: a] :
% 0.26/0.45 ( ( X2 != Y )
% 0.26/0.45 => ? [U: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ U )
% 0.26/0.45 & ( member_a @ X2 @ U )
% 0.26/0.45 & ~ ( member_a @ Y @ U ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % t1_space
% 0.26/0.45 thf(fact_6_separation__t0,axiom,
% 0.26/0.45 ! [X2: a,Y: a] :
% 0.26/0.45 ( ( X2 != Y )
% 0.26/0.45 = ( ? [U2: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ U2 )
% 0.26/0.45 & ( ( member_a @ X2 @ U2 )
% 0.26/0.45 != ( member_a @ Y @ U2 ) ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % separation_t0
% 0.26/0.45 thf(fact_7_separation__t1,axiom,
% 0.26/0.45 ! [X2: a,Y: a] :
% 0.26/0.45 ( ( X2 != Y )
% 0.26/0.45 = ( ? [U2: set_a] :
% 0.26/0.45 ( ( topolo1276428101open_a @ U2 )
% 0.26/0.45 & ( member_a @ X2 @ U2 )
% 0.26/0.45 & ~ ( member_a @ Y @ U2 ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 % separation_t1
% 0.26/0.45 thf(fact_8_minf_I7_J,axiom,
% 0.26/0.45 ! [T2: extended_ereal] :
% 0.26/0.45 ? [Z: extended_ereal] :
% 0.26/0.45 ! [X3: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.45 => ~ ( ord_le2001149050_ereal @ T2 @ X3 ) ) ).
% 0.26/0.45
% 0.26/0.45 % minf(7)
% 0.26/0.45 thf(fact_9_minf_I5_J,axiom,
% 0.26/0.45 ! [T2: extended_ereal] :
% 0.26/0.45 ? [Z: extended_ereal] :
% 0.26/0.45 ! [X3: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.45 => ( ord_le2001149050_ereal @ X3 @ T2 ) ) ).
% 0.26/0.45
% 0.26/0.45 % minf(5)
% 0.26/0.45 thf(fact_10_minf_I4_J,axiom,
% 0.26/0.45 ! [T2: extended_ereal] :
% 0.26/0.45 ? [Z: extended_ereal] :
% 0.26/0.45 ! [X3: extended_ereal] :
% 0.26/0.45 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.45 => ( X3 != T2 ) ) ).
% 0.26/0.45
% 0.26/0.45 % minf(4)
% 0.26/0.45 thf(fact_11_minf_I3_J,axiom,
% 0.26/0.46 ! [T2: extended_ereal] :
% 0.26/0.46 ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.46 => ( X3 != T2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % minf(3)
% 0.26/0.46 thf(fact_12_minf_I2_J,axiom,
% 0.26/0.46 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 0.26/0.46 ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 0.26/0.46 => ( ( P @ X4 )
% 0.26/0.46 = ( P2 @ X4 ) ) )
% 0.26/0.46 => ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 0.26/0.46 => ( ( Q @ X4 )
% 0.26/0.46 = ( Q2 @ X4 ) ) )
% 0.26/0.46 => ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.46 => ( ( ( P @ X3 )
% 0.26/0.46 | ( Q @ X3 ) )
% 0.26/0.46 = ( ( P2 @ X3 )
% 0.26/0.46 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % minf(2)
% 0.26/0.46 thf(fact_13_pinf_I1_J,axiom,
% 0.26/0.46 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 0.26/0.46 ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 0.26/0.46 => ( ( P @ X4 )
% 0.26/0.46 = ( P2 @ X4 ) ) )
% 0.26/0.46 => ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 0.26/0.46 => ( ( Q @ X4 )
% 0.26/0.46 = ( Q2 @ X4 ) ) )
% 0.26/0.46 => ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ( ( ( P @ X3 )
% 0.26/0.46 & ( Q @ X3 ) )
% 0.26/0.46 = ( ( P2 @ X3 )
% 0.26/0.46 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(1)
% 0.26/0.46 thf(fact_14_pinf_I2_J,axiom,
% 0.26/0.46 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 0.26/0.46 ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 0.26/0.46 => ( ( P @ X4 )
% 0.26/0.46 = ( P2 @ X4 ) ) )
% 0.26/0.46 => ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 0.26/0.46 => ( ( Q @ X4 )
% 0.26/0.46 = ( Q2 @ X4 ) ) )
% 0.26/0.46 => ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ( ( ( P @ X3 )
% 0.26/0.46 | ( Q @ X3 ) )
% 0.26/0.46 = ( ( P2 @ X3 )
% 0.26/0.46 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(2)
% 0.26/0.46 thf(fact_15_pinf_I3_J,axiom,
% 0.26/0.46 ! [T2: extended_ereal] :
% 0.26/0.46 ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ( X3 != T2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(3)
% 0.26/0.46 thf(fact_16_pinf_I4_J,axiom,
% 0.26/0.46 ! [T2: extended_ereal] :
% 0.26/0.46 ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ( X3 != T2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(4)
% 0.26/0.46 thf(fact_17_pinf_I5_J,axiom,
% 0.26/0.46 ! [T2: extended_ereal] :
% 0.26/0.46 ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ X3 @ T2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(5)
% 0.26/0.46 thf(fact_18_pinf_I7_J,axiom,
% 0.26/0.46 ! [T2: extended_ereal] :
% 0.26/0.46 ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ T2 @ X3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pinf(7)
% 0.26/0.46 thf(fact_19_minf_I1_J,axiom,
% 0.26/0.46 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 0.26/0.46 ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 0.26/0.46 => ( ( P @ X4 )
% 0.26/0.46 = ( P2 @ X4 ) ) )
% 0.26/0.46 => ( ? [Z2: extended_ereal] :
% 0.26/0.46 ! [X4: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 0.26/0.46 => ( ( Q @ X4 )
% 0.26/0.46 = ( Q2 @ X4 ) ) )
% 0.26/0.46 => ? [Z: extended_ereal] :
% 0.26/0.46 ! [X3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 0.26/0.46 => ( ( ( P @ X3 )
% 0.26/0.46 & ( Q @ X3 ) )
% 0.26/0.46 = ( ( P2 @ X3 )
% 0.26/0.46 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % minf(1)
% 0.26/0.46 thf(fact_20_ereal__MInfty__lessI,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( A
% 0.26/0.46 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_MInfty_lessI
% 0.26/0.46 thf(fact_21_ereal__infty__less_I2_J,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ X2 )
% 0.26/0.46 = ( X2
% 0.26/0.46 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_infty_less(2)
% 0.26/0.46 thf(fact_22_ereal__minus__less__minus,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ A ) @ ( uminus1208298309_ereal @ B ) )
% 0.26/0.46 = ( ord_le2001149050_ereal @ B @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_minus_less_minus
% 0.26/0.46 thf(fact_23_ereal__less__PInfty,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( A != extend1289208545_ereal )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_less_PInfty
% 0.26/0.46 thf(fact_24_ereal__infty__less_I1_J,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ extend1289208545_ereal )
% 0.26/0.46 = ( X2 != extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_infty_less(1)
% 0.26/0.46 thf(fact_25_less__ereal_Osimps_I3_J,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ~ ( ord_le2001149050_ereal @ A @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_ereal.simps(3)
% 0.26/0.46 thf(fact_26_less__ereal_Osimps_I6_J,axiom,
% 0.26/0.46 ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal ).
% 0.26/0.46
% 0.26/0.46 % less_ereal.simps(6)
% 0.26/0.46 thf(fact_27_ereal__uminus__eq__iff,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ( uminus1208298309_ereal @ A )
% 0.26/0.46 = ( uminus1208298309_ereal @ B ) )
% 0.26/0.46 = ( A = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_eq_iff
% 0.26/0.46 thf(fact_28_ereal__uminus__uminus,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ A ) )
% 0.26/0.46 = A ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_uminus
% 0.26/0.46 thf(fact_29_ereal__uminus__eq__reorder,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ( uminus1208298309_ereal @ A )
% 0.26/0.46 = B )
% 0.26/0.46 = ( A
% 0.26/0.46 = ( uminus1208298309_ereal @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_eq_reorder
% 0.26/0.46 thf(fact_30_MInfty__neq__PInfty_I1_J,axiom,
% 0.26/0.46 ( extend1289208545_ereal
% 0.26/0.46 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % MInfty_neq_PInfty(1)
% 0.26/0.46 thf(fact_31_less__ereal_Osimps_I2_J,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ~ ( ord_le2001149050_ereal @ extend1289208545_ereal @ A ) ).
% 0.26/0.46
% 0.26/0.46 % less_ereal.simps(2)
% 0.26/0.46 thf(fact_32_ereal__less__uminus__reorder,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ ( uminus1208298309_ereal @ B ) )
% 0.26/0.46 = ( ord_le2001149050_ereal @ B @ ( uminus1208298309_ereal @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_less_uminus_reorder
% 0.26/0.46 thf(fact_33_ereal__uminus__less__reorder,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ A ) @ B )
% 0.26/0.46 = ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ B ) @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_less_reorder
% 0.26/0.46 thf(fact_34_mem__Collect__eq,axiom,
% 0.26/0.46 ! [A: a,P: a > $o] :
% 0.26/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.26/0.46 = ( P @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % mem_Collect_eq
% 0.26/0.46 thf(fact_35_Collect__mem__eq,axiom,
% 0.26/0.46 ! [A2: set_a] :
% 0.26/0.46 ( ( collect_a
% 0.26/0.46 @ ^ [X: a] : ( member_a @ X @ A2 ) )
% 0.26/0.46 = A2 ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_mem_eq
% 0.26/0.46 thf(fact_36_Collect__cong,axiom,
% 0.26/0.46 ! [P: a > $o,Q: a > $o] :
% 0.26/0.46 ( ! [X4: a] :
% 0.26/0.46 ( ( P @ X4 )
% 0.26/0.46 = ( Q @ X4 ) )
% 0.26/0.46 => ( ( collect_a @ P )
% 0.26/0.46 = ( collect_a @ Q ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_cong
% 0.26/0.46 thf(fact_37_MInfty__eq__minfinity,axiom,
% 0.26/0.46 ( extended_MInfty
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % MInfty_eq_minfinity
% 0.26/0.46 thf(fact_38_verit__comp__simplify1_I1_J,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ~ ( ord_le2001149050_ereal @ A @ A ) ).
% 0.26/0.46
% 0.26/0.46 % verit_comp_simplify1(1)
% 0.26/0.46 thf(fact_39_uminus__ereal_Osimps_I2_J,axiom,
% 0.26/0.46 ( ( uminus1208298309_ereal @ extended_PInfty )
% 0.26/0.46 = extended_MInfty ) ).
% 0.26/0.46
% 0.26/0.46 % uminus_ereal.simps(2)
% 0.26/0.46 thf(fact_40_uminus__ereal_Osimps_I3_J,axiom,
% 0.26/0.46 ( ( uminus1208298309_ereal @ extended_MInfty )
% 0.26/0.46 = extended_PInfty ) ).
% 0.26/0.46
% 0.26/0.46 % uminus_ereal.simps(3)
% 0.26/0.46 thf(fact_41_ereal__less_I6_J,axiom,
% 0.26/0.46 ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ zero_z163181189_ereal ).
% 0.26/0.46
% 0.26/0.46 % ereal_less(6)
% 0.26/0.46 thf(fact_42_ex__gt__or__lt,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ? [B2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B2 )
% 0.26/0.46 | ( ord_le2001149050_ereal @ B2 @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % ex_gt_or_lt
% 0.26/0.46 thf(fact_43_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ B @ A )
% 0.26/0.46 => ( A != B ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.strict_implies_not_eq
% 0.26/0.46 thf(fact_44_ereal__uminus__zero__iff,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( ( uminus1208298309_ereal @ A )
% 0.26/0.46 = zero_z163181189_ereal )
% 0.26/0.46 = ( A = zero_z163181189_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_zero_iff
% 0.26/0.46 thf(fact_45_ereal__uminus__zero,axiom,
% 0.26/0.46 ( ( uminus1208298309_ereal @ zero_z163181189_ereal )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_zero
% 0.26/0.46 thf(fact_46_neg__0__less__iff__less__erea,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ ( uminus1208298309_ereal @ A ) )
% 0.26/0.46 = ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % neg_0_less_iff_less_erea
% 0.26/0.46 thf(fact_47_zero__reorient,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ( ( zero_z163181189_ereal = X2 )
% 0.26/0.46 = ( X2 = zero_z163181189_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % zero_reorient
% 0.26/0.46 thf(fact_48_Infty__neq__0_I1_J,axiom,
% 0.26/0.46 extend1289208545_ereal != zero_z163181189_ereal ).
% 0.26/0.46
% 0.26/0.46 % Infty_neq_0(1)
% 0.26/0.46 thf(fact_49_infinity__ereal__def,axiom,
% 0.26/0.46 extend1289208545_ereal = extended_PInfty ).
% 0.26/0.46
% 0.26/0.46 % infinity_ereal_def
% 0.26/0.46 thf(fact_50_ereal_Odistinct_I5_J,axiom,
% 0.26/0.46 extended_PInfty != extended_MInfty ).
% 0.26/0.46
% 0.26/0.46 % ereal.distinct(5)
% 0.26/0.46 thf(fact_51_Infty__neq__0_I3_J,axiom,
% 0.26/0.46 ( ( uminus1208298309_ereal @ extend1289208545_ereal )
% 0.26/0.46 != zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % Infty_neq_0(3)
% 0.26/0.46 thf(fact_52_ereal__less_I5_J,axiom,
% 0.26/0.46 ord_le2001149050_ereal @ zero_z163181189_ereal @ extend1289208545_ereal ).
% 0.26/0.46
% 0.26/0.46 % ereal_less(5)
% 0.26/0.46 thf(fact_53_ord__eq__less__subst,axiom,
% 0.26/0.46 ! [A: extended_ereal,F: extended_ereal > extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( A
% 0.26/0.46 = ( F @ B ) )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 0.26/0.46 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_less_subst
% 0.26/0.46 thf(fact_54_ord__less__eq__subst,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,F: extended_ereal > extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ( F @ B )
% 0.26/0.46 = C2 )
% 0.26/0.46 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_less_eq_subst
% 0.26/0.46 thf(fact_55_order__less__subst1,axiom,
% 0.26/0.46 ! [A: extended_ereal,F: extended_ereal > extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ ( F @ B ) )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 0.26/0.46 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_less_subst1
% 0.26/0.46 thf(fact_56_order__less__subst2,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,F: extended_ereal > extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ ( F @ B ) @ C2 )
% 0.26/0.46 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_less_subst2
% 0.26/0.46 thf(fact_57_neqE,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( X2 != Y )
% 0.26/0.46 => ( ~ ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % neqE
% 0.26/0.46 thf(fact_58_neq__iff,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( X2 != Y )
% 0.26/0.46 = ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 | ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % neq_iff
% 0.26/0.46 thf(fact_59_order_Oasym,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ B @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % order.asym
% 0.26/0.46 thf(fact_60_dense,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ? [Z: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Z )
% 0.26/0.46 & ( ord_le2001149050_ereal @ Z @ Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dense
% 0.26/0.46 thf(fact_61_less__imp__neq,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( X2 != Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_imp_neq
% 0.26/0.46 thf(fact_62_less__asym,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_asym
% 0.26/0.46 thf(fact_63_less__asym_H,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ B @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_asym'
% 0.26/0.46 thf(fact_64_less__trans,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ Y @ Z3 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ X2 @ Z3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_trans
% 0.26/0.46 thf(fact_65_less__linear,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 | ( X2 = Y )
% 0.26/0.46 | ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_linear
% 0.26/0.46 thf(fact_66_less__irrefl,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ~ ( ord_le2001149050_ereal @ X2 @ X2 ) ).
% 0.26/0.46
% 0.26/0.46 % less_irrefl
% 0.26/0.46 thf(fact_67_ord__eq__less__trans,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( A = B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_less_trans
% 0.26/0.46 thf(fact_68_ord__less__eq__trans,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( B = C2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_less_eq_trans
% 0.26/0.46 thf(fact_69_dual__order_Oasym,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ B @ A )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ A @ B ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.asym
% 0.26/0.46 thf(fact_70_less__imp__not__eq,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( X2 != Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_imp_not_eq
% 0.26/0.46 thf(fact_71_less__not__sym,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_not_sym
% 0.26/0.46 thf(fact_72_antisym__conv3,axiom,
% 0.26/0.46 ! [Y: extended_ereal,X2: extended_ereal] :
% 0.26/0.46 ( ~ ( ord_le2001149050_ereal @ Y @ X2 )
% 0.26/0.46 => ( ( ~ ( ord_le2001149050_ereal @ X2 @ Y ) )
% 0.26/0.46 = ( X2 = Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % antisym_conv3
% 0.26/0.46 thf(fact_73_less__imp__not__eq2,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( Y != X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_imp_not_eq2
% 0.26/0.46 thf(fact_74_less__imp__triv,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal,P: $o] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ Y @ X2 )
% 0.26/0.46 => P ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_imp_triv
% 0.26/0.46 thf(fact_75_linorder__cases,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ~ ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ( ( X2 != Y )
% 0.26/0.46 => ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % linorder_cases
% 0.26/0.46 thf(fact_76_dual__order_Oirrefl,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ~ ( ord_le2001149050_ereal @ A @ A ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.irrefl
% 0.26/0.46 thf(fact_77_order_Ostrict__trans,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 0.26/0.46 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order.strict_trans
% 0.26/0.46 thf(fact_78_less__imp__not__less,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 0.26/0.46 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_imp_not_less
% 0.26/0.46 thf(fact_79_linorder__less__wlog,axiom,
% 0.26/0.46 ! [P: extended_ereal > extended_ereal > $o,A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ! [A3: extended_ereal,B2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A3 @ B2 )
% 0.26/0.46 => ( P @ A3 @ B2 ) )
% 0.26/0.46 => ( ! [A3: extended_ereal] : ( P @ A3 @ A3 )
% 0.26/0.46 => ( ! [A3: extended_ereal,B2: extended_ereal] :
% 0.26/0.46 ( ( P @ B2 @ A3 )
% 0.26/0.46 => ( P @ A3 @ B2 ) )
% 0.26/0.46 => ( P @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % linorder_less_wlog
% 0.26/0.46 thf(fact_80_dual__order_Ostrict__trans,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ B @ A )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ B )
% 0.26/0.46 => ( ord_le2001149050_ereal @ C2 @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.strict_trans
% 0.26/0.46 thf(fact_81_not__less__iff__gr__or__eq,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( ~ ( ord_le2001149050_ereal @ X2 @ Y ) )
% 0.26/0.46 = ( ( ord_le2001149050_ereal @ Y @ X2 )
% 0.26/0.46 | ( X2 = Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % not_less_iff_gr_or_eq
% 0.26/0.46 thf(fact_82_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( A != B ) ) ).
% 0.26/0.46
% 0.26/0.46 % order.strict_implies_not_eq
% 0.26/0.46 thf(fact_83_ereal__mult__eq__PInfty,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ( times_1966848393_ereal @ A @ B )
% 0.26/0.46 = extend1289208545_ereal )
% 0.26/0.46 = ( ( ( A = extend1289208545_ereal )
% 0.26/0.46 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 & ( B = extend1289208545_ereal ) )
% 0.26/0.46 | ( ( A
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 0.26/0.46 & ( B
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_eq_PInfty
% 0.26/0.46 thf(fact_84_ereal__mult__eq__MInfty,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ( times_1966848393_ereal @ A @ B )
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 = ( ( ( A = extend1289208545_ereal )
% 0.26/0.46 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 0.26/0.46 & ( B = extend1289208545_ereal ) )
% 0.26/0.46 | ( ( A
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 & ( B
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_eq_MInfty
% 0.26/0.46 thf(fact_85_ereal__mult__infty,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( ( A = zero_z163181189_ereal )
% 0.26/0.46 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 0.26/0.46 = zero_z163181189_ereal ) )
% 0.26/0.46 & ( ( A != zero_z163181189_ereal )
% 0.26/0.46 => ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 0.26/0.46 = extend1289208545_ereal ) )
% 0.26/0.46 & ( ~ ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_infty
% 0.26/0.46 thf(fact_86_ereal__infty__mult,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( ( A = zero_z163181189_ereal )
% 0.26/0.46 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 0.26/0.46 = zero_z163181189_ereal ) )
% 0.26/0.46 & ( ( A != zero_z163181189_ereal )
% 0.26/0.46 => ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 0.26/0.46 = extend1289208545_ereal ) )
% 0.26/0.46 & ( ~ ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_infty_mult
% 0.26/0.46 thf(fact_87_ereal__divide__Infty_I2_J,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ( ( divide595620860_ereal @ X2 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_divide_Infty(2)
% 0.26/0.46 thf(fact_88_ereal__mult__minus__left,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ A ) @ B )
% 0.26/0.46 = ( uminus1208298309_ereal @ ( times_1966848393_ereal @ A @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_minus_left
% 0.26/0.46 thf(fact_89_ereal__mult__minus__right,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ A @ ( uminus1208298309_ereal @ B ) )
% 0.26/0.46 = ( uminus1208298309_ereal @ ( times_1966848393_ereal @ A @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_minus_right
% 0.26/0.46 thf(fact_90_ereal__zero__times,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ( times_1966848393_ereal @ A @ B )
% 0.26/0.46 = zero_z163181189_ereal )
% 0.26/0.46 = ( ( A = zero_z163181189_ereal )
% 0.26/0.46 | ( B = zero_z163181189_ereal ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_zero_times
% 0.26/0.46 thf(fact_91_ereal__zero__mult,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_zero_mult
% 0.26/0.46 thf(fact_92_ereal__mult__zero,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ A @ zero_z163181189_ereal )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_zero
% 0.26/0.46 thf(fact_93_ereal__uminus__divide,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal] :
% 0.26/0.46 ( ( divide595620860_ereal @ ( uminus1208298309_ereal @ X2 ) @ Y )
% 0.26/0.46 = ( uminus1208298309_ereal @ ( divide595620860_ereal @ X2 @ Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_uminus_divide
% 0.26/0.46 thf(fact_94_ereal__divide__zero__left,axiom,
% 0.26/0.46 ! [A: extended_ereal] :
% 0.26/0.46 ( ( divide595620860_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_divide_zero_left
% 0.26/0.46 thf(fact_95_ereal__times__divide__eq__left,axiom,
% 0.26/0.46 ! [B: extended_ereal,C2: extended_ereal,A: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ ( divide595620860_ereal @ B @ C2 ) @ A )
% 0.26/0.46 = ( divide595620860_ereal @ ( times_1966848393_ereal @ B @ A ) @ C2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_times_divide_eq_left
% 0.26/0.46 thf(fact_96_ereal__divide__Infty_I1_J,axiom,
% 0.26/0.46 ! [X2: extended_ereal] :
% 0.26/0.46 ( ( divide595620860_ereal @ X2 @ extend1289208545_ereal )
% 0.26/0.46 = zero_z163181189_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_divide_Infty(1)
% 0.26/0.46 thf(fact_97_mult_Oleft__commute,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ B @ ( times_1966848393_ereal @ A @ C2 ) )
% 0.26/0.46 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mult.left_commute
% 0.26/0.46 thf(fact_98_mult_Ocommute,axiom,
% 0.26/0.46 ( times_1966848393_ereal
% 0.26/0.46 = ( ^ [A4: extended_ereal,B3: extended_ereal] : ( times_1966848393_ereal @ B3 @ A4 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mult.commute
% 0.26/0.46 thf(fact_99_mult_Oassoc,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 )
% 0.26/0.46 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mult.assoc
% 0.26/0.46 thf(fact_100_ereal__times__divide__eq,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ A @ ( divide595620860_ereal @ B @ C2 ) )
% 0.26/0.46 = ( divide595620860_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_times_divide_eq
% 0.26/0.46 thf(fact_101_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( times_1966848393_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 )
% 0.26/0.46 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ab_semigroup_mult_class.mult_ac(1)
% 0.26/0.46 thf(fact_102_times__ereal_Osimps_I6_J,axiom,
% 0.26/0.46 ( ( times_1966848393_ereal @ extend1289208545_ereal @ extend1289208545_ereal )
% 0.26/0.46 = extend1289208545_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % times_ereal.simps(6)
% 0.26/0.46 thf(fact_103_ereal__right__mult__cong,axiom,
% 0.26/0.46 ! [C2: extended_ereal,D: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( C2 = D )
% 0.26/0.46 => ( ( ( D != zero_z163181189_ereal )
% 0.26/0.46 => ( A = B ) )
% 0.26/0.46 => ( ( times_1966848393_ereal @ C2 @ A )
% 0.26/0.46 = ( times_1966848393_ereal @ D @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_right_mult_cong
% 0.26/0.46 thf(fact_104_ereal__left__mult__cong,axiom,
% 0.26/0.46 ! [C2: extended_ereal,D: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( C2 = D )
% 0.26/0.46 => ( ( ( D != zero_z163181189_ereal )
% 0.26/0.46 => ( A = B ) )
% 0.26/0.46 => ( ( times_1966848393_ereal @ A @ C2 )
% 0.26/0.46 = ( times_1966848393_ereal @ B @ D ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_left_mult_cong
% 0.26/0.46 thf(fact_105_ereal__mult__divide,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ B @ extend1289208545_ereal )
% 0.26/0.46 => ( ( times_1966848393_ereal @ B @ ( divide595620860_ereal @ A @ B ) )
% 0.26/0.46 = A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_divide
% 0.26/0.46 thf(fact_106_ereal__divide__less__iff,axiom,
% 0.26/0.46 ! [C2: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ ( divide595620860_ereal @ A @ C2 ) @ B )
% 0.26/0.46 = ( ord_le2001149050_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_divide_less_iff
% 0.26/0.46 thf(fact_107_ereal__divide__less__pos,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ X2 )
% 0.26/0.46 => ( ( X2 != extend1289208545_ereal )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ ( divide595620860_ereal @ Y @ X2 ) @ Z3 )
% 0.26/0.46 = ( ord_le2001149050_ereal @ Y @ ( times_1966848393_ereal @ X2 @ Z3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_divide_less_pos
% 0.26/0.46 thf(fact_108_ereal__less__divide__iff,axiom,
% 0.26/0.46 ! [C2: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ A @ ( divide595620860_ereal @ B @ C2 ) )
% 0.26/0.46 = ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_less_divide_iff
% 0.26/0.46 thf(fact_109_ereal__less__divide__pos,axiom,
% 0.26/0.46 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ X2 )
% 0.26/0.46 => ( ( X2 != extend1289208545_ereal )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ Y @ ( divide595620860_ereal @ Z3 @ X2 ) )
% 0.26/0.46 = ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_less_divide_pos
% 0.26/0.46 thf(fact_110_times__ereal_Osimps_I9_J,axiom,
% 0.26/0.46 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 = extend1289208545_ereal ) ).
% 0.26/0.46
% 0.26/0.46 % times_ereal.simps(9)
% 0.26/0.46 thf(fact_111_times__ereal_Osimps_I8_J,axiom,
% 0.26/0.46 ( ( times_1966848393_ereal @ extend1289208545_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % times_ereal.simps(8)
% 0.26/0.46 thf(fact_112_times__ereal_Osimps_I7_J,axiom,
% 0.26/0.46 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal )
% 0.26/0.46 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 0.26/0.46
% 0.26/0.46 % times_ereal.simps(7)
% 0.26/0.46 thf(fact_113_ereal__mult__less__0__iff,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ B ) @ zero_z163181189_ereal )
% 0.26/0.46 = ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 0.26/0.46 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_less_0_iff
% 0.26/0.46 thf(fact_114_ereal__zero__less__0__iff,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ ( times_1966848393_ereal @ A @ B ) )
% 0.26/0.46 = ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 0.26/0.46 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 0.26/0.46 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_zero_less_0_iff
% 0.26/0.46 thf(fact_115_ereal__mult__mono__strict,axiom,
% 0.26/0.46 ! [B: extended_ereal,C2: extended_ereal,A: extended_ereal,D: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ D )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ D ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_mono_strict
% 0.26/0.46 thf(fact_116_ereal__mult__mono__strict_H,axiom,
% 0.26/0.46 ! [A: extended_ereal,C2: extended_ereal,B: extended_ereal,D: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ D )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ D ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_mono_strict'
% 0.26/0.46 thf(fact_117_ereal__mult__less__right,axiom,
% 0.26/0.46 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ B @ A ) @ ( times_1966848393_ereal @ C2 @ A ) )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ A @ extend1289208545_ereal )
% 0.26/0.46 => ( ord_le2001149050_ereal @ B @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_less_right
% 0.26/0.46 thf(fact_118_ereal__mult__strict__left__mono,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ C2 @ A ) @ ( times_1966848393_ereal @ C2 @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_strict_left_mono
% 0.26/0.46 thf(fact_119_ereal__mult__strict__right__mono,axiom,
% 0.26/0.46 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ A @ B )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 0.26/0.46 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 0.26/0.46 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ereal_mult_strict_right_mono
% 0.26/0.46
% 0.26/0.46 % Conjectures (1)
% 0.26/0.46 thf(conj_0,conjecture,
% 0.26/0.46 ( ( lower_191460856_ereal @ x0 @ f )
% 0.26/0.46 != ( ~ ! [C: extended_ereal] :
% 0.26/0.46 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 0.26/0.46 => ? [T: set_a] :
% 0.26/0.46 ( ( topolo1276428101open_a @ T )
% 0.26/0.46 & ( member_a @ x0 @ T )
% 0.26/0.46 & ! [X: a] :
% 0.26/0.46 ( ( member_a @ X @ T )
% 0.26/0.46 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 2.02/1.40 ---- Embedded in THF ---
% 2.36/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.36/1.41 %%% Generated on Tue Feb 24 08:24:57 EST 2026
% 2.36/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 2.36/1.41 %%% Logic specification used:
% 2.36/1.41 %%% thf(spec, logic, $$dhol).
% 2.36/1.41
% 2.36/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2DTF10757.p
% See solution above
% 2.36/1.41 ------------------------
% 2.36/1.42 ---- Cleaned THF ---
% 2.36/1.42 thf(ty_n_t__Extended____Real__Oereal,type,
% 2.36/1.42 extended_ereal: $tType ).
% 2.36/1.42
% 2.36/1.42 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.36/1.42 set_a: $tType ).
% 2.36/1.42
% 2.36/1.42 thf(ty_n_tf__a,type,
% 2.36/1.42 a: $tType ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity_001t__Extended____Real__Oereal,type,
% 2.36/1.42 extend1289208545_ereal: extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Extended__Real_Oereal_OMInfty,type,
% 2.36/1.42 extended_MInfty: extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Extended__Real_Oereal_OPInfty,type,
% 2.36/1.42 extended_PInfty: extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Real__Oereal,type,
% 2.36/1.42 times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Extended____Real__Oereal,type,
% 2.36/1.42 uminus1208298309_ereal: extended_ereal > extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Real__Oereal,type,
% 2.36/1.42 zero_z163181189_ereal: extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Olsc__at_001tf__a_001t__Extended____Real__Oereal,type,
% 2.36/1.42 lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Real__Oereal,type,
% 2.36/1.42 ord_le2001149050_ereal: extended_ereal > extended_ereal > $o ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Rings_Odivide__class_Odivide_001t__Extended____Real__Oereal,type,
% 2.36/1.42 divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.36/1.42 collect_a: ( a > $o ) > set_a ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001tf__a,type,
% 2.36/1.42 topolo1276428101open_a: set_a > $o ).
% 2.36/1.42
% 2.36/1.42 thf(sy_c_member_001tf__a,type,
% 2.36/1.42 member_a: a > set_a > $o ).
% 2.36/1.42
% 2.36/1.42 thf(sy_v_f,type,
% 2.36/1.42 f: a > extended_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(sy_v_x0,type,
% 2.36/1.42 x0: a ).
% 2.36/1.42
% 2.36/1.42 thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.36/1.42 ( ( ( f @ x0 )
% 2.36/1.42 = extend1289208545_ereal )
% 2.36/1.42 => ( ( lower_191460856_ereal @ x0 @ f )
% 2.36/1.42 = ( ! [C: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 2.36/1.42 => ? [T: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ T )
% 2.36/1.42 & ( member_a @ x0 @ T )
% 2.36/1.42 & ! [X: a] :
% 2.36/1.42 ( ( member_a @ X @ T )
% 2.36/1.42 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.36/1.42 ( ( ( f @ x0 )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 => ( ( lower_191460856_ereal @ x0 @ f )
% 2.36/1.42 = ( ! [C: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 2.36/1.42 => ? [T: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ T )
% 2.36/1.42 & ( member_a @ x0 @ T )
% 2.36/1.42 & ! [X: a] :
% 2.36/1.42 ( ( member_a @ X @ T )
% 2.36/1.42 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
% 2.36/1.42 ( ( ( f @ x0 )
% 2.36/1.42 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 => ( ( ( f @ x0 )
% 2.36/1.42 != extend1289208545_ereal )
% 2.36/1.42 => ( ( lower_191460856_ereal @ x0 @ f )
% 2.36/1.42 = ( ! [C: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 2.36/1.42 => ? [T: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ T )
% 2.36/1.42 & ( member_a @ x0 @ T )
% 2.36/1.42 & ! [X: a] :
% 2.36/1.42 ( ( member_a @ X @ T )
% 2.36/1.42 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_3_lsc__at__MInfty,axiom,
% 2.36/1.42 ! [F: a > extended_ereal,X0: a] :
% 2.36/1.42 ( ( ( F @ X0 )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 => ( lower_191460856_ereal @ X0 @ F ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_4_t0__space,axiom,
% 2.36/1.42 ! [X2: a,Y: a] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 => ? [U: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ U )
% 2.36/1.42 & ( ( member_a @ X2 @ U )
% 2.36/1.42 != ( member_a @ Y @ U ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_5_t1__space,axiom,
% 2.36/1.42 ! [X2: a,Y: a] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 => ? [U: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ U )
% 2.36/1.42 & ( member_a @ X2 @ U )
% 2.36/1.42 & ~ ( member_a @ Y @ U ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_6_separation__t0,axiom,
% 2.36/1.42 ! [X2: a,Y: a] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 = ( ? [U2: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ U2 )
% 2.36/1.42 & ( ( member_a @ X2 @ U2 )
% 2.36/1.42 != ( member_a @ Y @ U2 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_7_separation__t1,axiom,
% 2.36/1.42 ! [X2: a,Y: a] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 = ( ? [U2: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ U2 )
% 2.36/1.42 & ( member_a @ X2 @ U2 )
% 2.36/1.42 & ~ ( member_a @ Y @ U2 ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_8_minf_I7_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ T2 @ X3 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_9_minf_I5_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ( ord_le2001149050_ereal @ X3 @ T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_10_minf_I4_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ( X3 != T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_11_minf_I3_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ( X3 != T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_12_minf_I2_J,axiom,
% 2.36/1.42 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 2.36/1.42 ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 2.36/1.42 => ( ( P @ X4 )
% 2.36/1.42 = ( P2 @ X4 ) ) )
% 2.36/1.42 => ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 2.36/1.42 => ( ( Q @ X4 )
% 2.36/1.42 = ( Q2 @ X4 ) ) )
% 2.36/1.42 => ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ( ( ( P @ X3 )
% 2.36/1.42 | ( Q @ X3 ) )
% 2.36/1.42 = ( ( P2 @ X3 )
% 2.36/1.42 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_13_pinf_I1_J,axiom,
% 2.36/1.42 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 2.36/1.42 ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 2.36/1.42 => ( ( P @ X4 )
% 2.36/1.42 = ( P2 @ X4 ) ) )
% 2.36/1.42 => ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 2.36/1.42 => ( ( Q @ X4 )
% 2.36/1.42 = ( Q2 @ X4 ) ) )
% 2.36/1.42 => ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ( ( ( P @ X3 )
% 2.36/1.42 & ( Q @ X3 ) )
% 2.36/1.42 = ( ( P2 @ X3 )
% 2.36/1.42 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_14_pinf_I2_J,axiom,
% 2.36/1.42 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 2.36/1.42 ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 2.36/1.42 => ( ( P @ X4 )
% 2.36/1.42 = ( P2 @ X4 ) ) )
% 2.36/1.42 => ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z2 @ X4 )
% 2.36/1.42 => ( ( Q @ X4 )
% 2.36/1.42 = ( Q2 @ X4 ) ) )
% 2.36/1.42 => ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ( ( ( P @ X3 )
% 2.36/1.42 | ( Q @ X3 ) )
% 2.36/1.42 = ( ( P2 @ X3 )
% 2.36/1.42 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_15_pinf_I3_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ( X3 != T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_16_pinf_I4_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ( X3 != T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_17_pinf_I5_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ X3 @ T2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_18_pinf_I7_J,axiom,
% 2.36/1.42 ! [T2: extended_ereal] :
% 2.36/1.42 ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ Z @ X3 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ T2 @ X3 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_19_minf_I1_J,axiom,
% 2.36/1.42 ! [P: extended_ereal > $o,P2: extended_ereal > $o,Q: extended_ereal > $o,Q2: extended_ereal > $o] :
% 2.36/1.42 ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 2.36/1.42 => ( ( P @ X4 )
% 2.36/1.42 = ( P2 @ X4 ) ) )
% 2.36/1.42 => ( ? [Z2: extended_ereal] :
% 2.36/1.42 ! [X4: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Z2 )
% 2.36/1.42 => ( ( Q @ X4 )
% 2.36/1.42 = ( Q2 @ X4 ) ) )
% 2.36/1.42 => ? [Z: extended_ereal] :
% 2.36/1.42 ! [X3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X3 @ Z )
% 2.36/1.42 => ( ( ( P @ X3 )
% 2.36/1.42 & ( Q @ X3 ) )
% 2.36/1.42 = ( ( P2 @ X3 )
% 2.36/1.42 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_20_ereal__MInfty__lessI,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( A
% 2.36/1.42 != ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_21_ereal__infty__less_I2_J,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ X2 )
% 2.36/1.42 = ( X2
% 2.36/1.42 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_22_ereal__minus__less__minus,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ A ) @ ( uminus1208298309_ereal @ B ) )
% 2.36/1.42 = ( ord_le2001149050_ereal @ B @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_23_ereal__less__PInfty,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( A != extend1289208545_ereal )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_24_ereal__infty__less_I1_J,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ extend1289208545_ereal )
% 2.36/1.42 = ( X2 != extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_25_less__ereal_Osimps_I3_J,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ~ ( ord_le2001149050_ereal @ A @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_26_less__ereal_Osimps_I6_J,axiom,
% 2.36/1.42 ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(fact_27_ereal__uminus__eq__iff,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ( uminus1208298309_ereal @ A )
% 2.36/1.42 = ( uminus1208298309_ereal @ B ) )
% 2.36/1.42 = ( A = B ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_28_ereal__uminus__uminus,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( uminus1208298309_ereal @ ( uminus1208298309_ereal @ A ) )
% 2.36/1.42 = A ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_29_ereal__uminus__eq__reorder,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ( uminus1208298309_ereal @ A )
% 2.36/1.42 = B )
% 2.36/1.42 = ( A
% 2.36/1.42 = ( uminus1208298309_ereal @ B ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_30_MInfty__neq__PInfty_I1_J,axiom,
% 2.36/1.42 ( extend1289208545_ereal
% 2.36/1.42 != ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_31_less__ereal_Osimps_I2_J,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ~ ( ord_le2001149050_ereal @ extend1289208545_ereal @ A ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_32_ereal__less__uminus__reorder,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ ( uminus1208298309_ereal @ B ) )
% 2.36/1.42 = ( ord_le2001149050_ereal @ B @ ( uminus1208298309_ereal @ A ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_33_ereal__uminus__less__reorder,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ A ) @ B )
% 2.36/1.42 = ( ord_le2001149050_ereal @ ( uminus1208298309_ereal @ B ) @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_34_mem__Collect__eq,axiom,
% 2.36/1.42 ! [A: a,P: a > $o] :
% 2.36/1.42 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.36/1.42 = ( P @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_35_Collect__mem__eq,axiom,
% 2.36/1.42 ! [A2: set_a] :
% 2.36/1.42 ( ( collect_a
% 2.36/1.42 @ ^ [X: a] : ( member_a @ X @ A2 ) )
% 2.36/1.42 = A2 ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_36_Collect__cong,axiom,
% 2.36/1.42 ! [P: a > $o,Q: a > $o] :
% 2.36/1.42 ( ! [X4: a] :
% 2.36/1.42 ( ( P @ X4 )
% 2.36/1.42 = ( Q @ X4 ) )
% 2.36/1.42 => ( ( collect_a @ P )
% 2.36/1.42 = ( collect_a @ Q ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_37_MInfty__eq__minfinity,axiom,
% 2.36/1.42 ( extended_MInfty
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_38_verit__comp__simplify1_I1_J,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ~ ( ord_le2001149050_ereal @ A @ A ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_39_uminus__ereal_Osimps_I2_J,axiom,
% 2.36/1.42 ( ( uminus1208298309_ereal @ extended_PInfty )
% 2.36/1.42 = extended_MInfty ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_40_uminus__ereal_Osimps_I3_J,axiom,
% 2.36/1.42 ( ( uminus1208298309_ereal @ extended_MInfty )
% 2.36/1.42 = extended_PInfty ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_41_ereal__less_I6_J,axiom,
% 2.36/1.42 ord_le2001149050_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ zero_z163181189_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(fact_42_ex__gt__or__lt,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ? [B2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B2 )
% 2.36/1.42 | ( ord_le2001149050_ereal @ B2 @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_43_dual__order_Ostrict__implies__not__eq,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ B @ A )
% 2.36/1.42 => ( A != B ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_44_ereal__uminus__zero__iff,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( ( uminus1208298309_ereal @ A )
% 2.36/1.42 = zero_z163181189_ereal )
% 2.36/1.42 = ( A = zero_z163181189_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_45_ereal__uminus__zero,axiom,
% 2.36/1.42 ( ( uminus1208298309_ereal @ zero_z163181189_ereal )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_46_neg__0__less__iff__less__erea,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ ( uminus1208298309_ereal @ A ) )
% 2.36/1.42 = ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_47_zero__reorient,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ( ( zero_z163181189_ereal = X2 )
% 2.36/1.42 = ( X2 = zero_z163181189_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_48_Infty__neq__0_I1_J,axiom,
% 2.36/1.42 extend1289208545_ereal != zero_z163181189_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(fact_49_infinity__ereal__def,axiom,
% 2.36/1.42 extend1289208545_ereal = extended_PInfty ).
% 2.36/1.42
% 2.36/1.42 thf(fact_50_ereal_Odistinct_I5_J,axiom,
% 2.36/1.42 extended_PInfty != extended_MInfty ).
% 2.36/1.42
% 2.36/1.42 thf(fact_51_Infty__neq__0_I3_J,axiom,
% 2.36/1.42 ( ( uminus1208298309_ereal @ extend1289208545_ereal )
% 2.36/1.42 != zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_52_ereal__less_I5_J,axiom,
% 2.36/1.42 ord_le2001149050_ereal @ zero_z163181189_ereal @ extend1289208545_ereal ).
% 2.36/1.42
% 2.36/1.42 thf(fact_53_ord__eq__less__subst,axiom,
% 2.36/1.42 ! [A: extended_ereal,F: extended_ereal > extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( A
% 2.36/1.42 = ( F @ B ) )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 2.36/1.42 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ ( F @ C2 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_54_ord__less__eq__subst,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,F: extended_ereal > extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ( F @ B )
% 2.36/1.42 = C2 )
% 2.36/1.42 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ A ) @ C2 ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_55_order__less__subst1,axiom,
% 2.36/1.42 ! [A: extended_ereal,F: extended_ereal > extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ ( F @ B ) )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 2.36/1.42 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ ( F @ C2 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_56_order__less__subst2,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,F: extended_ereal > extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ ( F @ B ) @ C2 )
% 2.36/1.42 => ( ! [X4: extended_ereal,Y2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X4 @ Y2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( F @ A ) @ C2 ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_57_neqE,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 => ( ~ ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_58_neq__iff,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( X2 != Y )
% 2.36/1.42 = ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 | ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_59_order_Oasym,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ B @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_60_dense,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ? [Z: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Z )
% 2.36/1.42 & ( ord_le2001149050_ereal @ Z @ Y ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_61_less__imp__neq,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( X2 != Y ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_62_less__asym,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_63_less__asym_H,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ B @ A ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_64_less__trans,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ Y @ Z3 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ X2 @ Z3 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_65_less__linear,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 | ( X2 = Y )
% 2.36/1.42 | ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_66_less__irrefl,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ~ ( ord_le2001149050_ereal @ X2 @ X2 ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_67_ord__eq__less__trans,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( A = B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_68_ord__less__eq__trans,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( B = C2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_69_dual__order_Oasym,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ B @ A )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ A @ B ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_70_less__imp__not__eq,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( X2 != Y ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_71_less__not__sym,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_72_antisym__conv3,axiom,
% 2.36/1.42 ! [Y: extended_ereal,X2: extended_ereal] :
% 2.36/1.42 ( ~ ( ord_le2001149050_ereal @ Y @ X2 )
% 2.36/1.42 => ( ( ~ ( ord_le2001149050_ereal @ X2 @ Y ) )
% 2.36/1.42 = ( X2 = Y ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_73_less__imp__not__eq2,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( Y != X2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_74_less__imp__triv,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal,P: $o] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ Y @ X2 )
% 2.36/1.42 => P ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_75_linorder__cases,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ~ ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ( ( X2 != Y )
% 2.36/1.42 => ( ord_le2001149050_ereal @ Y @ X2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_76_dual__order_Oirrefl,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ~ ( ord_le2001149050_ereal @ A @ A ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_77_order_Ostrict__trans,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ B @ C2 )
% 2.36/1.42 => ( ord_le2001149050_ereal @ A @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_78_less__imp__not__less,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ X2 @ Y )
% 2.36/1.42 => ~ ( ord_le2001149050_ereal @ Y @ X2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_79_linorder__less__wlog,axiom,
% 2.36/1.42 ! [P: extended_ereal > extended_ereal > $o,A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ! [A3: extended_ereal,B2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A3 @ B2 )
% 2.36/1.42 => ( P @ A3 @ B2 ) )
% 2.36/1.42 => ( ! [A3: extended_ereal] : ( P @ A3 @ A3 )
% 2.36/1.42 => ( ! [A3: extended_ereal,B2: extended_ereal] :
% 2.36/1.42 ( ( P @ B2 @ A3 )
% 2.36/1.42 => ( P @ A3 @ B2 ) )
% 2.36/1.42 => ( P @ A @ B ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_80_dual__order_Ostrict__trans,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ B @ A )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ B )
% 2.36/1.42 => ( ord_le2001149050_ereal @ C2 @ A ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_81_not__less__iff__gr__or__eq,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( ~ ( ord_le2001149050_ereal @ X2 @ Y ) )
% 2.36/1.42 = ( ( ord_le2001149050_ereal @ Y @ X2 )
% 2.36/1.42 | ( X2 = Y ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_82_order_Ostrict__implies__not__eq,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( A != B ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_83_ereal__mult__eq__PInfty,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ( times_1966848393_ereal @ A @ B )
% 2.36/1.42 = extend1289208545_ereal )
% 2.36/1.42 = ( ( ( A = extend1289208545_ereal )
% 2.36/1.42 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 & ( B = extend1289208545_ereal ) )
% 2.36/1.42 | ( ( A
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 2.36/1.42 & ( B
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_84_ereal__mult__eq__MInfty,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ( times_1966848393_ereal @ A @ B )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 = ( ( ( A = extend1289208545_ereal )
% 2.36/1.42 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 2.36/1.42 & ( B = extend1289208545_ereal ) )
% 2.36/1.42 | ( ( A
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 & ( B
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_85_ereal__mult__infty,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( ( A = zero_z163181189_ereal )
% 2.36/1.42 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 2.36/1.42 = zero_z163181189_ereal ) )
% 2.36/1.42 & ( ( A != zero_z163181189_ereal )
% 2.36/1.42 => ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 2.36/1.42 = extend1289208545_ereal ) )
% 2.36/1.42 & ( ~ ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( times_1966848393_ereal @ A @ extend1289208545_ereal )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_86_ereal__infty__mult,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( ( A = zero_z163181189_ereal )
% 2.36/1.42 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 2.36/1.42 = zero_z163181189_ereal ) )
% 2.36/1.42 & ( ( A != zero_z163181189_ereal )
% 2.36/1.42 => ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 2.36/1.42 = extend1289208545_ereal ) )
% 2.36/1.42 & ( ~ ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( times_1966848393_ereal @ extend1289208545_ereal @ A )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_87_ereal__divide__Infty_I2_J,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ( ( divide595620860_ereal @ X2 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_88_ereal__mult__minus__left,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ A ) @ B )
% 2.36/1.42 = ( uminus1208298309_ereal @ ( times_1966848393_ereal @ A @ B ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_89_ereal__mult__minus__right,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ A @ ( uminus1208298309_ereal @ B ) )
% 2.36/1.42 = ( uminus1208298309_ereal @ ( times_1966848393_ereal @ A @ B ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_90_ereal__zero__times,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ( times_1966848393_ereal @ A @ B )
% 2.36/1.42 = zero_z163181189_ereal )
% 2.36/1.42 = ( ( A = zero_z163181189_ereal )
% 2.36/1.42 | ( B = zero_z163181189_ereal ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_91_ereal__zero__mult,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_92_ereal__mult__zero,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ A @ zero_z163181189_ereal )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_93_ereal__uminus__divide,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal] :
% 2.36/1.42 ( ( divide595620860_ereal @ ( uminus1208298309_ereal @ X2 ) @ Y )
% 2.36/1.42 = ( uminus1208298309_ereal @ ( divide595620860_ereal @ X2 @ Y ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_94_ereal__divide__zero__left,axiom,
% 2.36/1.42 ! [A: extended_ereal] :
% 2.36/1.42 ( ( divide595620860_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_95_ereal__times__divide__eq__left,axiom,
% 2.36/1.42 ! [B: extended_ereal,C2: extended_ereal,A: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ ( divide595620860_ereal @ B @ C2 ) @ A )
% 2.36/1.42 = ( divide595620860_ereal @ ( times_1966848393_ereal @ B @ A ) @ C2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_96_ereal__divide__Infty_I1_J,axiom,
% 2.36/1.42 ! [X2: extended_ereal] :
% 2.36/1.42 ( ( divide595620860_ereal @ X2 @ extend1289208545_ereal )
% 2.36/1.42 = zero_z163181189_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_97_mult_Oleft__commute,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ B @ ( times_1966848393_ereal @ A @ C2 ) )
% 2.36/1.42 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_98_mult_Ocommute,axiom,
% 2.36/1.42 ( times_1966848393_ereal
% 2.36/1.42 = ( ^ [A4: extended_ereal,B3: extended_ereal] : ( times_1966848393_ereal @ B3 @ A4 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_99_mult_Oassoc,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 )
% 2.36/1.42 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_100_ereal__times__divide__eq,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ A @ ( divide595620860_ereal @ B @ C2 ) )
% 2.36/1.42 = ( divide595620860_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_101_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( times_1966848393_ereal @ ( times_1966848393_ereal @ A @ B ) @ C2 )
% 2.36/1.42 = ( times_1966848393_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_102_times__ereal_Osimps_I6_J,axiom,
% 2.36/1.42 ( ( times_1966848393_ereal @ extend1289208545_ereal @ extend1289208545_ereal )
% 2.36/1.42 = extend1289208545_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_103_ereal__right__mult__cong,axiom,
% 2.36/1.42 ! [C2: extended_ereal,D: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( C2 = D )
% 2.36/1.42 => ( ( ( D != zero_z163181189_ereal )
% 2.36/1.42 => ( A = B ) )
% 2.36/1.42 => ( ( times_1966848393_ereal @ C2 @ A )
% 2.36/1.42 = ( times_1966848393_ereal @ D @ B ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_104_ereal__left__mult__cong,axiom,
% 2.36/1.42 ! [C2: extended_ereal,D: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( C2 = D )
% 2.36/1.42 => ( ( ( D != zero_z163181189_ereal )
% 2.36/1.42 => ( A = B ) )
% 2.36/1.42 => ( ( times_1966848393_ereal @ A @ C2 )
% 2.36/1.42 = ( times_1966848393_ereal @ B @ D ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_105_ereal__mult__divide,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ B @ extend1289208545_ereal )
% 2.36/1.42 => ( ( times_1966848393_ereal @ B @ ( divide595620860_ereal @ A @ B ) )
% 2.36/1.42 = A ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_106_ereal__divide__less__iff,axiom,
% 2.36/1.42 ! [C2: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ ( divide595620860_ereal @ A @ C2 ) @ B )
% 2.36/1.42 = ( ord_le2001149050_ereal @ A @ ( times_1966848393_ereal @ B @ C2 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_107_ereal__divide__less__pos,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ X2 )
% 2.36/1.42 => ( ( X2 != extend1289208545_ereal )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ ( divide595620860_ereal @ Y @ X2 ) @ Z3 )
% 2.36/1.42 = ( ord_le2001149050_ereal @ Y @ ( times_1966848393_ereal @ X2 @ Z3 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_108_ereal__less__divide__iff,axiom,
% 2.36/1.42 ! [C2: extended_ereal,A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ A @ ( divide595620860_ereal @ B @ C2 ) )
% 2.36/1.42 = ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ B ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_109_ereal__less__divide__pos,axiom,
% 2.36/1.42 ! [X2: extended_ereal,Y: extended_ereal,Z3: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ X2 )
% 2.36/1.42 => ( ( X2 != extend1289208545_ereal )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ Y @ ( divide595620860_ereal @ Z3 @ X2 ) )
% 2.36/1.42 = ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ X2 @ Y ) @ Z3 ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_110_times__ereal_Osimps_I9_J,axiom,
% 2.36/1.42 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 = extend1289208545_ereal ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_111_times__ereal_Osimps_I8_J,axiom,
% 2.36/1.42 ( ( times_1966848393_ereal @ extend1289208545_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_112_times__ereal_Osimps_I7_J,axiom,
% 2.36/1.42 ( ( times_1966848393_ereal @ ( uminus1208298309_ereal @ extend1289208545_ereal ) @ extend1289208545_ereal )
% 2.36/1.42 = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_113_ereal__mult__less__0__iff,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ B ) @ zero_z163181189_ereal )
% 2.36/1.42 = ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 2.36/1.42 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_114_ereal__zero__less__0__iff,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ ( times_1966848393_ereal @ A @ B ) )
% 2.36/1.42 = ( ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 & ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B ) )
% 2.36/1.42 | ( ( ord_le2001149050_ereal @ A @ zero_z163181189_ereal )
% 2.36/1.42 & ( ord_le2001149050_ereal @ B @ zero_z163181189_ereal ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_115_ereal__mult__mono__strict,axiom,
% 2.36/1.42 ! [B: extended_ereal,C2: extended_ereal,A: extended_ereal,D: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ D )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ D ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_116_ereal__mult__mono__strict_H,axiom,
% 2.36/1.42 ! [A: extended_ereal,C2: extended_ereal,B: extended_ereal,D: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ D )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ D ) ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_117_ereal__mult__less__right,axiom,
% 2.36/1.42 ! [B: extended_ereal,A: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ B @ A ) @ ( times_1966848393_ereal @ C2 @ A ) )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ A )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ A @ extend1289208545_ereal )
% 2.36/1.42 => ( ord_le2001149050_ereal @ B @ C2 ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_118_ereal__mult__strict__left__mono,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ C2 @ A ) @ ( times_1966848393_ereal @ C2 @ B ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(fact_119_ereal__mult__strict__right__mono,axiom,
% 2.36/1.42 ! [A: extended_ereal,B: extended_ereal,C2: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ A @ B )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ zero_z163181189_ereal @ C2 )
% 2.36/1.42 => ( ( ord_le2001149050_ereal @ C2 @ extend1289208545_ereal )
% 2.36/1.42 => ( ord_le2001149050_ereal @ ( times_1966848393_ereal @ A @ C2 ) @ ( times_1966848393_ereal @ B @ C2 ) ) ) ) ) ).
% 2.36/1.42
% 2.36/1.42 thf(conj_0,conjecture,
% 2.36/1.42 ( ( lower_191460856_ereal @ x0 @ f )
% 2.36/1.42 != ( ~ ! [C: extended_ereal] :
% 2.36/1.42 ( ( ord_le2001149050_ereal @ C @ ( f @ x0 ) )
% 2.36/1.42 => ? [T: set_a] :
% 2.36/1.42 ( ( topolo1276428101open_a @ T )
% 2.36/1.42 & ( member_a @ x0 @ T )
% 2.36/1.42 & ! [X: a] :
% 2.36/1.42 ( ( member_a @ X @ T )
% 2.36/1.42 => ( ord_le2001149050_ereal @ C @ ( f @ X ) ) ) ) ) ) ) ).
% 2.36/1.42 ------------------------
% 2.36/1.44 % (11027)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_10757 for (2999ds/275Mi)
% 2.36/1.44 % (11023)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_10757 for (2999ds/4Mi)
% 2.36/1.44 % (11024)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_10757 for (2999ds/27Mi)
% 2.36/1.44 % (11023)Instruction limit reached!
% 2.36/1.44 % (11023)------------------------------
% 2.36/1.44 % (11023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.44 % (11023)Termination reason: Unknown
% 2.36/1.44 % (11023)Termination phase: shuffling
% 2.36/1.44
% 2.36/1.44 % (11023)Memory used [KB]: 1151
% 2.36/1.44 % (11023)Time elapsed: 0.003 s
% 2.36/1.44 % (11023)Instructions burned: 7 (million)
% 2.36/1.44 % (11023)------------------------------
% 2.36/1.44 % (11023)------------------------------
% 2.36/1.44 % (11022)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/183Mi)
% 2.36/1.45 % (11025)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/2Mi)
% 2.36/1.45 % (11026)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_10757 for (2999ds/2Mi)
% 2.36/1.45 % (11028)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/18Mi)
% 2.36/1.45 % (11025)Instruction limit reached!
% 2.36/1.45 % (11025)------------------------------
% 2.36/1.45 % (11025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.45 % (11025)Termination reason: Unknown
% 2.36/1.45 % (11025)Termination phase: shuffling
% 2.36/1.45
% 2.36/1.45 % (11025)Memory used [KB]: 1023
% 2.36/1.45 % (11025)Time elapsed: 0.003 s
% 2.36/1.45 % (11025)Instructions burned: 2 (million)
% 2.36/1.45 % (11025)------------------------------
% 2.36/1.45 % (11025)------------------------------
% 2.36/1.45 % (11026)Instruction limit reached!
% 2.36/1.45 % (11026)------------------------------
% 2.36/1.45 % (11026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.45 % (11026)Termination reason: Unknown
% 2.36/1.45 % (11026)Termination phase: shuffling
% 2.36/1.45
% 2.36/1.45 % (11026)Memory used [KB]: 1023
% 2.36/1.45 % (11026)Time elapsed: 0.003 s
% 2.36/1.45 % (11026)Instructions burned: 2 (million)
% 2.36/1.45 % (11026)------------------------------
% 2.36/1.45 % (11026)------------------------------
% 2.36/1.45 % (11024)Instruction limit reached!
% 2.36/1.45 % (11024)------------------------------
% 2.36/1.45 % (11024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.45 % (11024)Termination reason: Unknown
% 2.36/1.45 % (11024)Termination phase: Property scanning
% 2.36/1.45
% 2.36/1.45 % (11024)Memory used [KB]: 1407
% 2.36/1.45 % (11024)Time elapsed: 0.010 s
% 2.36/1.45 % (11024)Instructions burned: 29 (million)
% 2.36/1.45 % (11024)------------------------------
% 2.36/1.45 % (11024)------------------------------
% 2.36/1.45 % (11029)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/3Mi)
% 2.36/1.45 % (11029)Instruction limit reached!
% 2.36/1.45 % (11029)------------------------------
% 2.36/1.45 % (11029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.45 % (11029)Termination reason: Unknown
% 2.36/1.45 % (11029)Termination phase: shuffling
% 2.36/1.45
% 2.36/1.45 % (11029)Memory used [KB]: 1151
% 2.36/1.45 % (11029)Time elapsed: 0.003 s
% 2.36/1.45 % (11029)Instructions burned: 4 (million)
% 2.36/1.45 % (11029)------------------------------
% 2.36/1.45 % (11029)------------------------------
% 2.36/1.46 % (11028)Instruction limit reached!
% 2.36/1.46 % (11028)------------------------------
% 2.36/1.46 % (11028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.46 % (11028)Termination reason: Unknown
% 2.36/1.46 % (11028)Termination phase: Preprocessing 3
% 2.36/1.46
% 2.36/1.46 % (11028)Memory used [KB]: 1407
% 2.36/1.46 % (11028)Time elapsed: 0.013 s
% 2.36/1.46 % (11028)Instructions burned: 19 (million)
% 2.36/1.46 % (11028)------------------------------
% 2.36/1.46 % (11028)------------------------------
% 2.36/1.46 % (11032)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_10757 for (2999ds/3Mi)
% 2.36/1.46 % (11032)Instruction limit reached!
% 2.36/1.46 % (11032)------------------------------
% 2.36/1.46 % (11032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.46 % (11032)Termination reason: Unknown
% 2.36/1.46 % (11032)Termination phase: shuffling
% 2.36/1.46
% 2.36/1.46 % (11032)Memory used [KB]: 1151
% 2.36/1.46 % (11032)Time elapsed: 0.003 s
% 2.36/1.46 % (11032)Instructions burned: 4 (million)
% 2.36/1.46 % (11032)------------------------------
% 2.36/1.46 % (11032)------------------------------
% 2.36/1.46 % (11033)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_10757 for (2999ds/1041Mi)
% 2.36/1.46 % (11030)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_10757 for (2999ds/37Mi)
% 2.36/1.46 % (11031)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_10757 for (2999ds/15Mi)
% 2.36/1.47 % (11035)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/16Mi)
% 2.36/1.47 % (11031)Instruction limit reached!
% 2.36/1.47 % (11031)------------------------------
% 2.36/1.47 % (11031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.47 % (11031)Termination reason: Unknown
% 2.36/1.47 % (11031)Termination phase: Preprocessing 3
% 2.36/1.47
% 2.36/1.47 % (11031)Memory used [KB]: 1407
% 2.36/1.47 % (11031)Time elapsed: 0.011 s
% 2.36/1.47 % (11031)Instructions burned: 15 (million)
% 2.36/1.47 % (11031)------------------------------
% 2.36/1.47 % (11031)------------------------------
% 2.36/1.47 % (11035)Instruction limit reached!
% 2.36/1.47 % (11035)------------------------------
% 2.36/1.47 % (11035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.47 % (11035)Termination reason: Unknown
% 2.36/1.47 % (11035)Termination phase: Preprocessing 3
% 2.36/1.47
% 2.36/1.47 % (11035)Memory used [KB]: 1279
% 2.36/1.47 % (11035)Time elapsed: 0.007 s
% 2.36/1.47 % (11035)Instructions burned: 16 (million)
% 2.36/1.47 % (11035)------------------------------
% 2.36/1.47 % (11035)------------------------------
% 2.36/1.47 % (11034)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/7Mi)
% 2.36/1.48 % (11034)Instruction limit reached!
% 2.36/1.48 % (11034)------------------------------
% 2.36/1.48 % (11034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (11034)Termination reason: Unknown
% 2.36/1.48 % (11034)Termination phase: shuffling
% 2.36/1.48
% 2.36/1.48 % (11034)Memory used [KB]: 1151
% 2.36/1.48 % (11034)Time elapsed: 0.006 s
% 2.36/1.48 % (11034)Instructions burned: 7 (million)
% 2.36/1.48 % (11034)------------------------------
% 2.36/1.48 % (11034)------------------------------
% 2.36/1.48 % (11030)Instruction limit reached!
% 2.36/1.48 % (11030)------------------------------
% 2.36/1.48 % (11030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (11030)Termination reason: Unknown
% 2.36/1.48 % (11030)Termination phase: Property scanning
% 2.36/1.48
% 2.36/1.48 % (11030)Memory used [KB]: 1407
% 2.36/1.48 % (11030)Time elapsed: 0.020 s
% 2.36/1.48 % (11030)Instructions burned: 37 (million)
% 2.36/1.48 % (11030)------------------------------
% 2.36/1.48 % (11030)------------------------------
% 2.36/1.48 % (11037)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_10757 for (2999ds/3Mi)
% 2.36/1.48 % (11037)Instruction limit reached!
% 2.36/1.48 % (11037)------------------------------
% 2.36/1.48 % (11037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (11037)Termination reason: Unknown
% 2.36/1.48 % (11037)Termination phase: shuffling
% 2.36/1.48
% 2.36/1.48 % (11037)Memory used [KB]: 1151
% 2.36/1.48 % (11037)Time elapsed: 0.003 s
% 2.36/1.48 % (11037)Instructions burned: 4 (million)
% 2.36/1.48 % (11037)------------------------------
% 2.36/1.48 % (11037)------------------------------
% 2.36/1.49 % (11036)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_10757 for (2999ds/3Mi)
% 2.36/1.49 % (11036)Instruction limit reached!
% 2.36/1.49 % (11036)------------------------------
% 2.36/1.49 % (11036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.49 % (11036)Termination reason: Unknown
% 2.36/1.49 % (11036)Termination phase: shuffling
% 2.36/1.49
% 2.36/1.49 % (11036)Memory used [KB]: 1151
% 2.36/1.49 % (11036)Time elapsed: 0.004 s
% 2.36/1.49 % (11036)Instructions burned: 4 (million)
% 2.36/1.49 % (11036)------------------------------
% 2.36/1.49 % (11036)------------------------------
% 2.36/1.49 % (11038)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/7Mi)
% 2.36/1.49 % (11040)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/4Mi)
% 2.36/1.50 % (11038)Instruction limit reached!
% 2.36/1.50 % (11038)------------------------------
% 2.36/1.50 % (11038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.50 % (11038)Termination reason: Unknown
% 2.36/1.50 % (11038)Termination phase: shuffling
% 2.36/1.50
% 2.36/1.50 % (11038)Memory used [KB]: 1279
% 2.36/1.50 % (11038)Time elapsed: 0.006 s
% 2.36/1.50 % (11038)Instructions burned: 9 (million)
% 2.36/1.50 % (11038)------------------------------
% 2.36/1.50 % (11038)------------------------------
% 2.36/1.50 % (11040)Instruction limit reached!
% 2.36/1.50 % (11040)------------------------------
% 2.36/1.50 % (11040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.50 % (11040)Termination reason: Unknown
% 2.36/1.50 % (11040)Termination phase: shuffling
% 2.36/1.50
% 2.36/1.50 % (11040)Memory used [KB]: 1151
% 2.36/1.50 % (11040)Time elapsed: 0.003 s
% 2.36/1.50 % (11040)Instructions burned: 4 (million)
% 2.36/1.50 % (11040)------------------------------
% 2.36/1.50 % (11040)------------------------------
% 2.38/1.50 % (11039)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/3Mi)
% 2.38/1.50 % (11039)Instruction limit reached!
% 2.38/1.50 % (11039)------------------------------
% 2.38/1.50 % (11039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.50 % (11039)Termination reason: Unknown
% 2.38/1.50 % (11039)Termination phase: shuffling
% 2.38/1.50
% 2.38/1.50 % (11039)Memory used [KB]: 1151
% 2.38/1.50 % (11039)Time elapsed: 0.004 s
% 2.38/1.50 % (11039)Instructions burned: 4 (million)
% 2.38/1.50 % (11039)------------------------------
% 2.38/1.50 % (11039)------------------------------
% 2.38/1.51 % (11042)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/710Mi)
% 2.38/1.51 % (11043)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/6Mi)
% 2.38/1.51 % (11043)Instruction limit reached!
% 2.38/1.51 % (11043)------------------------------
% 2.38/1.51 % (11043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.51 % (11043)Termination reason: Unknown
% 2.38/1.51 % (11043)Termination phase: shuffling
% 2.38/1.51
% 2.38/1.51 % (11043)Memory used [KB]: 1151
% 2.38/1.51 % (11043)Time elapsed: 0.004 s
% 2.38/1.51 % (11043)Instructions burned: 7 (million)
% 2.38/1.51 % (11043)------------------------------
% 2.38/1.51 % (11043)------------------------------
% 2.38/1.51 % (11041)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/18Mi)
% 2.38/1.52 % (11044)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_10757 for (2999ds/902Mi)
% 2.38/1.52 % (11045)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_10757 for (2999ds/21Mi)
% 2.38/1.52 % (11041)Instruction limit reached!
% 2.38/1.52 % (11041)------------------------------
% 2.38/1.52 % (11041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.52 % (11041)Termination reason: Unknown
% 2.38/1.52 % (11041)Termination phase: Property scanning
% 2.38/1.52
% 2.38/1.52 % (11041)Memory used [KB]: 1407
% 2.38/1.52 % (11041)Time elapsed: 0.013 s
% 2.38/1.52 % (11041)Instructions burned: 19 (million)
% 2.38/1.52 % (11041)------------------------------
% 2.38/1.52 % (11041)------------------------------
% 2.38/1.52 % (11027)Instruction limit reached!
% 2.38/1.52 % (11027)------------------------------
% 2.38/1.52 % (11027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.52 % (11027)Termination reason: Unknown
% 2.38/1.52 % (11027)Termination phase: Saturation
% 2.38/1.52
% 2.38/1.52 % (11027)Memory used [KB]: 6396
% 2.38/1.52 % (11027)Time elapsed: 0.086 s
% 2.38/1.52 % (11027)Instructions burned: 275 (million)
% 2.38/1.52 % (11027)------------------------------
% 2.38/1.52 % (11027)------------------------------
% 2.38/1.53 % (11045)Instruction limit reached!
% 2.38/1.53 % (11045)------------------------------
% 2.38/1.53 % (11045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.53 % (11045)Termination reason: Unknown
% 2.38/1.53 % (11045)Termination phase: Preprocessing 3
% 2.38/1.53
% 2.38/1.53 % (11045)Memory used [KB]: 1407
% 2.38/1.53 % (11045)Time elapsed: 0.009 s
% 2.38/1.53 % (11045)Instructions burned: 22 (million)
% 2.38/1.53 % (11045)------------------------------
% 2.38/1.53 % (11045)------------------------------
% 2.38/1.53 % (11047)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_10757 for (2999ds/6Mi)
% 2.38/1.53 % (11047)Instruction limit reached!
% 2.38/1.53 % (11047)------------------------------
% 2.38/1.53 % (11047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.53 % (11047)Termination reason: Unknown
% 2.38/1.53 % (11047)Termination phase: shuffling
% 2.38/1.53
% 2.38/1.53 % (11047)Memory used [KB]: 1151
% 2.38/1.53 % (11047)Time elapsed: 0.003 s
% 2.38/1.53 % (11047)Instructions burned: 7 (million)
% 2.38/1.53 % (11047)------------------------------
% 2.38/1.53 % (11047)------------------------------
% 2.38/1.54 % (11048)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/377Mi)
% 2.38/1.54 % (11046)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10757 for (2999ds/5Mi)
% 2.38/1.54 % (11046)Instruction limit reached!
% 2.38/1.54 % (11046)------------------------------
% 2.38/1.54 % (11046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.54 % (11046)Termination reason: Unknown
% 2.38/1.54 % (11046)Termination phase: shuffling
% 2.38/1.54
% 2.38/1.54 % (11046)Memory used [KB]: 1151
% 2.38/1.54 % (11046)Time elapsed: 0.005 s
% 2.38/1.54 % (11046)Instructions burned: 6 (million)
% 2.38/1.54 % (11046)------------------------------
% 2.38/1.54 % (11046)------------------------------
% 2.38/1.54 % (11049)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_10757 for (2999ds/779Mi)
% 2.38/1.54 % (11022)Instruction limit reached!
% 2.38/1.54 % (11022)------------------------------
% 2.38/1.54 % (11022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.54 % (11022)Termination reason: Unknown
% 2.38/1.54 % (11022)Termination phase: Saturation
% 2.38/1.54
% 2.38/1.54 % (11022)Memory used [KB]: 6268
% 2.38/1.54 % (11022)Time elapsed: 0.101 s
% 2.38/1.54 % (11022)Instructions burned: 184 (million)
% 2.38/1.54 % (11022)------------------------------
% 2.38/1.54 % (11022)------------------------------
% 2.38/1.55 % (11051)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10757 for (2998ds/879Mi)
% 2.38/1.56 % (11050)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_10757 for (2998ds/19Mi)
% 2.38/1.56 % (11050)Instruction limit reached!
% 2.38/1.56 % (11050)------------------------------
% 2.38/1.56 % (11050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.56 % (11050)Termination reason: Unknown
% 2.38/1.56 % (11050)Termination phase: Property scanning
% 2.38/1.56
% 2.38/1.56 % (11050)Memory used [KB]: 1407
% 2.38/1.56 % (11050)Time elapsed: 0.008 s
% 2.38/1.56 % (11050)Instructions burned: 20 (million)
% 2.38/1.56 % (11050)------------------------------
% 2.38/1.56 % (11050)------------------------------
% 2.38/1.57 % (11052)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10757 for (2998ds/17Mi)
% 2.38/1.58 % (11052)Instruction limit reached!
% 2.38/1.58 % (11052)------------------------------
% 2.38/1.58 % (11052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.58 % (11052)Termination reason: Unknown
% 2.38/1.58 % (11052)Termination phase: Property scanning
% 2.38/1.58
% 2.38/1.58 % (11052)Memory used [KB]: 1407
% 2.38/1.58 % (11052)Time elapsed: 0.007 s
% 2.38/1.58 % (11052)Instructions burned: 19 (million)
% 2.38/1.58 % (11052)------------------------------
% 2.38/1.58 % (11052)------------------------------
% 2.38/1.59 % (11053)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10757 for (2998ds/3Mi)
% 2.38/1.59 % (11053)Instruction limit reached!
% 2.38/1.59 % (11053)------------------------------
% 2.38/1.59 % (11053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.59 % (11053)Termination reason: Unknown
% 2.38/1.59 % (11053)Termination phase: shuffling
% 2.38/1.59
% 2.38/1.59 % (11053)Memory used [KB]: 1151
% 2.38/1.59 % (11053)Time elapsed: 0.003 s
% 2.38/1.59 % (11053)Instructions burned: 4 (million)
% 2.38/1.59 % (11053)------------------------------
% 2.38/1.59 % (11053)------------------------------
% 2.38/1.60 % (11054)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10757 for (2998ds/30Mi)
% 2.38/1.61 % (11054)Instruction limit reached!
% 2.38/1.61 % (11054)------------------------------
% 2.38/1.61 % (11054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.61 % (11054)Termination reason: Unknown
% 2.38/1.61 % (11054)Termination phase: Property scanning
% 2.38/1.61
% 2.38/1.61 % (11054)Memory used [KB]: 1407
% 2.38/1.61 % (11054)Time elapsed: 0.010 s
% 2.38/1.61 % (11054)Instructions burned: 30 (million)
% 2.38/1.61 % (11054)------------------------------
% 2.38/1.61 % (11054)------------------------------
% 2.38/1.62 % (11055)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10757 for (2998ds/127Mi)
% 2.38/1.65 % (11048)Refutation not found, non-redundant clauses discarded% (11048)------------------------------
% 2.38/1.65 % (11048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.65 % (11048)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.38/1.65
% 2.38/1.65 % (11048)Memory used [KB]: 6780
% 2.38/1.65 % (11048)Time elapsed: 0.117 s
% 2.38/1.65 % (11048)Instructions burned: 367 (million)
% 2.38/1.65 % (11048)------------------------------
% 2.38/1.65 % (11048)------------------------------
% 2.38/1.66 % (11056)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10757 for (2997ds/100Mi)
% 2.38/1.66 % (11055)Instruction limit reached!
% 2.38/1.66 % (11055)------------------------------
% 2.38/1.66 % (11055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.66 % (11055)Termination reason: Unknown
% 2.38/1.66 % (11055)Termination phase: Saturation
% 2.38/1.66
% 2.38/1.66 % (11055)Memory used [KB]: 6396
% 2.38/1.66 % (11055)Time elapsed: 0.066 s
% 2.38/1.66 % (11055)Instructions burned: 129 (million)
% 2.38/1.66 % (11055)------------------------------
% 2.38/1.66 % (11055)------------------------------
% 2.38/1.67 % (11057)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_10757 for (2997ds/3Mi)
% 2.38/1.67 % (11057)Instruction limit reached!
% 2.38/1.67 % (11057)------------------------------
% 2.38/1.67 % (11057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.67 % (11057)Termination reason: Unknown
% 2.38/1.67 % (11057)Termination phase: shuffling
% 2.38/1.67
% 2.38/1.67 % (11057)Memory used [KB]: 1151
% 2.38/1.67 % (11057)Time elapsed: 0.003 s
% 2.38/1.67 % (11057)Instructions burned: 5 (million)
% 2.38/1.67 % (11057)------------------------------
% 2.38/1.67 % (11057)------------------------------
% 2.38/1.68 % (11058)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_10757 for (2997ds/20Mi)
% 2.38/1.69 % (11058)Instruction limit reached!
% 2.38/1.69 % (11058)------------------------------
% 2.38/1.69 % (11058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.69 % (11058)Termination reason: Unknown
% 2.38/1.69 % (11058)Termination phase: Preprocessing 3
% 2.38/1.69
% 2.38/1.69 % (11058)Memory used [KB]: 1279
% 2.38/1.69 % (11058)Time elapsed: 0.008 s
% 2.38/1.69 % (11058)Instructions burned: 20 (million)
% 2.38/1.69 % (11058)------------------------------
% 2.38/1.69 % (11058)------------------------------
% 2.38/1.69 % (11056)Instruction limit reached!
% 2.38/1.69 % (11056)------------------------------
% 2.38/1.69 % (11056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.69 % (11056)Termination reason: Unknown
% 2.38/1.69 % (11056)Termination phase: Saturation
% 2.38/1.69
% 2.38/1.69 % (11056)Memory used [KB]: 6140
% 2.38/1.69 % (11056)Time elapsed: 0.032 s
% 2.38/1.69 % (11056)Instructions burned: 101 (million)
% 2.38/1.69 % (11056)------------------------------
% 2.38/1.69 % (11056)------------------------------
% 2.38/1.70 % (11059)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_10757 for (2997ds/86Mi)
% 2.38/1.70 % (11060)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_10757 for (2997ds/107Mi)
% 2.38/1.70 % (11042)Refutation not found, non-redundant clauses discarded% (11042)------------------------------
% 2.38/1.70 % (11042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.70 % (11042)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.38/1.70
% 2.38/1.70 % (11042)Memory used [KB]: 7675
% 2.38/1.70 % (11042)Time elapsed: 0.199 s
% 2.38/1.70 % (11042)Instructions burned: 613 (million)
% 2.38/1.70 % (11042)------------------------------
% 2.38/1.70 % (11042)------------------------------
% 2.38/1.71 % (11061)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_10757 for (2997ds/39Mi)
% 2.38/1.73 % (11061)Instruction limit reached!
% 2.38/1.73 % (11061)------------------------------
% 2.38/1.73 % (11061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.73 % (11061)Termination reason: Unknown
% 2.38/1.73 % (11061)Termination phase: Property scanning
% 2.38/1.73
% 2.38/1.73 % (11061)Memory used [KB]: 1535
% 2.38/1.73 % (11061)Time elapsed: 0.013 s
% 2.38/1.73 % (11061)Instructions burned: 41 (million)
% 2.38/1.73 % (11061)------------------------------
% 2.38/1.73 % (11061)------------------------------
% 2.38/1.73 % (11059)Instruction limit reached!
% 2.38/1.73 % (11059)------------------------------
% 2.38/1.73 % (11059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.73 % (11059)Termination reason: Unknown
% 2.38/1.73 % (11059)Termination phase: Saturation
% 2.38/1.73
% 2.38/1.73 % (11059)Memory used [KB]: 6268
% 2.38/1.73 % (11059)Time elapsed: 0.049 s
% 2.38/1.73 % (11059)Instructions burned: 86 (million)
% 2.38/1.73 % (11059)------------------------------
% 2.38/1.73 % (11059)------------------------------
% 2.38/1.74 % (11062)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_10757 for (2997ds/448Mi)
% 2.38/1.74 % (11060)Instruction limit reached!
% 2.38/1.74 % (11060)------------------------------
% 2.38/1.74 % (11060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.74 % (11060)Termination reason: Unknown
% 2.38/1.74 % (11060)Termination phase: Saturation
% 2.38/1.74
% 2.38/1.74 % (11060)Memory used [KB]: 6268
% 2.38/1.74 % (11060)Time elapsed: 0.036 s
% 2.38/1.74 % (11060)Instructions burned: 108 (million)
% 2.38/1.74 % (11060)------------------------------
% 2.38/1.74 % (11060)------------------------------
% 2.38/1.74 % (11063)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_10757 for (2996ds/46Mi)
% 2.38/1.75 % (11064)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_10757 for (2996ds/98Mi)
% 2.38/1.75 % (11063)Instruction limit reached!
% 2.38/1.75 % (11063)------------------------------
% 2.38/1.75 % (11063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.75 % (11063)Termination reason: Unknown
% 2.38/1.75 % (11063)Termination phase: Saturation
% 2.38/1.75
% 2.38/1.75 % (11063)Memory used [KB]: 5884
% 2.38/1.75 % (11063)Time elapsed: 0.016 s
% 2.38/1.75 % (11063)Instructions burned: 47 (million)
% 2.38/1.75 % (11063)------------------------------
% 2.38/1.75 % (11063)------------------------------
% 2.38/1.76 % (11065)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_10757 for (2996ds/507Mi)
% 2.38/1.78 % (11064)Instruction limit reached!
% 2.38/1.78 % (11064)------------------------------
% 2.38/1.78 % (11064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.78 % (11064)Termination reason: Unknown
% 2.38/1.78 % (11064)Termination phase: Saturation
% 2.38/1.78
% 2.38/1.78 % (11064)Memory used [KB]: 1663
% 2.38/1.78 % (11064)Time elapsed: 0.032 s
% 2.38/1.78 % (11064)Instructions burned: 100 (million)
% 2.38/1.78 % (11064)------------------------------
% 2.38/1.78 % (11064)------------------------------
% 2.38/1.79 % (11066)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_10757 for (2996ds/149Mi)
% 2.38/1.79 % (11049)Instruction limit reached!
% 2.38/1.79 % (11049)------------------------------
% 2.38/1.79 % (11049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.79 % (11049)Termination reason: Unknown
% 2.38/1.79 % (11049)Termination phase: Saturation
% 2.38/1.79
% 2.38/1.79 % (11049)Memory used [KB]: 7036
% 2.38/1.79 % (11049)Time elapsed: 0.249 s
% 2.38/1.79 % (11049)Instructions burned: 781 (million)
% 2.38/1.79 % (11049)------------------------------
% 2.38/1.79 % (11049)------------------------------
% 2.38/1.79 % (11065)Refutation not found, incomplete strategy
% 2.38/1.79 % (11065)------------------------------
% 2.38/1.79 % (11065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.79 % (11065)Termination reason: Refutation not found, incomplete strategy
% 2.38/1.79
% 2.38/1.79
% 2.38/1.79 % (11065)Memory used [KB]: 6396
% 2.38/1.79 % (11065)Time elapsed: 0.031 s
% 2.38/1.79 % (11065)Instructions burned: 91 (million)
% 2.38/1.79 % (11065)------------------------------
% 2.38/1.79 % (11065)------------------------------
% 2.38/1.79 % (11033)Instruction limit reached!
% 2.38/1.79 % (11033)------------------------------
% 2.38/1.79 % (11033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.79 % (11033)Termination reason: Unknown
% 2.38/1.79 % (11033)Termination phase: Saturation
% 2.38/1.79
% 2.38/1.79 % (11033)Memory used [KB]: 8315
% 2.38/1.79 % (11033)Time elapsed: 0.335 s
% 2.38/1.79 % (11033)Instructions burned: 1042 (million)
% 2.38/1.79 % (11033)------------------------------
% 2.38/1.79 % (11033)------------------------------
% 2.38/1.80 % (11067)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10757 for (2996ds/39Mi)
% 2.38/1.80 % (11068)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_10757 for (2996ds/6Mi)
% 2.38/1.80 % (11069)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_10757 for (2996ds/1087Mi)
% 2.38/1.81 % (11068)Instruction limit reached!
% 2.38/1.81 % (11068)------------------------------
% 2.38/1.81 % (11068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.81 % (11068)Termination reason: Unknown
% 2.38/1.81 % (11068)Termination phase: shuffling
% 2.38/1.81
% 2.38/1.81 % (11068)Memory used [KB]: 1151
% 2.38/1.81 % (11068)Time elapsed: 0.003 s
% 2.38/1.81 % (11068)Instructions burned: 7 (million)
% 2.38/1.81 % (11068)------------------------------
% 2.38/1.81 % (11068)------------------------------
% 2.38/1.81 % (11067)Instruction limit reached!
% 2.38/1.81 % (11067)------------------------------
% 2.38/1.81 % (11067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.81 % (11067)Termination reason: Unknown
% 2.38/1.81 % (11067)Termination phase: Saturation
% 2.38/1.81
% 2.38/1.81 % (11067)Memory used [KB]: 5884
% 2.38/1.81 % (11067)Time elapsed: 0.012 s
% 2.38/1.81 % (11067)Instructions burned: 39 (million)
% 2.38/1.81 % (11067)------------------------------
% 2.38/1.81 % (11067)------------------------------
% 2.38/1.82 % (11070)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10757 for (2996ds/47Mi)
% 2.38/1.82 % (11071)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_10757 for (2996ds/44Mi)
% 2.38/1.82 % (11044)Instruction limit reached!
% 2.38/1.82 % (11044)------------------------------
% 2.38/1.82 % (11044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.82 % (11044)Termination reason: Unknown
% 2.38/1.82 % (11044)Termination phase: Saturation
% 2.38/1.82
% 2.38/1.82 % (11044)Memory used [KB]: 8443
% 2.38/1.82 % (11044)Time elapsed: 0.308 s
% 2.38/1.82 % (11044)Instructions burned: 905 (million)
% 2.38/1.82 % (11044)------------------------------
% 2.38/1.82 % (11044)------------------------------
% 2.38/1.83 % (11070)Instruction limit reached!
% 2.38/1.83 % (11070)------------------------------
% 2.38/1.83 % (11070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.83 % (11070)Termination reason: Unknown
% 2.38/1.83 % (11070)Termination phase: Saturation
% 2.38/1.83
% 2.38/1.83 % (11070)Memory used [KB]: 6012
% 2.38/1.83 % (11070)Time elapsed: 0.016 s
% 2.38/1.83 % (11070)Instructions burned: 47 (million)
% 2.38/1.83 % (11070)------------------------------
% 2.38/1.83 % (11070)------------------------------
% 2.38/1.83 % (11071)Instruction limit reached!
% 2.38/1.83 % (11071)------------------------------
% 2.38/1.83 % (11071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.83 % (11071)Termination reason: Unknown
% 2.38/1.83 % (11071)Termination phase: Saturation
% 2.38/1.83
% 2.38/1.83 % (11071)Memory used [KB]: 1535
% 2.38/1.83 % (11071)Time elapsed: 0.013 s
% 2.38/1.83 % (11071)Instructions burned: 44 (million)
% 2.38/1.83 % (11071)------------------------------
% 2.38/1.83 % (11071)------------------------------
% 2.38/1.83 % (11072)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_10757 for (2995ds/432Mi)
% 2.38/1.84 % (11066)Instruction limit reached!
% 2.38/1.84 % (11066)------------------------------
% 2.38/1.84 % (11066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.84 % (11066)Termination reason: Unknown
% 2.38/1.84 % (11066)Termination phase: Saturation
% 2.38/1.84
% 2.38/1.84 % (11066)Memory used [KB]: 6268
% 2.38/1.84 % (11066)Time elapsed: 0.052 s
% 2.38/1.84 % (11066)Instructions burned: 151 (million)
% 2.38/1.84 % (11066)------------------------------
% 2.38/1.84 % (11066)------------------------------
% 2.38/1.84 % (11051)Refutation not found, non-redundant clauses discarded% (11051)------------------------------
% 2.38/1.84 % (11051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.84 % (11051)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.38/1.84
% 2.38/1.84 % (11051)Memory used [KB]: 6780
% 2.38/1.84 % (11051)Time elapsed: 0.287 s
% 2.38/1.84 % (11051)Instructions burned: 863 (million)
% 2.38/1.84 % (11051)------------------------------
% 2.38/1.84 % (11051)------------------------------
% 2.38/1.84 % (11073)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/62Mi)
% 2.38/1.84 % (11074)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_10757 for (2995ds/31Mi)
% 2.38/1.85 % (11075)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/96Mi)
% 2.38/1.85 % (11076)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_10757 for (2995ds/453Mi)
% 2.38/1.85 % (11074)Instruction limit reached!
% 2.38/1.85 % (11074)------------------------------
% 2.38/1.85 % (11074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.85 % (11074)Termination reason: Unknown
% 2.38/1.85 % (11074)Termination phase: Property scanning
% 2.38/1.85
% 2.38/1.85 % (11074)Memory used [KB]: 1407
% 2.38/1.85 % (11074)Time elapsed: 0.010 s
% 2.38/1.85 % (11074)Instructions burned: 32 (million)
% 2.38/1.85 % (11074)------------------------------
% 2.38/1.85 % (11074)------------------------------
% 2.38/1.86 % (11073)Instruction limit reached!
% 2.38/1.86 % (11073)------------------------------
% 2.38/1.86 % (11073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.86 % (11073)Termination reason: Unknown
% 2.38/1.86 % (11073)Termination phase: Saturation
% 2.38/1.86
% 2.38/1.86 % (11073)Memory used [KB]: 6012
% 2.38/1.86 % (11073)Time elapsed: 0.019 s
% 2.38/1.86 % (11073)Instructions burned: 62 (million)
% 2.38/1.86 % (11073)------------------------------
% 2.38/1.86 % (11073)------------------------------
% 2.38/1.86 % (11077)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_10757 for (2995ds/71Mi)
% 2.38/1.87 % (11078)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/83Mi)
% 2.38/1.88 % (11075)Instruction limit reached!
% 2.38/1.88 % (11075)------------------------------
% 2.38/1.88 % (11075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.88 % (11075)Termination reason: Unknown
% 2.38/1.88 % (11075)Termination phase: Saturation
% 2.38/1.88
% 2.38/1.88 % (11075)Memory used [KB]: 6268
% 2.38/1.88 % (11075)Time elapsed: 0.030 s
% 2.38/1.88 % (11075)Instructions burned: 96 (million)
% 2.38/1.88 % (11075)------------------------------
% 2.38/1.88 % (11075)------------------------------
% 2.38/1.88 % (11077)Instruction limit reached!
% 2.38/1.88 % (11077)------------------------------
% 2.38/1.88 % (11077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.88 % (11077)Termination reason: Unknown
% 2.38/1.88 % (11077)Termination phase: Saturation
% 2.38/1.88
% 2.38/1.88 % (11077)Memory used [KB]: 6140
% 2.38/1.88 % (11077)Time elapsed: 0.023 s
% 2.38/1.88 % (11077)Instructions burned: 73 (million)
% 2.38/1.88 % (11077)------------------------------
% 2.38/1.88 % (11077)------------------------------
% 2.38/1.88 % (11062)Instruction limit reached!
% 2.38/1.88 % (11062)------------------------------
% 2.38/1.88 % (11062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.88 % (11062)Termination reason: Unknown
% 2.38/1.88 % (11062)Termination phase: Saturation
% 2.38/1.88
% 2.38/1.88 % (11062)Memory used [KB]: 6908
% 2.38/1.88 % (11062)Time elapsed: 0.170 s
% 2.38/1.88 % (11062)Instructions burned: 449 (million)
% 2.38/1.88 % (11062)------------------------------
% 2.38/1.88 % (11062)------------------------------
% 2.38/1.88 % (11079)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/11Mi)
% 2.38/1.89 % (11079)Instruction limit reached!
% 2.38/1.89 % (11079)------------------------------
% 2.38/1.89 % (11079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.89 % (11079)Termination reason: Unknown
% 2.38/1.89 % (11079)Termination phase: shuffling
% 2.38/1.89
% 2.38/1.89 % (11079)Memory used [KB]: 1279
% 2.38/1.89 % (11079)Time elapsed: 0.004 s
% 2.38/1.89 % (11079)Instructions burned: 12 (million)
% 2.38/1.89 % (11079)------------------------------
% 2.38/1.89 % (11079)------------------------------
% 2.38/1.89 % (11080)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_10757 for (2995ds/41Mi)
% 2.38/1.89 % (11081)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/6Mi)
% 2.38/1.89 % (11078)Instruction limit reached!
% 2.38/1.89 % (11078)------------------------------
% 2.38/1.89 % (11078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.89 % (11081)Instruction limit reached!
% 2.38/1.89 % (11081)------------------------------
% 2.38/1.89 % (11081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.89 % (11078)Termination reason: Unknown
% 2.38/1.89 % (11078)Termination phase: Saturation
% 2.38/1.89
% 2.38/1.89 % (11078)Memory used [KB]: 6140
% 2.38/1.89 % (11078)Time elapsed: 0.028 s
% 2.38/1.89 % (11078)Instructions burned: 84 (million)
% 2.38/1.89 % (11078)------------------------------
% 2.38/1.89 % (11078)------------------------------
% 2.38/1.89 % (11081)Termination reason: Unknown
% 2.38/1.89 % (11081)Termination phase: shuffling
% 2.38/1.89
% 2.38/1.89 % (11081)Memory used [KB]: 1151
% 2.38/1.89 % (11081)Time elapsed: 0.003 s
% 2.38/1.89 % (11081)Instructions burned: 7 (million)
% 2.38/1.89 % (11081)------------------------------
% 2.38/1.89 % (11081)------------------------------
% 2.38/1.90 % (11082)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/150Mi)
% 2.38/1.90 % (11080)Instruction limit reached!
% 2.38/1.90 % (11080)------------------------------
% 2.38/1.90 % (11080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.90 % (11080)Termination reason: Unknown
% 2.38/1.90 % (11080)Termination phase: Property scanning
% 2.38/1.90
% 2.38/1.90 % (11080)Memory used [KB]: 1407
% 2.38/1.90 % (11080)Time elapsed: 0.012 s
% 2.38/1.90 % (11080)Instructions burned: 43 (million)
% 2.38/1.90 % (11080)------------------------------
% 2.38/1.90 % (11080)------------------------------
% 2.38/1.90 % (11084)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_10757 for (2995ds/109Mi)
% 2.38/1.90 % (11083)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10757 for (2995ds/343Mi)
% 2.38/1.91 % (11085)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_10757 for (2995ds/253Mi)
% 2.38/1.93 % (11084)Instruction limit reached!
% 2.38/1.93 % (11084)------------------------------
% 2.38/1.93 % (11084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.93 % (11084)Termination reason: Unknown
% 2.38/1.93 % (11084)Termination phase: Saturation
% 2.38/1.93
% 2.38/1.93 % (11084)Memory used [KB]: 6268
% 2.38/1.93 % (11084)Time elapsed: 0.032 s
% 2.38/1.93 % (11084)Instructions burned: 109 (million)
% 2.38/1.93 % (11084)------------------------------
% 2.38/1.93 % (11084)------------------------------
% 2.38/1.94 % (11086)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10757 for (2994ds/140Mi)
% 2.38/1.95 % (11082)Instruction limit reached!
% 2.38/1.95 % (11082)------------------------------
% 2.38/1.95 % (11082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.95 % (11082)Termination reason: Unknown
% 2.38/1.95 % (11082)Termination phase: Saturation
% 2.38/1.95
% 2.38/1.95 % (11082)Memory used [KB]: 6396
% 2.38/1.95 % (11082)Time elapsed: 0.049 s
% 2.38/1.95 % (11082)Instructions burned: 152 (million)
% 2.38/1.95 % (11082)------------------------------
% 2.38/1.95 % (11082)------------------------------
% 2.38/1.95 % (11076)First to succeed.
% 2.38/1.95 % (11076)Refutation found. Thanks to Tanya!
% 2.38/1.95 % SZS status Theorem for DTF2THF_10757
% 2.38/1.95 % SZS output start Proof for DTF2THF_10757
% 2.38/1.95 thf(type_def_5, type, extended_ereal: $tType).
% 2.38/1.95 thf(type_def_7, type, a: $tType).
% 2.38/1.95 thf(type_def_8, type, set_a: $tType).
% 2.38/1.95 thf(func_def_0, type, extended_ereal: $tType).
% 2.38/1.95 thf(func_def_1, type, set_a: $tType).
% 2.38/1.95 thf(func_def_2, type, a: $tType).
% 2.38/1.95 thf(func_def_3, type, extend1289208545_ereal: extended_ereal).
% 2.38/1.95 thf(func_def_4, type, extended_MInfty: extended_ereal).
% 2.38/1.95 thf(func_def_5, type, extended_PInfty: extended_ereal).
% 2.38/1.95 thf(func_def_6, type, times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_7, type, uminus1208298309_ereal: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_8, type, zero_z163181189_ereal: extended_ereal).
% 2.38/1.95 thf(func_def_9, type, lower_191460856_ereal: a > (a > extended_ereal) > $o).
% 2.38/1.95 thf(func_def_10, type, ord_le2001149050_ereal: extended_ereal > extended_ereal > $o).
% 2.38/1.95 thf(func_def_11, type, divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_12, type, collect_a: (a > $o) > set_a).
% 2.38/1.95 thf(func_def_13, type, topolo1276428101open_a: set_a > $o).
% 2.38/1.95 thf(func_def_14, type, member_a: a > set_a > $o).
% 2.38/1.95 thf(func_def_15, type, f: a > extended_ereal).
% 2.38/1.95 thf(func_def_16, type, x0: a).
% 2.38/1.95 thf(func_def_35, type, ph1: !>[X0: $tType]:(X0)).
% 2.38/1.95 thf(func_def_36, type, sK2: extended_ereal).
% 2.38/1.95 thf(func_def_37, type, sK3: set_a > a).
% 2.38/1.95 thf(func_def_38, type, sK4: extended_ereal > set_a).
% 2.38/1.95 thf(func_def_39, type, sK5: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_40, type, sK6: extended_ereal > set_a).
% 2.38/1.95 thf(func_def_41, type, sK7: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_42, type, sK8: extended_ereal).
% 2.38/1.95 thf(func_def_43, type, sK9: set_a > a).
% 2.38/1.95 thf(func_def_44, type, sK10: extended_ereal).
% 2.38/1.95 thf(func_def_45, type, sK11: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_46, type, sK12: extended_ereal > set_a).
% 2.38/1.95 thf(func_def_47, type, sK13: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_48, type, sK14: extended_ereal).
% 2.38/1.95 thf(func_def_49, type, sK15: set_a > a).
% 2.38/1.95 thf(func_def_50, type, sK16: extended_ereal > extended_ereal).
% 2.38/1.95 thf(func_def_51, type, sK17: extended_ereal > extended_ereal).
% 2.38/1.95 thf(f1418,plain,(
% 2.38/1.95 $false),
% 2.38/1.95 inference(avatar_sat_refutation,[status(thm)],[f562,f688,f702,f761,f884,f948,f987,f1281,f1402,f1417])).
% 2.38/1.95 thf(f1417,plain,(
% 2.38/1.95 ~spl0_2 | ~spl0_4),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f1416])).
% 2.38/1.95 thf(f1416,plain,(
% 2.38/1.95 $false | (~spl0_2 | ~spl0_4)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1415])).
% 2.38/1.95 thf(f1415,plain,(
% 2.38/1.95 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1406,f692])).
% 2.38/1.95 thf(f692,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((ord_le2001149050_ereal @ X1 @ extended_MInfty) = $false)) )),
% 2.38/1.95 inference(not_proxy_clausification,[status(thm)],[f691])).
% 2.38/1.95 thf(f691,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (~ (ord_le2001149050_ereal @ X1 @ extended_MInfty)))) )),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f690,f475])).
% 2.38/1.95 thf(f475,plain,(
% 2.38/1.95 (extended_MInfty = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f379,f474])).
% 2.38/1.95 thf(f474,plain,(
% 2.38/1.95 (extend1289208545_ereal = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f429,f469])).
% 2.38/1.95 thf(f469,plain,(
% 2.38/1.95 (extended_PInfty = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f352])).
% 2.38/1.95 thf(f352,plain,(
% 2.38/1.95 (extended_PInfty = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f41])).
% 2.38/1.95 thf(f41,axiom,(
% 2.38/1.95 (extended_PInfty = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_40_uminus__ereal_Osimps_I3_J)).
% 2.38/1.95 thf(f429,plain,(
% 2.38/1.95 (extend1289208545_ereal = extended_PInfty)),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f235])).
% 2.38/1.95 thf(f235,plain,(
% 2.38/1.95 (extend1289208545_ereal = extended_PInfty)),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f50])).
% 2.38/1.95 thf(f50,axiom,(
% 2.38/1.95 (extend1289208545_ereal = extended_PInfty)),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_49_infinity__ereal__def)).
% 2.38/1.95 thf(f379,plain,(
% 2.38/1.95 ((uminus1208298309_ereal @ extend1289208545_ereal) = extended_MInfty)),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f134])).
% 2.38/1.95 thf(f134,plain,(
% 2.38/1.95 ((uminus1208298309_ereal @ extend1289208545_ereal) = extended_MInfty)),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f38])).
% 2.38/1.95 thf(f38,axiom,(
% 2.38/1.95 ((uminus1208298309_ereal @ extend1289208545_ereal) = extended_MInfty)),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_37_MInfty__eq__minfinity)).
% 2.38/1.95 thf(f690,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((~ (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) = $true)) )),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f689])).
% 2.38/1.95 thf(f689,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : extended_ereal]: (~ (ord_le2001149050_ereal @ Y0 @ (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))))) @ X1))) )),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f497])).
% 2.38/1.95 thf(f497,plain,(
% 2.38/1.95 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: (~ (ord_le2001149050_ereal @ Y0 @ (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))))))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f423,f474])).
% 2.38/1.95 thf(f423,plain,(
% 2.38/1.95 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: (~ (ord_le2001149050_ereal @ Y0 @ (uminus1208298309_ereal @ extend1289208545_ereal))))))),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f322])).
% 2.38/1.95 thf(f322,plain,(
% 2.38/1.95 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: (~ (ord_le2001149050_ereal @ Y0 @ (uminus1208298309_ereal @ extend1289208545_ereal))))))),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f321])).
% 2.38/1.95 thf(f321,plain,(
% 2.38/1.95 ! [X0 : extended_ereal] : ~(ord_le2001149050_ereal @ X0 @ (uminus1208298309_ereal @ extend1289208545_ereal))),
% 2.38/1.95 inference(rectify,[status(thm)],[f26])).
% 2.38/1.95 thf(f26,axiom,(
% 2.38/1.95 ! [X18 : extended_ereal] : ~(ord_le2001149050_ereal @ X18 @ (uminus1208298309_ereal @ extend1289208545_ereal))),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_25_less__ereal_Osimps_I3_J)).
% 2.38/1.95 thf(f1406,plain,(
% 2.38/1.95 ($true = (ord_le2001149050_ereal @ sK2 @ extended_MInfty)) | (~spl0_2 | ~spl0_4)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f1310,f634])).
% 2.38/1.95 thf(f634,plain,(
% 2.38/1.95 ((f @ x0) = extended_MInfty) | ~spl0_4),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f633])).
% 2.38/1.95 thf(f633,definition,(
% 2.38/1.95 spl0_4 <=> ((f @ x0) = extended_MInfty)),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.38/1.95 thf(f1310,plain,(
% 2.38/1.95 ($true = (ord_le2001149050_ereal @ sK2 @ (f @ x0))) | ~spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1308])).
% 2.38/1.95 thf(f1308,plain,(
% 2.38/1.95 (((ord_le2001149050_ereal @ sK2 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1))))))))) = $false) | ~spl0_2),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1307])).
% 2.38/1.95 thf(f1307,plain,(
% 2.38/1.95 (((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))) @ sK2) = $false) | ~spl0_2),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f561])).
% 2.38/1.95 thf(f561,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))))))))) = $false) | ~spl0_2),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f559])).
% 2.38/1.95 thf(f559,definition,(
% 2.38/1.95 spl0_2 <=> ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))))))))) = $false)),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.38/1.95 thf(f1402,plain,(
% 2.38/1.95 ~spl0_2 | ~spl0_7),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f1401])).
% 2.38/1.95 thf(f1401,plain,(
% 2.38/1.95 $false | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1400])).
% 2.38/1.95 thf(f1400,plain,(
% 2.38/1.95 ($true = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f1310,f1399])).
% 2.38/1.95 thf(f1399,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK2 @ (f @ x0)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1396])).
% 2.38/1.95 thf(f1396,plain,(
% 2.38/1.95 ($true = $false) | ((ord_le2001149050_ereal @ sK2 @ (f @ x0)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(superposition,[status(thm)],[f1390,f1366])).
% 2.38/1.95 thf(f1366,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (member_a @ x0 @ (sK12 @ X1))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | ~spl0_7),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1364])).
% 2.38/1.95 thf(f1364,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false) | ($true = ((member_a @ x0 @ (sK12 @ X1)) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK12 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))))) ) | ~spl0_7),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1362])).
% 2.38/1.95 thf(f1362,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (((member_a @ x0 @ (sK12 @ X1)) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK12 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))) & (topolo1276428101open_a @ (sK12 @ X1)))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | ~spl0_7),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1361])).
% 2.38/1.95 thf(f1361,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0))) @ (sK12 @ X1))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | ~spl0_7),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f1360])).
% 2.38/1.95 thf(f1360,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0))))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | ~spl0_7),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1359])).
% 2.38/1.95 thf(f1359,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((ord_le2001149050_ereal @ X1 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0))))))) ) | ~spl0_7),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1358])).
% 2.38/1.95 thf(f1358,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))) @ X1))) ) | ~spl0_7),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f701])).
% 2.38/1.95 thf(f701,plain,(
% 2.38/1.95 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ~spl0_7),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f699])).
% 2.38/1.95 thf(f699,definition,(
% 2.38/1.95 spl0_7 <=> ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))))),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 2.38/1.95 thf(f1390,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK12 @ sK2)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1389])).
% 2.38/1.95 thf(f1389,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK12 @ sK2)) = $false) | ($true = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1388,f1373])).
% 2.38/1.95 thf(f1373,plain,(
% 2.38/1.95 ((topolo1276428101open_a @ (sK12 @ sK2)) = $true) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1367])).
% 2.38/1.95 thf(f1367,plain,(
% 2.38/1.95 ($true = $false) | ((topolo1276428101open_a @ (sK12 @ sK2)) = $true) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(superposition,[status(thm)],[f1363,f1310])).
% 2.38/1.95 thf(f1363,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false) | ($true = (topolo1276428101open_a @ (sK12 @ X1)))) ) | ~spl0_7),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1362])).
% 2.38/1.95 thf(f1388,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK12 @ sK2)) = $false) | ((topolo1276428101open_a @ (sK12 @ sK2)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1387])).
% 2.38/1.95 thf(f1387,plain,(
% 2.38/1.95 ($true = $false) | ((topolo1276428101open_a @ (sK12 @ sK2)) = $false) | ((member_a @ x0 @ (sK12 @ sK2)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1386,f1310])).
% 2.38/1.95 thf(f1386,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK2 @ (f @ x0)) = $false) | ((member_a @ x0 @ (sK12 @ sK2)) = $false) | ((topolo1276428101open_a @ (sK12 @ sK2)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1379])).
% 2.38/1.95 thf(f1379,plain,(
% 2.38/1.95 ((topolo1276428101open_a @ (sK12 @ sK2)) = $false) | ($true = $false) | ((ord_le2001149050_ereal @ sK2 @ (f @ x0)) = $false) | ((member_a @ x0 @ (sK12 @ sK2)) = $false) | (~spl0_2 | ~spl0_7)),
% 2.38/1.95 inference(superposition,[status(thm)],[f1365,f1322])).
% 2.38/1.95 thf(f1322,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0))))) = $false) | ((member_a @ x0 @ X1) = $false) | ((topolo1276428101open_a @ X1) = $false)) ) | ~spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1321])).
% 2.38/1.95 thf(f1321,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0))))) = $false) | (((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1)) = $false)) ) | ~spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1320])).
% 2.38/1.95 thf(f1320,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (($false = (((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1)) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0)))))))) ) | ~spl0_2),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1319])).
% 2.38/1.95 thf(f1319,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : ((((^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1))))))) @ X1) = $false)) ) | ~spl0_2),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f1309])).
% 2.38/1.95 thf(f1309,plain,(
% 2.38/1.95 ((?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1)))))))) = $false) | ~spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1308])).
% 2.38/1.95 thf(f1365,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK12 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | ~spl0_7),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1364])).
% 2.38/1.95 thf(f1281,plain,(
% 2.38/1.95 ~spl0_1 | spl0_2 | ~spl0_6),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f1280])).
% 2.38/1.95 thf(f1280,plain,(
% 2.38/1.95 $false | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1279])).
% 2.38/1.95 thf(f1279,plain,(
% 2.38/1.95 ($true = $false) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f1216,f1278])).
% 2.38/1.95 thf(f1278,plain,(
% 2.38/1.95 ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1276])).
% 2.38/1.95 thf(f1276,plain,(
% 2.38/1.95 ($true = $false) | ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(superposition,[status(thm)],[f995,f1258])).
% 2.38/1.95 thf(f1258,plain,(
% 2.38/1.95 ($false = (member_a @ x0 @ (sK6 @ sK14))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1257])).
% 2.38/1.95 thf(f1257,plain,(
% 2.38/1.95 ($false = (member_a @ x0 @ (sK6 @ sK14))) | ($true = $false) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1256,f1216])).
% 2.38/1.95 thf(f1256,plain,(
% 2.38/1.95 ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | ($false = (member_a @ x0 @ (sK6 @ sK14))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1255])).
% 2.38/1.95 thf(f1255,plain,(
% 2.38/1.95 ($true = $false) | ($false = (member_a @ x0 @ (sK6 @ sK14))) | ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1248,f1230])).
% 2.38/1.95 thf(f1230,plain,(
% 2.38/1.95 ($true = (topolo1276428101open_a @ (sK6 @ sK14))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1218])).
% 2.38/1.95 thf(f1218,plain,(
% 2.38/1.95 ($true = $false) | ($true = (topolo1276428101open_a @ (sK6 @ sK14))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(superposition,[status(thm)],[f1216,f994])).
% 2.38/1.95 thf(f994,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty))) | ($true = (topolo1276428101open_a @ (sK6 @ X1)))) ) | (spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f825,f686])).
% 2.38/1.95 thf(f686,plain,(
% 2.38/1.95 ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ~spl0_6),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f685])).
% 2.38/1.95 thf(f685,definition,(
% 2.38/1.95 spl0_6 <=> ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.38/1.95 thf(f825,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false) | ($true = (topolo1276428101open_a @ (sK6 @ X1)))) ) | spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f824])).
% 2.38/1.95 thf(f824,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false) | ($true = ((member_a @ x0 @ (sK6 @ X1)) & (topolo1276428101open_a @ (sK6 @ X1))))) ) | spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f822])).
% 2.38/1.95 thf(f822,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (((member_a @ x0 @ (sK6 @ X1)) & (topolo1276428101open_a @ (sK6 @ X1))) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK6 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0))))))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | spl0_2),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f821])).
% 2.38/1.95 thf(f821,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))))) @ (sK6 @ X1))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | spl0_2),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f802])).
% 2.38/1.95 thf(f802,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (((?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1)))))))) = $true) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f801])).
% 2.38/1.95 thf(f801,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((ord_le2001149050_ereal @ X1 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))))))))) ) | spl0_2),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f800])).
% 2.38/1.95 thf(f800,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))) @ X1))) ) | spl0_2),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f560])).
% 2.38/1.95 thf(f560,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))))))))) != $false) | spl0_2),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f559])).
% 2.38/1.95 thf(f1248,plain,(
% 2.38/1.95 ($false = (member_a @ x0 @ (sK6 @ sK14))) | ((topolo1276428101open_a @ (sK6 @ sK14)) = $false) | ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f1245])).
% 2.38/1.95 thf(f1245,plain,(
% 2.38/1.95 ((topolo1276428101open_a @ (sK6 @ sK14)) = $false) | ($false = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | ($true = $false) | ($false = (member_a @ x0 @ (sK6 @ sK14))) | (~spl0_1 | spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(superposition,[status(thm)],[f993,f1240])).
% 2.38/1.95 thf(f1240,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK14 @ (f @ Y0))))) = $false) | ((topolo1276428101open_a @ X1) = $false) | ((member_a @ x0 @ X1) = $false)) ) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1239])).
% 2.38/1.95 thf(f1239,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((member_a @ x0 @ X1) = $false) | (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK14 @ (f @ Y0))))) & (topolo1276428101open_a @ X1)) = $false)) ) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1238])).
% 2.38/1.95 thf(f1238,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (($false = (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK14 @ (f @ Y0))))) & (topolo1276428101open_a @ X1)) & (member_a @ x0 @ X1)))) ) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1237])).
% 2.38/1.95 thf(f1237,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : ((((^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK14 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))) @ X1) = $false)) ) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f1215])).
% 2.38/1.95 thf(f1215,plain,(
% 2.38/1.95 ((?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK14 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0)))) = $false) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1214])).
% 2.38/1.95 thf(f1214,plain,(
% 2.38/1.95 (((ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty)) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK14 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))))) = $false) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f1213,f686])).
% 2.38/1.95 thf(f1213,plain,(
% 2.38/1.95 (((ord_le2001149050_ereal @ sK14 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK14 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))))) = $false) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f1212])).
% 2.38/1.95 thf(f1212,plain,(
% 2.38/1.95 (((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1)))))) @ sK14) = $false) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f1005])).
% 2.38/1.95 thf(f1005,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $false) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(subsumption_resolution,[status(thm)],[f770,f686])).
% 2.38/1.95 thf(f770,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $false) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ~spl0_1),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f766])).
% 2.38/1.95 thf(f766,plain,(
% 2.38/1.95 ($true = $false) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $false) | ~spl0_1),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f527,f557])).
% 2.38/1.95 thf(f557,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = $false) | ~spl0_1),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f555])).
% 2.38/1.95 thf(f555,definition,(
% 2.38/1.95 spl0_1 <=> ((lower_191460856_ereal @ x0 @ f) = $false)),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.38/1.95 thf(f527,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $false) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $true)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f526])).
% 2.38/1.95 thf(f526,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1)))))))) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f525])).
% 2.38/1.95 thf(f525,plain,(
% 2.38/1.95 ($true = ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))))) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f524])).
% 2.38/1.95 thf(f524,plain,(
% 2.38/1.95 (((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) = $false) | ($true = ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1)))))))))),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f503])).
% 2.38/1.95 thf(f503,plain,(
% 2.38/1.95 ($true = (((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) => ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))))))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f441,f474])).
% 2.38/1.95 thf(f441,plain,(
% 2.38/1.95 ($true = (((f @ x0) = extend1289208545_ereal) => ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))))))),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f142])).
% 2.38/1.95 thf(f142,plain,(
% 2.38/1.95 ($true = (((f @ x0) = extend1289208545_ereal) => ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))))))),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f141])).
% 2.38/1.95 thf(f141,plain,(
% 2.38/1.95 ((f @ x0) = extend1289208545_ereal) => ((lower_191460856_ereal @ x0 @ f) = ! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))))))),
% 2.38/1.95 inference(rectify,[status(thm)],[f1])).
% 2.38/1.95 thf(f1,axiom,(
% 2.38/1.95 ((f @ x0) = extend1289208545_ereal) => ((lower_191460856_ereal @ x0 @ f) = ! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))))))),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 2.38/1.95 thf(f993,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK6 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f823,f686])).
% 2.38/1.95 thf(f823,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK6 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f822])).
% 2.38/1.95 thf(f995,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (member_a @ x0 @ (sK6 @ X1))) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (spl0_2 | ~spl0_6)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f826,f686])).
% 2.38/1.95 thf(f826,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (member_a @ x0 @ (sK6 @ X1))) | ((ord_le2001149050_ereal @ X1 @ (f @ x0)) = $false)) ) | spl0_2),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f824])).
% 2.38/1.95 thf(f1216,plain,(
% 2.38/1.95 ($true = (ord_le2001149050_ereal @ sK14 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_1 | ~spl0_6)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f1214])).
% 2.38/1.95 thf(f987,plain,(
% 2.38/1.95 ~spl0_1 | ~spl0_4),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f986])).
% 2.38/1.95 thf(f986,plain,(
% 2.38/1.95 $false | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f985])).
% 2.38/1.95 thf(f985,plain,(
% 2.38/1.95 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(boolean_simplification,[status(thm)],[f984])).
% 2.38/1.95 thf(f984,plain,(
% 2.38/1.95 (($false => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK10 @ (f @ Y1))))) & (member_a @ x0 @ Y0)) & (topolo1276428101open_a @ Y0))))) = $false) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f983,f692])).
% 2.38/1.95 thf(f983,plain,(
% 2.38/1.95 ($false = ((ord_le2001149050_ereal @ sK10 @ extended_MInfty) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK10 @ (f @ Y1))))) & (member_a @ x0 @ Y0)) & (topolo1276428101open_a @ Y0)))))) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f982,f634])).
% 2.38/1.95 thf(f982,plain,(
% 2.38/1.95 ($false = ((ord_le2001149050_ereal @ sK10 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK10 @ (f @ Y1))))) & (member_a @ x0 @ Y0)) & (topolo1276428101open_a @ Y0)))))) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f981])).
% 2.38/1.95 thf(f981,plain,(
% 2.38/1.95 (((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1)))))) @ sK10) = $false) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f975])).
% 2.38/1.95 thf(f975,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = $false) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f974])).
% 2.38/1.95 thf(f974,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = $false) | (extended_MInfty != extended_MInfty) | (~spl0_1 | ~spl0_4)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f953,f634])).
% 2.38/1.95 thf(f953,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = $false) | ((f @ x0) != extended_MInfty) | ~spl0_1),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f952])).
% 2.38/1.95 thf(f952,plain,(
% 2.38/1.95 ($true = $false) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = $false) | ((f @ x0) != extended_MInfty) | ~spl0_1),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f544,f557])).
% 2.38/1.95 thf(f544,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = $true) | ((f @ x0) != extended_MInfty) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = $false)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f543])).
% 2.38/1.95 thf(f543,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1)))))))) | ((f @ x0) != extended_MInfty)),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f542])).
% 2.38/1.95 thf(f542,plain,(
% 2.38/1.95 ((f @ x0) != extended_MInfty) | ($true = ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f541])).
% 2.38/1.95 thf(f541,plain,(
% 2.38/1.95 (((f @ x0) = extended_MInfty) = $false) | ($true = ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f540])).
% 2.38/1.95 thf(f540,plain,(
% 2.38/1.95 ($true = (((f @ x0) = extended_MInfty) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))))),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f480,f475])).
% 2.38/1.95 thf(f480,plain,(
% 2.38/1.95 ($true = (((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f370,f474])).
% 2.38/1.95 thf(f370,plain,(
% 2.38/1.95 ($true = (((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))))),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f188])).
% 2.38/1.95 thf(f188,plain,(
% 2.38/1.95 ($true = (((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (member_a @ x0 @ Y1)) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))))),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f187])).
% 2.38/1.95 thf(f187,plain,(
% 2.38/1.95 ((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)) => (! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((topolo1276428101open_a @ X1) & (member_a @ x0 @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))))) = (lower_191460856_ereal @ x0 @ f))),
% 2.38/1.95 inference(rectify,[status(thm)],[f2])).
% 2.38/1.95 thf(f2,axiom,(
% 2.38/1.95 ((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal)) => (! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((topolo1276428101open_a @ X1) & (member_a @ x0 @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))))) = (lower_191460856_ereal @ x0 @ f))),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 2.38/1.95 thf(f948,plain,(
% 2.38/1.95 spl0_2 | ~spl0_8),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f947])).
% 2.38/1.95 thf(f947,plain,(
% 2.38/1.95 $false | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f946])).
% 2.38/1.95 thf(f946,plain,(
% 2.38/1.95 ($true = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f890,f945])).
% 2.38/1.95 thf(f945,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f943])).
% 2.38/1.95 thf(f943,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | ($true = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(superposition,[status(thm)],[f826,f929])).
% 2.38/1.95 thf(f929,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK6 @ sK8)) = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f928])).
% 2.38/1.95 thf(f928,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK6 @ sK8)) = $false) | ($true = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f927,f890])).
% 2.38/1.95 thf(f927,plain,(
% 2.38/1.95 ((member_a @ x0 @ (sK6 @ sK8)) = $false) | ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f926])).
% 2.38/1.95 thf(f926,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | ($true = $false) | ((member_a @ x0 @ (sK6 @ sK8)) = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(forward_demodulation,[status(thm)],[f922,f905])).
% 2.38/1.95 thf(f905,plain,(
% 2.38/1.95 ($true = (topolo1276428101open_a @ (sK6 @ sK8))) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f891])).
% 2.38/1.95 thf(f891,plain,(
% 2.38/1.95 ($true = (topolo1276428101open_a @ (sK6 @ sK8))) | ($true = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(superposition,[status(thm)],[f890,f825])).
% 2.38/1.95 thf(f922,plain,(
% 2.38/1.95 ((topolo1276428101open_a @ (sK6 @ sK8)) = $false) | ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | ((member_a @ x0 @ (sK6 @ sK8)) = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f917])).
% 2.38/1.95 thf(f917,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK8 @ (f @ x0)) = $false) | ((topolo1276428101open_a @ (sK6 @ sK8)) = $false) | ((member_a @ x0 @ (sK6 @ sK8)) = $false) | ($true = $false) | (spl0_2 | ~spl0_8)),
% 2.38/1.95 inference(superposition,[status(thm)],[f823,f913])).
% 2.38/1.95 thf(f913,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK8 @ (f @ Y0))))) = $false) | ((topolo1276428101open_a @ X1) = $false) | ((member_a @ x0 @ X1) = $false)) ) | ~spl0_8),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f912])).
% 2.38/1.95 thf(f912,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : ((((member_a @ x0 @ X1) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK8 @ (f @ Y0)))))) = $false) | ((topolo1276428101open_a @ X1) = $false)) ) | ~spl0_8),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f911])).
% 2.38/1.95 thf(f911,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : (((((member_a @ x0 @ X1) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK8 @ (f @ Y0)))))) & (topolo1276428101open_a @ X1)) = $false)) ) | ~spl0_8),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f910])).
% 2.38/1.95 thf(f910,plain,(
% 2.38/1.95 ( ! [X1 : set_a] : ((((^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK8 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0))) @ X1) = $false)) ) | ~spl0_8),
% 2.38/1.95 inference(pi_clausification,[status(thm)],[f889])).
% 2.38/1.95 thf(f889,plain,(
% 2.38/1.95 ((?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK8 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0)))) = $false) | ~spl0_8),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f888])).
% 2.38/1.95 thf(f888,plain,(
% 2.38/1.95 (((ord_le2001149050_ereal @ sK8 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK8 @ (f @ Y1)))))) & (topolo1276428101open_a @ Y0))))) = $false) | ~spl0_8),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f887])).
% 2.38/1.95 thf(f887,plain,(
% 2.38/1.95 (((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))) @ sK8) = $false) | ~spl0_8),
% 2.38/1.95 inference(sigma_clausification,[status(thm)],[f883])).
% 2.38/1.95 thf(f883,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | ~spl0_8),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f881])).
% 2.38/1.95 thf(f881,definition,(
% 2.38/1.95 spl0_8 <=> ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false)),
% 2.38/1.95 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 2.38/1.95 thf(f890,plain,(
% 2.38/1.95 ($true = (ord_le2001149050_ereal @ sK8 @ (f @ x0))) | ~spl0_8),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f888])).
% 2.38/1.95 thf(f884,plain,(
% 2.38/1.95 spl0_8 | spl0_6 | ~spl0_1 | spl0_4),
% 2.38/1.95 inference(avatar_split_clause,[status(thm)],[f768,f633,f555,f685,f881])).
% 2.38/1.95 thf(f768,plain,(
% 2.38/1.95 ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | (~spl0_1 | spl0_4)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f765])).
% 2.38/1.95 thf(f765,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | ($true = $false) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | (~spl0_1 | spl0_4)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f764,f557])).
% 2.38/1.95 thf(f764,plain,(
% 2.38/1.95 ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $true) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | spl0_4),
% 2.38/1.95 inference(subsumption_resolution,[status(thm)],[f531,f635])).
% 2.38/1.95 thf(f635,plain,(
% 2.38/1.95 ((f @ x0) != extended_MInfty) | spl0_4),
% 2.38/1.95 inference(avatar_component_clause,[status(thm)],[f633])).
% 2.38/1.95 thf(f531,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | ((f @ x0) = extended_MInfty) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $true)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f522,f475])).
% 2.38/1.95 thf(f522,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = $true) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f520])).
% 2.38/1.95 thf(f520,plain,(
% 2.38/1.95 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = $false) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $true)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f519])).
% 2.38/1.95 thf(f519,plain,(
% 2.38/1.95 ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f518])).
% 2.38/1.95 thf(f518,plain,(
% 2.38/1.95 ($true = ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) | ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))))),
% 2.38/1.95 inference(not_proxy_clausification,[status(thm)],[f517])).
% 2.38/1.95 thf(f517,plain,(
% 2.38/1.95 ((~ ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) = $false) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) | ((lower_191460856_ereal @ x0 @ f) = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))))),
% 2.38/1.95 inference(equality_proxy_clausification,[status(thm)],[f516])).
% 2.38/1.95 thf(f516,plain,(
% 2.38/1.95 ($true = ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))) | ((~ ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) = $false) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))))),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f515])).
% 2.38/1.95 thf(f515,plain,(
% 2.38/1.95 ($true = ((~ ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))))),
% 2.38/1.95 inference(not_proxy_clausification,[status(thm)],[f514])).
% 2.38/1.95 thf(f514,plain,(
% 2.38/1.95 ($false = (~ ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))))) | ($true = ((~ ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f))))),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f489])).
% 2.38/1.95 thf(f489,plain,(
% 2.38/1.95 ($true = ((~ ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) => ((~ ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty))) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))))),
% 2.38/1.95 inference(definition_unfolding,[status(thm)],[f391,f474,f474])).
% 2.38/1.95 thf(f391,plain,(
% 2.38/1.95 ($true = ((~ ((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal))) => ((~ ((f @ x0) = extend1289208545_ereal)) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))))),
% 2.38/1.95 inference(cnf_transformation,[status(thm)],[f184])).
% 2.38/1.95 thf(f184,plain,(
% 2.38/1.95 ($true = ((~ ((f @ x0) = (uminus1208298309_ereal @ extend1289208545_ereal))) => ((~ ((f @ x0) = extend1289208545_ereal)) => ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))) = (lower_191460856_ereal @ x0 @ f)))))),
% 2.38/1.95 inference(fool_elimination,[status(thm)],[f183])).
% 2.38/1.95 thf(f183,plain,(
% 2.38/1.95 ((f @ x0) != (uminus1208298309_ereal @ extend1289208545_ereal)) => (((f @ x0) != extend1289208545_ereal) => (! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((topolo1276428101open_a @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))) & (member_a @ x0 @ X1))) = (lower_191460856_ereal @ x0 @ f)))),
% 2.38/1.95 inference(rectify,[status(thm)],[f3])).
% 2.38/1.95 thf(f3,axiom,(
% 2.38/1.95 ((f @ x0) != (uminus1208298309_ereal @ extend1289208545_ereal)) => (((f @ x0) != extend1289208545_ereal) => (! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : ((topolo1276428101open_a @ X1) & ! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))) & (member_a @ x0 @ X1))) = (lower_191460856_ereal @ x0 @ f)))),
% 2.38/1.95 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062)).
% 2.38/1.95 thf(f761,plain,(
% 2.38/1.95 ~spl0_2 | ~spl0_5 | ~spl0_6),
% 2.38/1.95 inference(avatar_contradiction_clause,[status(thm)],[f760])).
% 2.38/1.95 thf(f760,plain,(
% 2.38/1.95 $false | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f759])).
% 2.38/1.95 thf(f759,plain,(
% 2.38/1.95 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(backward_demodulation,[status(thm)],[f703,f758])).
% 2.38/1.95 thf(f758,plain,(
% 2.38/1.95 ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(trivial_inequality_removal,[status(thm)],[f755])).
% 2.38/1.95 thf(f755,plain,(
% 2.38/1.95 ($true = $false) | ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(superposition,[status(thm)],[f753,f723])).
% 2.38/1.95 thf(f723,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (member_a @ x0 @ (sK4 @ X1))) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(binary_proxy_clausification,[status(thm)],[f722])).
% 2.38/1.95 thf(f722,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($true = (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK4 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0))))) & (topolo1276428101open_a @ (sK4 @ X1))) & (member_a @ x0 @ (sK4 @ X1)))) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.95 inference(beta_eta_normalization,[status(thm)],[f721])).
% 2.38/1.95 thf(f721,plain,(
% 2.38/1.95 ( ! [X1 : extended_ereal] : (($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty))) | ($true = ((^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))) @ (sK4 @ X1)))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(sigma_clausification,[status(thm)],[f720])).
% 2.38/1.96 thf(f720,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (((?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0)))) = $true) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f719])).
% 2.38/1.96 thf(f719,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($true = ((ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))))))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(forward_demodulation,[status(thm)],[f718,f686])).
% 2.38/1.96 thf(f718,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($true = ((ord_le2001149050_ereal @ X1 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ X1 @ (f @ Y1))))) & (topolo1276428101open_a @ Y0)) & (member_a @ x0 @ Y0))))))) ) | ~spl0_5),
% 2.38/1.96 inference(beta_eta_normalization,[status(thm)],[f717])).
% 2.38/1.96 thf(f717,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($true = ((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1)))))) @ X1))) ) | ~spl0_5),
% 2.38/1.96 inference(pi_clausification,[status(thm)],[f683])).
% 2.38/1.96 thf(f683,plain,(
% 2.38/1.96 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $true) | ~spl0_5),
% 2.38/1.96 inference(avatar_component_clause,[status(thm)],[f681])).
% 2.38/1.96 thf(f681,definition,(
% 2.38/1.96 spl0_5 <=> ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $true)),
% 2.38/1.96 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 2.38/1.96 thf(f753,plain,(
% 2.38/1.96 ((member_a @ x0 @ (sK4 @ sK2)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f752])).
% 2.38/1.96 thf(f752,plain,(
% 2.38/1.96 ((member_a @ x0 @ (sK4 @ sK2)) = $false) | ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(forward_demodulation,[status(thm)],[f751,f703])).
% 2.38/1.96 thf(f751,plain,(
% 2.38/1.96 ((member_a @ x0 @ (sK4 @ sK2)) = $false) | ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f750])).
% 2.38/1.96 thf(f750,plain,(
% 2.38/1.96 ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | ((member_a @ x0 @ (sK4 @ sK2)) = $false) | ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(forward_demodulation,[status(thm)],[f749,f737])).
% 2.38/1.96 thf(f737,plain,(
% 2.38/1.96 ($true = (topolo1276428101open_a @ (sK4 @ sK2))) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f729])).
% 2.38/1.96 thf(f729,plain,(
% 2.38/1.96 ($true = (topolo1276428101open_a @ (sK4 @ sK2))) | ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(superposition,[status(thm)],[f725,f703])).
% 2.38/1.96 thf(f725,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty))) | ((topolo1276428101open_a @ (sK4 @ X1)) = $true)) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f724])).
% 2.38/1.96 thf(f724,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty))) | ($true = ((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK4 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0))))) & (topolo1276428101open_a @ (sK4 @ X1))))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f722])).
% 2.38/1.96 thf(f749,plain,(
% 2.38/1.96 ((topolo1276428101open_a @ (sK4 @ sK2)) = $false) | ((member_a @ x0 @ (sK4 @ sK2)) = $false) | ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f745])).
% 2.38/1.96 thf(f745,plain,(
% 2.38/1.96 ($true = $false) | ((topolo1276428101open_a @ (sK4 @ sK2)) = $false) | ((member_a @ x0 @ (sK4 @ sK2)) = $false) | ((ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(superposition,[status(thm)],[f726,f578])).
% 2.38/1.96 thf(f578,plain,(
% 2.38/1.96 ( ! [X1 : set_a] : (((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0))))) = $false) | ((member_a @ x0 @ X1) = $false) | ((topolo1276428101open_a @ X1) = $false)) ) | ~spl0_2),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f577])).
% 2.38/1.96 thf(f577,plain,(
% 2.38/1.96 ( ! [X1 : set_a] : ((((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1)) = $false) | ((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0))))) = $false)) ) | ~spl0_2),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f576])).
% 2.38/1.96 thf(f576,plain,(
% 2.38/1.96 ( ! [X1 : set_a] : (($false = (((member_a @ x0 @ X1) & (topolo1276428101open_a @ X1)) & (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ X1) => (ord_le2001149050_ereal @ sK2 @ (f @ Y0)))))))) ) | ~spl0_2),
% 2.38/1.96 inference(beta_eta_normalization,[status(thm)],[f575])).
% 2.38/1.96 thf(f575,plain,(
% 2.38/1.96 ( ! [X1 : set_a] : ((((^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1))))))) @ X1) = $false)) ) | ~spl0_2),
% 2.38/1.96 inference(pi_clausification,[status(thm)],[f573])).
% 2.38/1.96 thf(f573,plain,(
% 2.38/1.96 ((?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1)))))))) = $false) | ~spl0_2),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f572])).
% 2.38/1.96 thf(f572,plain,(
% 2.38/1.96 (((ord_le2001149050_ereal @ sK2 @ (f @ x0)) => (?? @ set_a @ (^[Y0 : set_a]: (((member_a @ x0 @ Y0) & (topolo1276428101open_a @ Y0)) & (!! @ a @ (^[Y1 : a]: ((member_a @ Y1 @ Y0) => (ord_le2001149050_ereal @ sK2 @ (f @ Y1))))))))) = $false) | ~spl0_2),
% 2.38/1.96 inference(beta_eta_normalization,[status(thm)],[f571])).
% 2.38/1.96 thf(f571,plain,(
% 2.38/1.96 (((^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))) @ sK2) = $false) | ~spl0_2),
% 2.38/1.96 inference(sigma_clausification,[status(thm)],[f561])).
% 2.38/1.96 thf(f726,plain,(
% 2.38/1.96 ( ! [X1 : extended_ereal] : (($true = (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ (sK4 @ X1)) => (ord_le2001149050_ereal @ X1 @ (f @ Y0)))))) | ($false = (ord_le2001149050_ereal @ X1 @ (uminus1208298309_ereal @ extended_MInfty)))) ) | (~spl0_5 | ~spl0_6)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f724])).
% 2.38/1.96 thf(f703,plain,(
% 2.38/1.96 ($true = (ord_le2001149050_ereal @ sK2 @ (uminus1208298309_ereal @ extended_MInfty))) | (~spl0_2 | ~spl0_6)),
% 2.38/1.96 inference(backward_demodulation,[status(thm)],[f574,f686])).
% 2.38/1.96 thf(f574,plain,(
% 2.38/1.96 ($true = (ord_le2001149050_ereal @ sK2 @ (f @ x0))) | ~spl0_2),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f572])).
% 2.38/1.96 thf(f702,plain,(
% 2.38/1.96 spl0_7 | spl0_6 | spl0_4 | ~spl0_2),
% 2.38/1.96 inference(avatar_split_clause,[status(thm)],[f570,f559,f633,f685,f699])).
% 2.38/1.96 thf(f570,plain,(
% 2.38/1.96 ((f @ x0) = extended_MInfty) | ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ~spl0_2),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f566])).
% 2.38/1.96 thf(f566,plain,(
% 2.38/1.96 ($true = $false) | ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((f @ x0) = extended_MInfty) | ~spl0_2),
% 2.38/1.96 inference(backward_demodulation,[status(thm)],[f530,f564])).
% 2.38/1.96 thf(f564,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = $true) | ~spl0_2),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f563])).
% 2.38/1.96 thf(f563,plain,(
% 2.38/1.96 ($true = $false) | ((lower_191460856_ereal @ x0 @ f) = $true) | ~spl0_2),
% 2.38/1.96 inference(backward_demodulation,[status(thm)],[f539,f561])).
% 2.38/1.96 thf(f539,plain,(
% 2.38/1.96 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))) | ((lower_191460856_ereal @ x0 @ f) = $true)),
% 2.38/1.96 inference(not_proxy_clausification,[status(thm)],[f536])).
% 2.38/1.96 thf(f536,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = $true) | ((~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))) = $false)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f535])).
% 2.38/1.96 thf(f535,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = (~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))))),
% 2.38/1.96 inference(equality_proxy_clausification,[status(thm)],[f513])).
% 2.38/1.96 thf(f513,plain,(
% 2.38/1.96 ($true = ((~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))) = (lower_191460856_ereal @ x0 @ f)))),
% 2.38/1.96 inference(boolean_simplification,[status(thm)],[f428])).
% 2.38/1.96 thf(f428,plain,(
% 2.38/1.96 ($true = (~ (~ ((~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))) = (lower_191460856_ereal @ x0 @ f)))))),
% 2.38/1.96 inference(cnf_transformation,[status(thm)],[f156])).
% 2.38/1.96 thf(f156,plain,(
% 2.38/1.96 ($true = (~ (~ ((~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))) = (lower_191460856_ereal @ x0 @ f)))))),
% 2.38/1.96 inference(fool_elimination,[status(thm)],[f155])).
% 2.38/1.96 thf(f155,plain,(
% 2.38/1.96 ~(~! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : (! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))) & (topolo1276428101open_a @ X1) & (member_a @ x0 @ X1))) != (lower_191460856_ereal @ x0 @ f))),
% 2.38/1.96 inference(rectify,[status(thm)],[f122])).
% 2.38/1.96 thf(f122,negated_conjecture,(
% 2.38/1.96 ~(~! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : (! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))) & (topolo1276428101open_a @ X1) & (member_a @ x0 @ X1))) != (lower_191460856_ereal @ x0 @ f))),
% 2.38/1.96 inference(negated_conjecture,[status(cth)],[f121])).
% 2.38/1.96 thf(f121,conjecture,(
% 2.38/1.96 (~! [X0 : extended_ereal] : ((ord_le2001149050_ereal @ X0 @ (f @ x0)) => ? [X1 : set_a] : (! [X2 : a] : ((member_a @ X2 @ X1) => (ord_le2001149050_ereal @ X0 @ (f @ X2))) & (topolo1276428101open_a @ X1) & (member_a @ x0 @ X1))) != (lower_191460856_ereal @ x0 @ f))),
% 2.38/1.96 file('/export/starexec/sandbox2/tmp/tmp.BbyRU8vfwF/DTF2THF_10757.p',conj_0)).
% 2.38/1.96 thf(f530,plain,(
% 2.38/1.96 ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ((f @ x0) = extended_MInfty) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $false)),
% 2.38/1.96 inference(backward_demodulation,[status(thm)],[f523,f475])).
% 2.38/1.96 thf(f523,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = $false) | ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty))) | ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1))))))))),
% 2.38/1.96 inference(equality_proxy_clausification,[status(thm)],[f521])).
% 2.38/1.96 thf(f521,plain,(
% 2.38/1.96 ((f @ x0) = (uminus1208298309_ereal @ extended_MInfty)) | ($true = (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))) & (topolo1276428101open_a @ Y1)))))))) | ($true = ((f @ x0) = (uminus1208298309_ereal @ (uminus1208298309_ereal @ extended_MInfty)))) | ((lower_191460856_ereal @ x0 @ f) = $false)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f519])).
% 2.38/1.96 thf(f688,plain,(
% 2.38/1.96 spl0_5 | ~spl0_6 | ~spl0_2),
% 2.38/1.96 inference(avatar_split_clause,[status(thm)],[f568,f559,f685,f681])).
% 2.38/1.96 thf(f568,plain,(
% 2.38/1.96 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $true) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ~spl0_2),
% 2.38/1.96 inference(trivial_inequality_removal,[status(thm)],[f565])).
% 2.38/1.96 thf(f565,plain,(
% 2.38/1.96 ($true = $false) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $true) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ~spl0_2),
% 2.38/1.96 inference(backward_demodulation,[status(thm)],[f528,f564])).
% 2.38/1.96 thf(f528,plain,(
% 2.38/1.96 ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))) & (topolo1276428101open_a @ Y1)) & (member_a @ x0 @ Y1))))))) = $true) | ((f @ x0) != (uminus1208298309_ereal @ extended_MInfty)) | ((lower_191460856_ereal @ x0 @ f) = $false)),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f526])).
% 2.38/1.96 thf(f562,plain,(
% 2.38/1.96 spl0_1 | spl0_2),
% 2.38/1.96 inference(avatar_split_clause,[status(thm)],[f538,f559,f555])).
% 2.38/1.96 thf(f538,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = $false) | ((!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2))))))))))) = $false)),
% 2.38/1.96 inference(not_proxy_clausification,[status(thm)],[f537])).
% 2.38/1.96 thf(f537,plain,(
% 2.38/1.96 ((lower_191460856_ereal @ x0 @ f) = $false) | ($true = (~ (!! @ extended_ereal @ (^[Y0 : extended_ereal]: ((ord_le2001149050_ereal @ Y0 @ (f @ x0)) => (?? @ set_a @ (^[Y1 : set_a]: (((member_a @ x0 @ Y1) & (topolo1276428101open_a @ Y1)) & (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) => (ord_le2001149050_ereal @ Y0 @ (f @ Y2)))))))))))))),
% 2.38/1.96 inference(binary_proxy_clausification,[status(thm)],[f535])).
% 2.38/1.96 % SZS output end Proof for DTF2THF_10757
% 2.38/1.96 % (11076)------------------------------
% 2.38/1.96 % (11076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.38/1.96 % (11076)Termination reason: Refutation
% 2.38/1.96
% 2.38/1.96 % (11076)Memory used [KB]: 6652
% 2.38/1.96 % (11076)Time elapsed: 0.104 s
% 2.38/1.96 % (11076)Instructions burned: 294 (million)
% 2.38/1.96 % (11076)------------------------------
% 2.38/1.96 % (11076)------------------------------
% 2.38/1.96 % (11021)Success in time 0.523 s
%------------------------------------------------------------------------------