%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP201^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 08:56:22 AM UTC 2026
% Result : Theorem 2.95s 1.82s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 23 unt; 0 typ; 8 def)
% Number of atoms : 341 ( 115 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1045 ( 78 ~; 71 |; 1 &; 874 @)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 173 ( 170 usr; 18 con; 0-5 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
variable: $tType ).
thf(type_def_6,type,
real: $tType ).
thf(type_def_8,type,
set_variable: $tType ).
thf(type_def_9,type,
denotational_interp: $tType ).
thf(type_def_10,type,
game: $tType ).
thf(type_def_11,type,
set_variable_real: $tType ).
thf(type_def_12,type,
produc1078154247n_game: $tType ).
thf(type_def_13,type,
produc2038871085e_real: $tType ).
thf(type_def_14,type,
produc1755325794riable: $tType ).
thf(type_def_15,type,
produc1794985442e_real: $tType ).
thf(type_def_16,type,
produc432717079riable: $tType ).
thf(type_def_17,type,
set_Pr166476775n_game: $tType ).
thf(type_def_18,type,
option_game: $tType ).
thf(type_def_19,type,
produc735959047riable: $tType ).
thf(type_def_20,type,
produc1418842292n_game: $tType ).
thf(func_def_0,type,
produc1418842292n_game: $tType ).
thf(func_def_1,type,
produc2038871085e_real: $tType ).
thf(func_def_2,type,
produc1794985442e_real: $tType ).
thf(func_def_3,type,
produc1755325794riable: $tType ).
thf(func_def_4,type,
set_Pr166476775n_game: $tType ).
thf(func_def_5,type,
produc1078154247n_game: $tType ).
thf(func_def_6,type,
produc735959047riable: $tType ).
thf(func_def_7,type,
produc432717079riable: $tType ).
thf(func_def_8,type,
set_variable_real: $tType ).
thf(func_def_9,type,
option_game: $tType ).
thf(func_def_10,type,
denotational_interp: $tType ).
thf(func_def_11,type,
set_variable: $tType ).
thf(func_def_12,type,
variable: $tType ).
thf(func_def_13,type,
game: $tType ).
thf(func_def_14,type,
real: $tType ).
thf(func_def_15,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_16,type,
denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
thf(func_def_17,type,
uminus970116630real_o: ( ( variable > real ) > $o ) > ( variable > real ) > $o ).
thf(func_def_18,type,
uminus679091071game_o: ( produc1078154247n_game > $o ) > produc1078154247n_game > $o ).
thf(func_def_19,type,
uminus1666842273able_o: ( variable > $o ) > variable > $o ).
thf(func_def_20,type,
uminus_uminus_o: $o > $o ).
thf(func_def_21,type,
uminus501400228e_real: produc2038871085e_real > produc2038871085e_real ).
thf(func_def_22,type,
uminus2115124697riable: produc1755325794riable > produc1755325794riable ).
thf(func_def_23,type,
uminus7300697e_real: produc1794985442e_real > produc1794985442e_real ).
thf(func_def_24,type,
uminus269410190riable: produc432717079riable > produc432717079riable ).
thf(func_def_25,type,
uminus430703407e_real: set_variable_real > set_variable_real ).
thf(func_def_26,type,
uminus2030647006n_game: set_Pr166476775n_game > set_Pr166476775n_game ).
thf(func_def_27,type,
uminus1851247844riable: set_variable > set_variable ).
thf(func_def_28,type,
sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
thf(func_def_29,type,
sup_sup_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_30,type,
none_game: option_game ).
thf(func_def_31,type,
the_game: option_game > game ).
thf(func_def_32,type,
ord_le1354144447real_o: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > $o ).
thf(func_def_33,type,
ord_le2134856704game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > $o ).
thf(func_def_34,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_35,type,
ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
thf(func_def_36,type,
ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o ).
thf(func_def_37,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_38,type,
produc1140431679riable: option_game > set_variable > produc735959047riable ).
thf(func_def_39,type,
produc86945893e_real: set_variable_real > set_variable_real > produc2038871085e_real ).
thf(func_def_40,type,
produc544095770riable: set_variable_real > set_variable > produc1755325794riable ).
thf(func_def_41,type,
produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
thf(func_def_42,type,
produc1400669210e_real: set_variable > set_variable_real > produc1794985442e_real ).
thf(func_def_43,type,
produc1766592463riable: set_variable > set_variable > produc432717079riable ).
thf(func_def_44,type,
produc884810027riable: produc735959047riable > option_game ).
thf(func_def_45,type,
produc702045265e_real: produc2038871085e_real > set_variable_real ).
thf(func_def_46,type,
produc944271878riable: produc1755325794riable > set_variable_real ).
thf(func_def_47,type,
produc893821739n_game: produc1078154247n_game > set_variable ).
thf(func_def_48,type,
produc1800845318e_real: produc1794985442e_real > set_variable ).
thf(func_def_49,type,
produc1300679611riable: produc432717079riable > set_variable ).
thf(func_def_50,type,
produc284475501riable: produc735959047riable > set_variable ).
thf(func_def_51,type,
produc220849299e_real: produc2038871085e_real > set_variable_real ).
thf(func_def_52,type,
produc1192298056riable: produc1755325794riable > set_variable ).
thf(func_def_53,type,
produc293487213n_game: produc1078154247n_game > option_game ).
thf(func_def_54,type,
produc2048871496e_real: produc1794985442e_real > set_variable_real ).
thf(func_def_55,type,
produc319712253riable: produc432717079riable > set_variable ).
thf(func_def_56,type,
produc345397471riable: produc735959047riable > produc1078154247n_game ).
thf(func_def_57,type,
produc354409183n_game: produc1078154247n_game > produc735959047riable ).
thf(func_def_58,type,
collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
thf(func_def_59,type,
collec1702522994n_game: ( produc1078154247n_game > $o ) > set_Pr166476775n_game ).
thf(func_def_60,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_61,type,
skip: game ).
thf(func_def_62,type,
choice: game > game > game ).
thf(func_def_63,type,
dual: game > game ).
thf(func_def_64,type,
loop: game > game ).
thf(func_def_65,type,
uSubst1484167963hoiceo: option_game > option_game > option_game ).
thf(func_def_66,type,
uSubst1916713664_Dualo: option_game > option_game ).
thf(func_def_67,type,
uSubst23177304_Loopo: option_game > option_game ).
thf(func_def_68,type,
uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
thf(func_def_69,type,
uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
thf(func_def_70,type,
member_variable_real: ( variable > real ) > set_variable_real > $o ).
thf(func_def_71,type,
member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o ).
thf(func_def_72,type,
member_variable: variable > set_variable > $o ).
thf(func_def_73,type,
i: denotational_interp ).
thf(func_def_74,type,
u: set_variable ).
thf(func_def_75,type,
ua: set_variable ).
thf(func_def_76,type,
xa: set_variable_real ).
thf(func_def_77,type,
alpha: game ).
thf(func_def_78,type,
nu: variable > real ).
thf(func_def_79,type,
nu2: variable > real ).
thf(func_def_80,type,
omega: variable > real ).
thf(func_def_81,type,
omega2: variable > real ).
thf(func_def_82,type,
sigma: produc1418842292n_game ).
thf(func_def_96,type,
sK0: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_97,type,
sK1: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_98,type,
sK2: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_99,type,
sK3: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_100,type,
sK4: produc1078154247n_game > set_variable ).
thf(func_def_101,type,
sK5: produc1078154247n_game > option_game ).
thf(func_def_102,type,
sK6: ( variable > $o ) > set_variable > variable ).
thf(func_def_103,type,
sK7: set_variable > ( variable > $o ) > variable ).
thf(func_def_104,type,
sK8: set_variable > ( variable > $o ) > set_variable > variable ).
thf(func_def_105,type,
sK9: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_106,type,
sK10: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_107,type,
sK11: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_108,type,
sK12: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_109,type,
sK13: ( set_variable > option_game > $o ) > set_variable ).
thf(func_def_110,type,
sK14: ( set_variable > option_game > $o ) > option_game ).
thf(func_def_111,type,
sK15: ( set_variable > set_variable ) > set_variable ).
thf(func_def_112,type,
sK16: ( set_variable > set_variable ) > set_variable ).
thf(func_def_113,type,
sK17: ( produc1078154247n_game > $o ) > option_game ).
thf(func_def_114,type,
sK18: ( produc1078154247n_game > $o ) > set_variable ).
thf(func_def_115,type,
sK19: ( set_variable > set_variable ) > set_variable ).
thf(func_def_116,type,
sK20: ( set_variable > set_variable ) > set_variable ).
thf(func_def_117,type,
sK21: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_118,type,
sK22: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_119,type,
sK23: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_120,type,
sK24: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_121,type,
sK25: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_122,type,
sK26: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_123,type,
sK27: ( option_game > set_variable > $o ) > option_game ).
thf(func_def_124,type,
sK28: ( option_game > set_variable > $o ) > set_variable ).
thf(func_def_125,type,
sK29: produc1078154247n_game > option_game > set_variable ).
thf(func_def_126,type,
sK30: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_127,type,
sK31: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_128,type,
sK32: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_129,type,
sK33: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_130,type,
sK34: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_131,type,
sK35: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_132,type,
sK36: ( set_variable_real > set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_133,type,
sK37: produc1078154247n_game > option_game ).
thf(func_def_134,type,
sK38: produc1078154247n_game > set_variable ).
thf(func_def_135,type,
sK39: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_136,type,
sK40: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_137,type,
sK41: ( set_variable > set_variable ) > set_variable ).
thf(func_def_138,type,
sK42: ( set_variable > set_variable ) > set_variable ).
thf(func_def_139,type,
sK43: ( variable > $o ) > set_variable > variable ).
thf(func_def_140,type,
sK44: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_141,type,
sK45: set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_142,type,
sK46: ( variable > $o ) > set_variable > set_variable > variable ).
thf(func_def_143,type,
sK47: ( variable > $o ) > set_variable > variable ).
thf(func_def_144,type,
sK48: ( variable > $o ) > set_variable > variable ).
thf(func_def_145,type,
sK49: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_146,type,
sK50: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_147,type,
sK51: set_variable > set_variable > variable ).
thf(func_def_148,type,
sK52: ( variable > $o ) > set_variable > ( variable > $o ) > variable ).
thf(func_def_149,type,
sK53: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_150,type,
sK54: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_151,type,
sK55: ( produc1078154247n_game > $o ) > option_game ).
thf(func_def_152,type,
sK56: ( produc1078154247n_game > $o ) > set_variable ).
thf(func_def_153,type,
sK57: set_Pr166476775n_game > set_Pr166476775n_game > set_variable ).
thf(func_def_154,type,
sK58: set_Pr166476775n_game > set_Pr166476775n_game > option_game ).
thf(func_def_155,type,
sK59: ( set_variable > $o ) > set_variable ).
thf(func_def_156,type,
sK60: ( set_variable > $o ) > set_variable ).
thf(func_def_157,type,
sK61: set_variable_real > set_variable_real > variable > real ).
thf(func_def_158,type,
sK62: set_variable_real > set_variable_real > set_variable_real > set_variable_real ).
thf(func_def_159,type,
sK63: set_variable_real > set_variable_real > set_variable_real > set_variable_real ).
thf(func_def_160,type,
sK64: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_161,type,
sK65: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_162,type,
sK66: ( set_variable_real > set_variable ) > set_variable_real ).
thf(func_def_163,type,
sK67: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_164,type,
sK68: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_165,type,
sK69: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_166,type,
sK70: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_167,type,
sK71: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_168,type,
sK72: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_169,type,
sK73: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_170,type,
sK74: ( set_variable_real > set_variable_real > $o ) > set_variable_real ).
thf(func_def_171,type,
sK75: ( set_variable_real > set_variable_real > $o ) > set_variable_real ).
thf(func_def_172,type,
sK76: ( set_variable > set_variable ) > set_variable ).
thf(func_def_173,type,
sK77: ( set_variable > set_variable ) > set_variable ).
thf(func_def_174,type,
sK78: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_175,type,
sK79: ( set_variable_real > $o ) > set_variable_real ).
thf(func_def_176,type,
sK80: ( set_variable_real > $o ) > set_variable_real ).
thf(func_def_177,type,
sK81: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_178,type,
sK82: set_variable > produc1078154247n_game > option_game ).
thf(func_def_179,type,
sK83: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_180,type,
sK84: ( set_variable > set_variable_real ) > set_variable ).
thf(func_def_181,type,
sK85: set_variable > set_variable > set_variable > set_variable ).
thf(func_def_182,type,
sK86: set_variable > set_variable > set_variable > set_variable ).
thf(func_def_183,type,
sK87: produc1418842292n_game > denotational_interp > game > set_variable > variable > real ).
thf(func_def_184,type,
sK88: produc1418842292n_game > denotational_interp > game > set_variable > set_variable_real ).
thf(func_def_185,type,
sK89: produc1418842292n_game > denotational_interp > game > set_variable > variable > real ).
thf(func_def_186,type,
sK90: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_187,type,
sK91: ( set_variable_real > set_variable_real ) > set_variable_real ).
thf(func_def_188,type,
sK92: ( ( variable > real ) > $o ) > set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_190,type,
ph94:
!>[X0: $tType] : X0 ).
thf(f3759,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1977,f1986,f2777,f2788,f2865,f3545,f3575,f3587,f3624,f3660,f3757]) ).
thf(f3757,plain,
( spl93_23
| ~ spl93_5 ),
inference(avatar_split_clause,[status(thm)],[f3742,f2018,f2755]) ).
thf(f2755,definition,
( spl93_23
<=> ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl93_23])],[avatar_definition]) ).
thf(f2018,definition,
( spl93_5
<=> ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl93_5])],[avatar_definition]) ).
thf(f3742,plain,
( ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_5 ),
inference(superposition,[status(thm)],[f1512,f2019]) ).
thf(f2019,plain,
( ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_5 ),
inference(avatar_component_clause,[status(thm)],[f2018]) ).
thf(f1512,plain,
! [X0: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062) ).
thf(f3660,plain,
( spl93_8
| spl93_7
| ~ spl93_3 ),
inference(avatar_split_clause,[status(thm)],[f3626,f1979,f2027,f2031]) ).
thf(f2031,definition,
( spl93_8
<=> ! [X0: set_variable] :
( ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) )
| ( $false
= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl93_8])],[avatar_definition]) ).
thf(f2027,definition,
( spl93_7
<=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
= none_game ) ),
introduced(definition,[new_symbols(naming,[spl93_7])],[avatar_definition]) ).
thf(f1979,definition,
( spl93_3
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl93_3])],[avatar_definition]) ).
thf(f3626,plain,
( ! [X0: set_variable] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
= none_game )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) )
| ( $false
= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) ) )
| ~ spl93_3 ),
inference(superposition,[status(thm)],[f1981,f1651]) ).
thf(f1651,plain,
! [X2: set_variable,X3: set_variable,X0: game,X1: produc1418842292n_game] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1167]) ).
thf(f1167,plain,
! [X0: game,X1: produc1418842292n_game,X2: set_variable,X3: set_variable] :
( ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
| ( ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f1166]) ).
thf(f1166,plain,
! [X0: game,X1: produc1418842292n_game,X2: set_variable,X3: set_variable] :
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f994]) ).
thf(f994,plain,
! [X0: game,X1: produc1418842292n_game,X2: set_variable,X3: set_variable] :
( ( none_game
!= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) ) )
=> ( ( none_game
!= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X3 @ X0 ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ X1 @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,axiom,
! [X10: game,X8: produc1418842292n_game,X11: set_variable,X9: set_variable] :
( ( none_game
!= ( produc293487213n_game @ ( uSubst516392814stappp @ X8 @ X9 @ X10 ) ) )
=> ( ( none_game
!= ( produc293487213n_game @ ( uSubst516392814stappp @ X8 @ X11 @ X10 ) ) )
=> ( ( produc293487213n_game @ ( uSubst516392814stappp @ X8 @ X9 @ X10 ) )
= ( produc293487213n_game @ ( uSubst516392814stappp @ X8 @ X11 @ X10 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_27_usubstappp__det) ).
thf(f1981,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $false )
| ~ spl93_3 ),
inference(avatar_component_clause,[status(thm)],[f1979]) ).
thf(f3624,plain,
( spl93_5
| spl93_1 ),
inference(avatar_split_clause,[status(thm)],[f3610,f1970,f2018]) ).
thf(f1970,definition,
( spl93_1
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl93_1])],[avatar_definition]) ).
thf(f3610,plain,
( ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| spl93_1 ),
inference(trivial_inequality_removal,[status(thm)],[f3606]) ).
thf(f3606,plain,
( ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ( $true != $true )
| spl93_1 ),
inference(superposition,[status(thm)],[f1971,f1563]) ).
thf(f1563,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
| ( $true
= ( member_variable_real @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1296]) ).
thf(f1296,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
| ( $true
= ( member_variable_real @ X0 @ X1 ) ) )
& ( ( $true
!= ( member_variable_real @ X0 @ X1 ) )
| ( $true
!= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f940]) ).
thf(f940,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
<=> ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f601]) ).
thf(f601,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
<=> ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f600]) ).
thf(f600,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) )
= ( ~ ( member_variable_real @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X2: variable > real,X3: set_variable_real] :
( ( member_variable_real @ X2 @ ( uminus430703407e_real @ X3 ) )
= ( ~ ( member_variable_real @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_13_Compl__iff) ).
thf(f1971,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= $true )
| spl93_1 ),
inference(avatar_component_clause,[status(thm)],[f1970]) ).
thf(f3587,plain,
( ~ spl93_23
| ~ spl93_2 ),
inference(avatar_split_clause,[status(thm)],[f3584,f1974,f2755]) ).
thf(f1974,definition,
( spl93_2
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl93_2])],[avatar_definition]) ).
thf(f3584,plain,
( ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_2 ),
inference(trivial_inequality_removal,[status(thm)],[f3582]) ).
thf(f3582,plain,
( ( $true != $true )
| ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_2 ),
inference(superposition,[status(thm)],[f1792,f1976]) ).
thf(f1976,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $true )
| ~ spl93_2 ),
inference(avatar_component_clause,[status(thm)],[f1974]) ).
thf(f1792,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
!= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
| ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1201]) ).
thf(f1201,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
!= ( member_variable_real @ X0 @ X1 ) )
| ( $true
!= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f901]) ).
thf(f901,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
=> ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f375]) ).
thf(f375,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
=> ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f374]) ).
thf(f374,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) )
=> ~ ( member_variable_real @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,axiom,
! [X2: variable > real,X3: set_variable_real] :
( ( member_variable_real @ X2 @ ( uminus430703407e_real @ X3 ) )
=> ~ ( member_variable_real @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_33_ComplD) ).
thf(f3575,plain,
( ~ spl93_23
| spl93_5 ),
inference(avatar_split_clause,[status(thm)],[f3574,f2018,f2755]) ).
thf(f3574,plain,
( ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| spl93_5 ),
inference(trivial_inequality_removal,[status(thm)],[f3573]) ).
thf(f3573,plain,
( ( $true != $true )
| ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| spl93_5 ),
inference(forward_demodulation,[status(thm)],[f3562,f1498]) ).
thf(f1498,plain,
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
= $true ),
inference(cnf_transformation,[status(thm)],[f745]) ).
thf(f745,plain,
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
= $true ),
inference(fool_elimination,[status(thm)],[f744]) ).
thf(f744,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_2_uv) ).
thf(f3562,plain,
( ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
!= $true )
| ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| spl93_5 ),
inference(superposition,[status(thm)],[f2020,f1872]) ).
thf(f1872,plain,
! [X0: set_variable_real] :
( ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) )
| ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1194]) ).
thf(f1194,plain,
! [X0: set_variable_real] :
( ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
!= $true )
| ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f695]) ).
thf(f695,plain,
! [X0: set_variable_real] :
( ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
= $true )
=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f694]) ).
thf(f694,plain,
! [X0: set_variable_real] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: set_variable_real] :
( ( denota1419872369iation @ nu2 @ omega2 @ ua )
=> ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X0 ) )
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_1_IH_092_060alpha_062) ).
thf(f2020,plain,
( ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| spl93_5 ),
inference(avatar_component_clause,[status(thm)],[f2018]) ).
thf(f3545,plain,
( ~ spl93_7
| ~ spl93_7 ),
inference(avatar_split_clause,[status(thm)],[f3506,f2027,f2027]) ).
thf(f3506,plain,
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
!= none_game )
| ~ spl93_7 ),
inference(superposition,[status(thm)],[f1813,f3505]) ).
thf(f3505,plain,
( ( ( uSubst516392814stappp @ sigma @ ua @ alpha )
= ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
| ~ spl93_7 ),
inference(forward_demodulation,[status(thm)],[f2859,f2840]) ).
thf(f2840,plain,
( ( ( uSubst516392814stappp @ sigma @ ua @ alpha )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ none_game ) )
| ~ spl93_7 ),
inference(superposition,[status(thm)],[f1787,f2029]) ).
thf(f2029,plain,
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
= none_game )
| ~ spl93_7 ),
inference(avatar_component_clause,[status(thm)],[f2027]) ).
thf(f1787,plain,
! [X0: produc1078154247n_game] :
( ( produc1149443391n_game @ ( produc893821739n_game @ X0 ) @ ( produc293487213n_game @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f897]) ).
thf(f897,plain,
! [X0: produc1078154247n_game] :
( ( produc1149443391n_game @ ( produc893821739n_game @ X0 ) @ ( produc293487213n_game @ X0 ) )
= X0 ),
inference(rectify,[status(thm)],[f154]) ).
thf(f154,axiom,
! [X43: produc1078154247n_game] :
( ( produc1149443391n_game @ ( produc893821739n_game @ X43 ) @ ( produc293487213n_game @ X43 ) )
= X43 ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_153_prod_Oexhaust__sel) ).
thf(f2859,plain,
( ( ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ none_game ) )
| ~ spl93_7 ),
inference(forward_demodulation,[status(thm)],[f2828,f1455]) ).
thf(f1455,plain,
( none_game
= ( uSubst1916713664_Dualo @ none_game ) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
thf(f173,axiom,
( none_game
= ( uSubst1916713664_Dualo @ none_game ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_172_Dualo_Osimps_I2_J) ).
thf(f2828,plain,
( ( ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ ( uSubst1916713664_Dualo @ none_game ) ) )
| ~ spl93_7 ),
inference(superposition,[status(thm)],[f1450,f2029]) ).
thf(f1450,plain,
! [X2: game,X0: produc1418842292n_game,X1: set_variable] :
( ( uSubst516392814stappp @ X0 @ X1 @ ( dual @ X2 ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ X0 @ X1 @ X2 ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ X0 @ X1 @ X2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f949]) ).
thf(f949,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: game] :
( ( uSubst516392814stappp @ X0 @ X1 @ ( dual @ X2 ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ X0 @ X1 @ X2 ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ X0 @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f160]) ).
thf(f160,axiom,
! [X8: produc1418842292n_game,X9: set_variable,X10: game] :
( ( uSubst516392814stappp @ X8 @ X9 @ ( dual @ X10 ) )
= ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ X8 @ X9 @ X10 ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ X8 @ X9 @ X10 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_159_usubstappp__dual) ).
thf(f1813,plain,
( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= none_game ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
!= none_game ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_7_def) ).
thf(f2865,plain,
( spl93_23
| ~ spl93_4 ),
inference(avatar_split_clause,[status(thm)],[f2752,f1983,f2755]) ).
thf(f1983,definition,
( spl93_4
<=> ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl93_4])],[avatar_definition]) ).
thf(f2752,plain,
( ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_4 ),
inference(trivial_inequality_removal,[status(thm)],[f2731]) ).
thf(f2731,plain,
( ( $true = $false )
| ( $true
= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_4 ),
inference(superposition,[status(thm)],[f1985,f1563]) ).
thf(f1985,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $false )
| ~ spl93_4 ),
inference(avatar_component_clause,[status(thm)],[f1983]) ).
thf(f2788,plain,
( spl93_7
| ~ spl93_1
| ~ spl93_8 ),
inference(avatar_split_clause,[status(thm)],[f2772,f2031,f1970,f2027]) ).
thf(f2772,plain,
( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
= none_game )
| ~ spl93_1
| ~ spl93_8 ),
inference(trivial_inequality_removal,[status(thm)],[f2768]) ).
thf(f2768,plain,
( ( $true = $false )
| ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
= none_game )
| ~ spl93_1
| ~ spl93_8 ),
inference(superposition,[status(thm)],[f1972,f2032]) ).
thf(f2032,plain,
( ! [X0: set_variable] :
( ( $false
= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) ) )
| ( none_game
= ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ X0 @ alpha ) ) ) )
| ~ spl93_8 ),
inference(avatar_component_clause,[status(thm)],[f2031]) ).
thf(f1972,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $true )
| ~ spl93_1 ),
inference(avatar_component_clause,[status(thm)],[f1970]) ).
thf(f2777,plain,
( ~ spl93_5
| ~ spl93_1 ),
inference(avatar_split_clause,[status(thm)],[f2774,f1970,f2018]) ).
thf(f2774,plain,
( ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ~ spl93_1 ),
inference(trivial_inequality_removal,[status(thm)],[f2770]) ).
thf(f2770,plain,
( ( $true
!= ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ( $true != $true )
| ~ spl93_1 ),
inference(superposition,[status(thm)],[f1562,f1972]) ).
thf(f1562,plain,
! [X0: variable > real,X1: set_variable_real] :
( ( $true
!= ( member_variable_real @ X0 @ ( uminus430703407e_real @ X1 ) ) )
| ( $true
!= ( member_variable_real @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1296]) ).
thf(f1986,plain,
( spl93_3
| spl93_4 ),
inference(avatar_split_clause,[status(thm)],[f1968,f1983,f1979]) ).
thf(f1968,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $false )
| ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1444]) ).
thf(f1444,plain,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f985]) ).
thf(f985,plain,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(flattening,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
!= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',conj_0) ).
thf(f1977,plain,
( spl93_1
| spl93_2 ),
inference(avatar_split_clause,[status(thm)],[f1967,f1974,f1970]) ).
thf(f1967,plain,
( ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) )
= $true )
| ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP201^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.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 08:30:19 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP201^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer USubst problem prob_1580__6355392_1
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des21]
% 0.30/0.45 % Names : USubst/prob_1580__6355392_1 [Des21]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 438 ( 187 unt; 83 typ; 0 def)
% 0.30/0.45 % Number of atoms : 872 ( 335 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 6 ( 2 avg)
% 0.30/0.45 % Number of connectives : 2594 ( 63 ~; 1 |; 42 &;2168 @)
% 0.30/0.45 % ( 0 <=>; 320 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 19 ( 6 avg)
% 0.30/0.45 % Number of types : 16 ( 15 usr)
% 0.30/0.45 % Number of type conns : 268 ( 268 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 70 ( 68 usr; 9 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 972 ( 142 ^; 819 !; 11 ?; 972 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:17.179
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (15)
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.30/0.45 produc1418842292n_game: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/0.45 produc2038871085e_real: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/0.45 produc1794985442e_real: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/0.45 produc1755325794riable: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/0.45 set_Pr166476775n_game: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/0.45 produc1078154247n_game: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/0.45 produc735959047riable: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/0.45 produc432717079riable: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 set_variable_real: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/0.45 option_game: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.30/0.45 denotational_interp: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 set_variable: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Syntax__Ovariable,type,
% 0.30/0.45 variable: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Syntax__Ogame,type,
% 0.30/0.45 game: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Real__Oreal,type,
% 0.30/0.45 real: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (68)
% 0.30/0.45 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.30/0.45 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Denotational__Semantics_Ogame__sem,type,
% 0.30/0.45 denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 0.30/0.45 uminus970116630real_o: ( ( variable > real ) > $o ) > ( variable > real ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J,type,
% 0.30/0.45 uminus679091071game_o: ( produc1078154247n_game > $o ) > produc1078154247n_game > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.30/0.45 uminus1666842273able_o: ( variable > $o ) > variable > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001_Eo,type,
% 0.30/0.45 uminus_uminus_o: $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/0.45 uminus501400228e_real: produc2038871085e_real > produc2038871085e_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/0.45 uminus2115124697riable: produc1755325794riable > produc1755325794riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/0.45 uminus7300697e_real: produc1794985442e_real > produc1794985442e_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/0.45 uminus269410190riable: produc432717079riable > produc432717079riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 uminus430703407e_real: set_variable_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/0.45 uminus2030647006n_game: set_Pr166476775n_game > set_Pr166476775n_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 uminus1851247844riable: set_variable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 sup_sup_set_variable: set_variable > set_variable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.30/0.45 none_game: option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.30/0.45 the_game: option_game > game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 0.30/0.45 ord_le1354144447real_o: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
% 0.30/0.45 ord_le2134856704game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.30/0.45 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/0.45 ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc1140431679riable: option_game > set_variable > produc735959047riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc86945893e_real: set_variable_real > set_variable_real > produc2038871085e_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc544095770riable: set_variable_real > set_variable > produc1755325794riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/0.45 produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc1400669210e_real: set_variable > set_variable_real > produc1794985442e_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc1766592463riable: set_variable > set_variable > produc432717079riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc884810027riable: produc735959047riable > option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc702045265e_real: produc2038871085e_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc944271878riable: produc1755325794riable > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/0.45 produc893821739n_game: produc1078154247n_game > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc1800845318e_real: produc1794985442e_real > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc1300679611riable: produc432717079riable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc284475501riable: produc735959047riable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc220849299e_real: produc2038871085e_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc1192298056riable: produc1755325794riable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/0.45 produc293487213n_game: produc1078154247n_game > option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/0.45 produc2048871496e_real: produc1794985442e_real > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc319712253riable: produc432717079riable > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/0.45 produc345397471riable: produc735959047riable > produc1078154247n_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/0.45 produc354409183n_game: produc1078154247n_game > produc735959047riable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Set_OCollect_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.30/0.45 collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/0.45 collec1702522994n_game: ( produc1078154247n_game > $o ) > set_Pr166476775n_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.30/0.45 collect_variable: ( variable > $o ) > set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_OSkip,type,
% 0.30/0.45 skip: game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Ogame_OChoice,type,
% 0.30/0.45 choice: game > game > game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Ogame_ODual,type,
% 0.30/0.45 dual: game > game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax_Ogame_OLoop,type,
% 0.30/0.45 loop: game > game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OChoiceo,type,
% 0.30/0.45 uSubst1484167963hoiceo: option_game > option_game > option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODualo,type,
% 0.30/0.45 uSubst1916713664_Dualo: option_game > option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OLoopo,type,
% 0.30/0.45 uSubst23177304_Loopo: option_game > option_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Oadjoint,type,
% 0.30/0.45 uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappp,type,
% 0.30/0.45 uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_member_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.30/0.45 member_variable_real: ( variable > real ) > set_variable_real > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/0.45 member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.30/0.45 member_variable: variable > set_variable > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_I,type,
% 0.30/0.45 i: denotational_interp ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_U,type,
% 0.30/0.45 u: set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_Ua____,type,
% 0.30/0.45 ua: set_variable ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_Xa____,type,
% 0.30/0.45 xa: set_variable_real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060alpha_062_H_H____,type,
% 0.30/0.45 alpha: game ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060nu_062,type,
% 0.30/0.45 nu: variable > real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060nu_062_H____,type,
% 0.30/0.45 nu2: variable > real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060omega_062,type,
% 0.30/0.45 omega: variable > real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060omega_062_H____,type,
% 0.30/0.45 omega2: variable > real ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.30/0.45 sigma: produc1418842292n_game ).
% 0.30/0.45
% 0.30/0.45 % Relevant facts (354)
% 0.30/0.45 thf(fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,axiom,
% 0.30/0.45 ! [X: set_variable_real] :
% 0.30/0.45 ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/0.45 = ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % \<open>\<And>X. (\<nu> \<in> game_sem I (the (snd (usubstappp \<sigma> U \<alpha>))) X) = (\<nu> \<in> game_sem (USubst_Mirabelle_vidvnmlwwz.adjoint \<sigma> I \<omega>) \<alpha> X)\<close>
% 0.30/0.45 thf(fact_1_IH_092_060alpha_062,axiom,
% 0.30/0.45 ! [X: set_variable_real] :
% 0.30/0.45 ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
% 0.30/0.45 => ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/0.45 = ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % IH\<alpha>
% 0.30/0.45 thf(fact_2_uv,axiom,
% 0.30/0.45 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.30/0.45
% 0.30/0.45 % uv
% 0.30/0.45 thf(fact_3_snd__uminus,axiom,
% 0.30/0.45 ! [X2: produc432717079riable] :
% 0.30/0.45 ( ( produc319712253riable @ ( uminus269410190riable @ X2 ) )
% 0.30/0.45 = ( uminus1851247844riable @ ( produc319712253riable @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % snd_uminus
% 0.30/0.45 thf(fact_4_snd__uminus,axiom,
% 0.30/0.45 ! [X2: produc1794985442e_real] :
% 0.30/0.45 ( ( produc2048871496e_real @ ( uminus7300697e_real @ X2 ) )
% 0.30/0.45 = ( uminus430703407e_real @ ( produc2048871496e_real @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % snd_uminus
% 0.30/0.45 thf(fact_5_snd__uminus,axiom,
% 0.30/0.45 ! [X2: produc1755325794riable] :
% 0.30/0.45 ( ( produc1192298056riable @ ( uminus2115124697riable @ X2 ) )
% 0.30/0.45 = ( uminus1851247844riable @ ( produc1192298056riable @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % snd_uminus
% 0.30/0.45 thf(fact_6_snd__uminus,axiom,
% 0.30/0.45 ! [X2: produc2038871085e_real] :
% 0.30/0.45 ( ( produc220849299e_real @ ( uminus501400228e_real @ X2 ) )
% 0.30/0.45 = ( uminus430703407e_real @ ( produc220849299e_real @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % snd_uminus
% 0.30/0.45 thf(fact_7_def,axiom,
% 0.30/0.45 ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
% 0.30/0.45 != none_game ) ).
% 0.30/0.45
% 0.30/0.45 % def
% 0.30/0.45 thf(fact_8_ComplI,axiom,
% 0.30/0.45 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/0.45 ( ~ ( member171223600n_game @ C @ A )
% 0.30/0.45 => ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplI
% 0.30/0.45 thf(fact_9_ComplI,axiom,
% 0.30/0.45 ! [C: variable,A: set_variable] :
% 0.30/0.45 ( ~ ( member_variable @ C @ A )
% 0.30/0.45 => ( member_variable @ C @ ( uminus1851247844riable @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplI
% 0.30/0.45 thf(fact_10_ComplI,axiom,
% 0.30/0.45 ! [C: variable > real,A: set_variable_real] :
% 0.30/0.45 ( ~ ( member_variable_real @ C @ A )
% 0.30/0.45 => ( member_variable_real @ C @ ( uminus430703407e_real @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplI
% 0.30/0.45 thf(fact_11_Compl__iff,axiom,
% 0.30/0.45 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/0.45 ( ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) )
% 0.30/0.45 = ( ~ ( member171223600n_game @ C @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Compl_iff
% 0.30/0.45 thf(fact_12_Compl__iff,axiom,
% 0.30/0.45 ! [C: variable,A: set_variable] :
% 0.30/0.45 ( ( member_variable @ C @ ( uminus1851247844riable @ A ) )
% 0.30/0.45 = ( ~ ( member_variable @ C @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Compl_iff
% 0.30/0.45 thf(fact_13_Compl__iff,axiom,
% 0.30/0.45 ! [C: variable > real,A: set_variable_real] :
% 0.30/0.45 ( ( member_variable_real @ C @ ( uminus430703407e_real @ A ) )
% 0.30/0.45 = ( ~ ( member_variable_real @ C @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Compl_iff
% 0.30/0.45 thf(fact_14_Compl__eq__Compl__iff,axiom,
% 0.30/0.45 ! [A: set_variable,B: set_variable] :
% 0.30/0.45 ( ( ( uminus1851247844riable @ A )
% 0.30/0.45 = ( uminus1851247844riable @ B ) )
% 0.30/0.45 = ( A = B ) ) ).
% 0.30/0.45
% 0.30/0.45 % Compl_eq_Compl_iff
% 0.30/0.45 thf(fact_15_Compl__eq__Compl__iff,axiom,
% 0.30/0.45 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.45 ( ( ( uminus430703407e_real @ A )
% 0.30/0.45 = ( uminus430703407e_real @ B ) )
% 0.30/0.45 = ( A = B ) ) ).
% 0.30/0.45
% 0.30/0.45 % Compl_eq_Compl_iff
% 0.30/0.45 thf(fact_16_uminus__apply,axiom,
% 0.30/0.45 ( uminus1666842273able_o
% 0.30/0.45 = ( ^ [A2: variable > $o,X3: variable] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % uminus_apply
% 0.30/0.45 thf(fact_17_uminus__apply,axiom,
% 0.30/0.45 ( uminus970116630real_o
% 0.30/0.45 = ( ^ [A2: ( variable > real ) > $o,X3: variable > real] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % uminus_apply
% 0.30/0.45 thf(fact_18_double__compl,axiom,
% 0.30/0.45 ! [X2: variable > $o] :
% 0.30/0.45 ( ( uminus1666842273able_o @ ( uminus1666842273able_o @ X2 ) )
% 0.30/0.45 = X2 ) ).
% 0.30/0.45
% 0.30/0.45 % double_compl
% 0.30/0.45 thf(fact_19_double__compl,axiom,
% 0.30/0.45 ! [X2: ( variable > real ) > $o] :
% 0.30/0.45 ( ( uminus970116630real_o @ ( uminus970116630real_o @ X2 ) )
% 0.30/0.45 = X2 ) ).
% 0.30/0.45
% 0.30/0.45 % double_compl
% 0.30/0.45 thf(fact_20_double__compl,axiom,
% 0.30/0.45 ! [X2: set_variable_real] :
% 0.30/0.45 ( ( uminus430703407e_real @ ( uminus430703407e_real @ X2 ) )
% 0.30/0.45 = X2 ) ).
% 0.30/0.45
% 0.30/0.45 % double_compl
% 0.30/0.45 thf(fact_21_double__compl,axiom,
% 0.30/0.45 ! [X2: set_variable] :
% 0.30/0.45 ( ( uminus1851247844riable @ ( uminus1851247844riable @ X2 ) )
% 0.30/0.45 = X2 ) ).
% 0.30/0.45
% 0.30/0.45 % double_compl
% 0.30/0.45 thf(fact_22_vaouter,axiom,
% 0.30/0.45 denota1419872369iation @ nu @ omega @ u ).
% 0.30/0.45
% 0.30/0.45 % vaouter
% 0.30/0.45 thf(fact_23_compl__eq__compl__iff,axiom,
% 0.30/0.45 ! [X2: variable > $o,Y: variable > $o] :
% 0.30/0.45 ( ( ( uminus1666842273able_o @ X2 )
% 0.30/0.45 = ( uminus1666842273able_o @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_eq_compl_iff
% 0.30/0.45 thf(fact_24_compl__eq__compl__iff,axiom,
% 0.30/0.45 ! [X2: ( variable > real ) > $o,Y: ( variable > real ) > $o] :
% 0.30/0.45 ( ( ( uminus970116630real_o @ X2 )
% 0.30/0.45 = ( uminus970116630real_o @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_eq_compl_iff
% 0.30/0.45 thf(fact_25_compl__eq__compl__iff,axiom,
% 0.30/0.45 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.45 ( ( ( uminus430703407e_real @ X2 )
% 0.30/0.45 = ( uminus430703407e_real @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_eq_compl_iff
% 0.30/0.45 thf(fact_26_compl__eq__compl__iff,axiom,
% 0.30/0.45 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.45 ( ( ( uminus1851247844riable @ X2 )
% 0.30/0.45 = ( uminus1851247844riable @ Y ) )
% 0.30/0.45 = ( X2 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 % compl_eq_compl_iff
% 0.30/0.45 thf(fact_27_usubstappp__det,axiom,
% 0.30/0.45 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,V: set_variable] :
% 0.30/0.45 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.45 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % usubstappp_det
% 0.30/0.45 thf(fact_28_fun__Compl__def,axiom,
% 0.30/0.45 ( uminus1666842273able_o
% 0.30/0.45 = ( ^ [A2: variable > $o,X3: variable] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % fun_Compl_def
% 0.30/0.45 thf(fact_29_fun__Compl__def,axiom,
% 0.30/0.45 ( uminus970116630real_o
% 0.30/0.45 = ( ^ [A2: ( variable > real ) > $o,X3: variable > real] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % fun_Compl_def
% 0.30/0.45 thf(fact_30_double__complement,axiom,
% 0.30/0.45 ! [A: set_variable_real] :
% 0.30/0.45 ( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
% 0.30/0.45 = A ) ).
% 0.30/0.45
% 0.30/0.45 % double_complement
% 0.30/0.45 thf(fact_31_double__complement,axiom,
% 0.30/0.45 ! [A: set_variable] :
% 0.30/0.45 ( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
% 0.30/0.45 = A ) ).
% 0.30/0.45
% 0.30/0.45 % double_complement
% 0.30/0.45 thf(fact_32_ComplD,axiom,
% 0.30/0.45 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/0.45 ( ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) )
% 0.30/0.45 => ~ ( member171223600n_game @ C @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplD
% 0.30/0.45 thf(fact_33_ComplD,axiom,
% 0.30/0.45 ! [C: variable > real,A: set_variable_real] :
% 0.30/0.45 ( ( member_variable_real @ C @ ( uminus430703407e_real @ A ) )
% 0.30/0.45 => ~ ( member_variable_real @ C @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplD
% 0.30/0.45 thf(fact_34_ComplD,axiom,
% 0.30/0.45 ! [C: variable,A: set_variable] :
% 0.30/0.45 ( ( member_variable @ C @ ( uminus1851247844riable @ A ) )
% 0.30/0.45 => ~ ( member_variable @ C @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 % ComplD
% 0.30/0.45 thf(fact_35_game__sem_Osimps_I7_J,axiom,
% 0.30/0.45 ! [I: denotational_interp,Alpha: game] :
% 0.30/0.45 ( ( denota1245701238me_sem @ I @ ( dual @ Alpha ) )
% 0.30/0.45 = ( ^ [X4: set_variable_real] : ( uminus430703407e_real @ ( denota1245701238me_sem @ I @ Alpha @ ( uminus430703407e_real @ X4 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % game_sem.simps(7)
% 0.30/0.45 thf(fact_36_Dual_OIH,axiom,
% 0.30/0.45 ! [Nu: variable > real,Omega: variable > real,X: set_variable_real] :
% 0.30/0.45 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( denota1419872369iation @ Nu @ Omega @ ua )
% 0.30/0.45 => ( ( member_variable_real @ Nu @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/0.45 = ( member_variable_real @ Nu @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ Omega ) @ alpha @ X ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Dual.IH
% 0.30/0.45 thf(fact_37_game_Oinject_I7_J,axiom,
% 0.30/0.45 ! [X7: game,Y7: game] :
% 0.30/0.45 ( ( ( dual @ X7 )
% 0.30/0.45 = ( dual @ Y7 ) )
% 0.30/0.45 = ( X7 = Y7 ) ) ).
% 0.30/0.45
% 0.30/0.45 % game.inject(7)
% 0.30/0.45 thf(fact_38_Dual_Oprems_I2_J,axiom,
% 0.30/0.45 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.30/0.45
% 0.30/0.45 % Dual.prems(2)
% 0.30/0.45 thf(fact_39_option_Oexpand,axiom,
% 0.30/0.45 ! [Option: option_game,Option2: option_game] :
% 0.30/0.45 ( ( ( Option = none_game )
% 0.30/0.45 = ( Option2 = none_game ) )
% 0.30/0.45 => ( ( ( Option != none_game )
% 0.30/0.45 => ( ( Option2 != none_game )
% 0.30/0.45 => ( ( the_game @ Option )
% 0.30/0.45 = ( the_game @ Option2 ) ) ) )
% 0.30/0.45 => ( Option = Option2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % option.expand
% 0.30/0.45 thf(fact_40_usubst__game__loop,axiom,
% 0.30/0.45 ! [Nu: variable > real,Omega: variable > real,U: set_variable,Sigma: produc1418842292n_game,Alpha: game,I: denotational_interp,X: set_variable_real] :
% 0.30/0.45 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 0.30/0.45 => ( ! [Nu2: variable > real,Omega2: variable > real,X5: set_variable_real] :
% 0.30/0.45 ( ( denota1419872369iation @ Nu2 @ Omega2 @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) )
% 0.30/0.45 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( member_variable_real @ Nu2 @ ( denota1245701238me_sem @ I @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) @ X5 ) )
% 0.30/0.45 = ( member_variable_real @ Nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ Sigma @ I @ Omega2 ) @ Alpha @ X5 ) ) ) ) )
% 0.30/0.45 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( member_variable_real @ Nu @ ( denota1245701238me_sem @ I @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) ) ) @ X ) )
% 0.30/0.45 = ( member_variable_real @ Nu @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ Sigma @ I @ Omega ) @ ( loop @ Alpha ) @ X ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % usubst_game_loop
% 0.30/0.45 thf(fact_41_Uvariation__def,axiom,
% 0.30/0.45 ( denota1419872369iation
% 0.30/0.45 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 0.30/0.45 ! [I2: variable] :
% 0.30/0.45 ( ~ ( member_variable @ I2 @ U2 )
% 0.30/0.45 => ( ( Nu3 @ I2 )
% 0.30/0.45 = ( Nu4 @ I2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Uvariation_def
% 0.30/0.45 thf(fact_42_Uvariation__sym,axiom,
% 0.30/0.45 ( denota1419872369iation
% 0.30/0.45 = ( ^ [Omega3: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % Uvariation_sym
% 0.30/0.45 thf(fact_43_Uvariation__refl,axiom,
% 0.30/0.45 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.30/0.45
% 0.30/0.45 % Uvariation_refl
% 0.30/0.45 thf(fact_44_Uvariation__sym__rel,axiom,
% 0.30/0.45 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 0.30/0.45 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/0.45 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.30/0.45
% 0.30/0.45 % Uvariation_sym_rel
% 0.30/0.45 thf(fact_45_usubstappp__choice__conv,axiom,
% 0.30/0.45 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.30/0.45 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.45 != none_game )
% 0.30/0.45 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) )
% 0.30/0.45 != none_game ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % usubstappp_choice_conv
% 0.30/0.45 thf(fact_46_game_Oinject_I6_J,axiom,
% 0.30/0.45 ! [X6: game,Y6: game] :
% 0.30/0.45 ( ( ( loop @ X6 )
% 0.30/0.45 = ( loop @ Y6 ) )
% 0.30/0.45 = ( X6 = Y6 ) ) ).
% 0.30/0.45
% 0.30/0.45 % game.inject(6)
% 0.30/0.45 thf(fact_47_game_Oinject_I4_J,axiom,
% 0.30/0.45 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 0.30/0.45 ( ( ( choice @ X41 @ X42 )
% 0.30/0.45 = ( choice @ Y41 @ Y42 ) )
% 0.30/0.45 = ( ( X41 = Y41 )
% 0.30/0.45 & ( X42 = Y42 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % game.inject(4)
% 0.30/0.45 thf(fact_48_fst__uminus,axiom,
% 0.30/0.45 ! [X2: produc432717079riable] :
% 0.30/0.45 ( ( produc1300679611riable @ ( uminus269410190riable @ X2 ) )
% 0.30/0.45 = ( uminus1851247844riable @ ( produc1300679611riable @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % fst_uminus
% 0.30/0.45 thf(fact_49_fst__uminus,axiom,
% 0.30/0.45 ! [X2: produc1794985442e_real] :
% 0.30/0.46 ( ( produc1800845318e_real @ ( uminus7300697e_real @ X2 ) )
% 0.30/0.46 = ( uminus1851247844riable @ ( produc1800845318e_real @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_uminus
% 0.30/0.46 thf(fact_50_fst__uminus,axiom,
% 0.30/0.46 ! [X2: produc1755325794riable] :
% 0.30/0.46 ( ( produc944271878riable @ ( uminus2115124697riable @ X2 ) )
% 0.30/0.46 = ( uminus430703407e_real @ ( produc944271878riable @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_uminus
% 0.30/0.46 thf(fact_51_fst__uminus,axiom,
% 0.30/0.46 ! [X2: produc2038871085e_real] :
% 0.30/0.46 ( ( produc702045265e_real @ ( uminus501400228e_real @ X2 ) )
% 0.30/0.46 = ( uminus430703407e_real @ ( produc702045265e_real @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_uminus
% 0.30/0.46 thf(fact_52_Uvariation__univ,axiom,
% 0.30/0.46 ! [Nu: variable > real,Nu5: variable > real] :
% 0.30/0.46 ( denota1419872369iation @ Nu @ Nu5
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] : $true ) ) ).
% 0.30/0.46
% 0.30/0.46 % Uvariation_univ
% 0.30/0.46 thf(fact_53_game_Odistinct_I39_J,axiom,
% 0.30/0.46 ! [X41: game,X42: game,X6: game] :
% 0.30/0.46 ( ( choice @ X41 @ X42 )
% 0.30/0.46 != ( loop @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % game.distinct(39)
% 0.30/0.46 thf(fact_54_uminus__set__def,axiom,
% 0.30/0.46 ( uminus2030647006n_game
% 0.30/0.46 = ( ^ [A2: set_Pr166476775n_game] :
% 0.30/0.46 ( collec1702522994n_game
% 0.30/0.46 @ ( uminus679091071game_o
% 0.30/0.46 @ ^ [X3: produc1078154247n_game] : ( member171223600n_game @ X3 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_set_def
% 0.30/0.46 thf(fact_55_uminus__set__def,axiom,
% 0.30/0.46 ( uminus430703407e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real] :
% 0.30/0.46 ( collec633296133e_real
% 0.30/0.46 @ ( uminus970116630real_o
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_set_def
% 0.30/0.46 thf(fact_56_uminus__set__def,axiom,
% 0.30/0.46 ( uminus1851247844riable
% 0.30/0.46 = ( ^ [A2: set_variable] :
% 0.30/0.46 ( collect_variable
% 0.30/0.46 @ ( uminus1666842273able_o
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_set_def
% 0.30/0.46 thf(fact_57_Collect__neg__eq,axiom,
% 0.30/0.46 ! [P: ( variable > real ) > $o] :
% 0.30/0.46 ( ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ~ ( P @ X3 ) )
% 0.30/0.46 = ( uminus430703407e_real @ ( collec633296133e_real @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_neg_eq
% 0.30/0.46 thf(fact_58_Collect__neg__eq,axiom,
% 0.30/0.46 ! [P: variable > $o] :
% 0.30/0.46 ( ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ~ ( P @ X3 ) )
% 0.30/0.46 = ( uminus1851247844riable @ ( collect_variable @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_neg_eq
% 0.30/0.46 thf(fact_59_Compl__eq,axiom,
% 0.30/0.46 ( uminus2030647006n_game
% 0.30/0.46 = ( ^ [A2: set_Pr166476775n_game] :
% 0.30/0.46 ( collec1702522994n_game
% 0.30/0.46 @ ^ [X3: produc1078154247n_game] :
% 0.30/0.46 ~ ( member171223600n_game @ X3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_eq
% 0.30/0.46 thf(fact_60_Compl__eq,axiom,
% 0.30/0.46 ( uminus430703407e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real] :
% 0.30/0.46 ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ~ ( member_variable_real @ X3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_eq
% 0.30/0.46 thf(fact_61_Compl__eq,axiom,
% 0.30/0.46 ( uminus1851247844riable
% 0.30/0.46 = ( ^ [A2: set_variable] :
% 0.30/0.46 ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ~ ( member_variable @ X3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_eq
% 0.30/0.46 thf(fact_62_game_Odistinct_I51_J,axiom,
% 0.30/0.46 ! [X6: game,X7: game] :
% 0.30/0.46 ( ( loop @ X6 )
% 0.30/0.46 != ( dual @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % game.distinct(51)
% 0.30/0.46 thf(fact_63_game_Odistinct_I41_J,axiom,
% 0.30/0.46 ! [X41: game,X42: game,X7: game] :
% 0.30/0.46 ( ( choice @ X41 @ X42 )
% 0.30/0.46 != ( dual @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % game.distinct(41)
% 0.30/0.46 thf(fact_64_usubstappp__loop__conv,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/0.46 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.30/0.46 != none_game )
% 0.30/0.46 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.46 != none_game )
% 0.30/0.46 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.30/0.46 != none_game ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_loop_conv
% 0.30/0.46 thf(fact_65_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A3: produc1078154247n_game,P: produc1078154247n_game > $o] :
% 0.30/0.46 ( ( member171223600n_game @ A3 @ ( collec1702522994n_game @ P ) )
% 0.30/0.46 = ( P @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_66_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A3: variable > real,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ( member_variable_real @ A3 @ ( collec633296133e_real @ P ) )
% 0.30/0.46 = ( P @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_67_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A3: variable,P: variable > $o] :
% 0.30/0.46 ( ( member_variable @ A3 @ ( collect_variable @ P ) )
% 0.30/0.46 = ( P @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_68_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Pr166476775n_game] :
% 0.30/0.46 ( ( collec1702522994n_game
% 0.30/0.46 @ ^ [X3: produc1078154247n_game] : ( member171223600n_game @ X3 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_69_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_variable_real] :
% 0.30/0.46 ( ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_70_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_variable] :
% 0.30/0.46 ( ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_71_Collect__cong,axiom,
% 0.30/0.46 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/0.46 ( ! [X8: variable > real] :
% 0.30/0.46 ( ( P @ X8 )
% 0.30/0.46 = ( Q @ X8 ) )
% 0.30/0.46 => ( ( collec633296133e_real @ P )
% 0.30/0.46 = ( collec633296133e_real @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_72_Collect__cong,axiom,
% 0.30/0.46 ! [P: variable > $o,Q: variable > $o] :
% 0.30/0.46 ( ! [X8: variable] :
% 0.30/0.46 ( ( P @ X8 )
% 0.30/0.46 = ( Q @ X8 ) )
% 0.30/0.46 => ( ( collect_variable @ P )
% 0.30/0.46 = ( collect_variable @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_73_skip__id,axiom,
% 0.30/0.46 ! [I: denotational_interp,X: set_variable_real] :
% 0.30/0.46 ( ( denota1245701238me_sem @ I @ skip @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % skip_id
% 0.30/0.46 thf(fact_74_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc432717079riable,Q2: produc432717079riable] :
% 0.30/0.46 ( ( ( produc1300679611riable @ P2 )
% 0.30/0.46 = ( produc1300679611riable @ Q2 ) )
% 0.30/0.46 => ( ( ( produc319712253riable @ P2 )
% 0.30/0.46 = ( produc319712253riable @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_75_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc1794985442e_real,Q2: produc1794985442e_real] :
% 0.30/0.46 ( ( ( produc1800845318e_real @ P2 )
% 0.30/0.46 = ( produc1800845318e_real @ Q2 ) )
% 0.30/0.46 => ( ( ( produc2048871496e_real @ P2 )
% 0.30/0.46 = ( produc2048871496e_real @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_76_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc1755325794riable,Q2: produc1755325794riable] :
% 0.30/0.46 ( ( ( produc944271878riable @ P2 )
% 0.30/0.46 = ( produc944271878riable @ Q2 ) )
% 0.30/0.46 => ( ( ( produc1192298056riable @ P2 )
% 0.30/0.46 = ( produc1192298056riable @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_77_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc2038871085e_real,Q2: produc2038871085e_real] :
% 0.30/0.46 ( ( ( produc702045265e_real @ P2 )
% 0.30/0.46 = ( produc702045265e_real @ Q2 ) )
% 0.30/0.46 => ( ( ( produc220849299e_real @ P2 )
% 0.30/0.46 = ( produc220849299e_real @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_78_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc735959047riable,Q2: produc735959047riable] :
% 0.30/0.46 ( ( ( produc884810027riable @ P2 )
% 0.30/0.46 = ( produc884810027riable @ Q2 ) )
% 0.30/0.46 => ( ( ( produc284475501riable @ P2 )
% 0.30/0.46 = ( produc284475501riable @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_79_prod__eqI,axiom,
% 0.30/0.46 ! [P2: produc1078154247n_game,Q2: produc1078154247n_game] :
% 0.30/0.46 ( ( ( produc893821739n_game @ P2 )
% 0.30/0.46 = ( produc893821739n_game @ Q2 ) )
% 0.30/0.46 => ( ( ( produc293487213n_game @ P2 )
% 0.30/0.46 = ( produc293487213n_game @ Q2 ) )
% 0.30/0.46 => ( P2 = Q2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eqI
% 0.30/0.46 thf(fact_80_exE__realizer_H,axiom,
% 0.30/0.46 ! [P: set_variable_real > set_variable_real > $o,P2: produc2038871085e_real] :
% 0.30/0.46 ( ( P @ ( produc220849299e_real @ P2 ) @ ( produc702045265e_real @ P2 ) )
% 0.30/0.46 => ~ ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exE_realizer'
% 0.30/0.46 thf(fact_81_exE__realizer_H,axiom,
% 0.30/0.46 ! [P: set_variable > option_game > $o,P2: produc735959047riable] :
% 0.30/0.46 ( ( P @ ( produc284475501riable @ P2 ) @ ( produc884810027riable @ P2 ) )
% 0.30/0.46 => ~ ! [X8: option_game,Y2: set_variable] :
% 0.30/0.46 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exE_realizer'
% 0.30/0.46 thf(fact_82_exE__realizer_H,axiom,
% 0.30/0.46 ! [P: option_game > set_variable > $o,P2: produc1078154247n_game] :
% 0.30/0.46 ( ( P @ ( produc293487213n_game @ P2 ) @ ( produc893821739n_game @ P2 ) )
% 0.30/0.46 => ~ ! [X8: set_variable,Y2: option_game] :
% 0.30/0.46 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % exE_realizer'
% 0.30/0.46 thf(fact_83_prod_Oexpand,axiom,
% 0.30/0.46 ! [Prod: produc1078154247n_game,Prod2: produc1078154247n_game] :
% 0.30/0.46 ( ( ( ( produc893821739n_game @ Prod )
% 0.30/0.46 = ( produc893821739n_game @ Prod2 ) )
% 0.30/0.46 & ( ( produc293487213n_game @ Prod )
% 0.30/0.46 = ( produc293487213n_game @ Prod2 ) ) )
% 0.30/0.46 => ( Prod = Prod2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.expand
% 0.30/0.46 thf(fact_84_prod__eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: produc1078154247n_game,Z: produc1078154247n_game] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [S: produc1078154247n_game,T: produc1078154247n_game] :
% 0.30/0.46 ( ( ( produc893821739n_game @ S )
% 0.30/0.46 = ( produc893821739n_game @ T ) )
% 0.30/0.46 & ( ( produc293487213n_game @ S )
% 0.30/0.46 = ( produc293487213n_game @ T ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_eq_iff
% 0.30/0.46 thf(fact_85_uminus__prod__def,axiom,
% 0.30/0.46 ( uminus501400228e_real
% 0.30/0.46 = ( ^ [X3: produc2038871085e_real] : ( produc86945893e_real @ ( uminus430703407e_real @ ( produc702045265e_real @ X3 ) ) @ ( uminus430703407e_real @ ( produc220849299e_real @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_prod_def
% 0.30/0.46 thf(fact_86_uminus__prod__def,axiom,
% 0.30/0.46 ( uminus2115124697riable
% 0.30/0.46 = ( ^ [X3: produc1755325794riable] : ( produc544095770riable @ ( uminus430703407e_real @ ( produc944271878riable @ X3 ) ) @ ( uminus1851247844riable @ ( produc1192298056riable @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_prod_def
% 0.30/0.46 thf(fact_87_uminus__prod__def,axiom,
% 0.30/0.46 ( uminus7300697e_real
% 0.30/0.46 = ( ^ [X3: produc1794985442e_real] : ( produc1400669210e_real @ ( uminus1851247844riable @ ( produc1800845318e_real @ X3 ) ) @ ( uminus430703407e_real @ ( produc2048871496e_real @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_prod_def
% 0.30/0.46 thf(fact_88_uminus__prod__def,axiom,
% 0.30/0.46 ( uminus269410190riable
% 0.30/0.46 = ( ^ [X3: produc432717079riable] : ( produc1766592463riable @ ( uminus1851247844riable @ ( produc1300679611riable @ X3 ) ) @ ( uminus1851247844riable @ ( produc319712253riable @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_prod_def
% 0.30/0.46 thf(fact_89_usubstappp__antimon,axiom,
% 0.30/0.46 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.30/0.46 ( ( ord_le282106107riable @ V @ U )
% 0.30/0.46 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.46 != none_game )
% 0.30/0.46 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/0.46 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_antimon
% 0.30/0.46 thf(fact_90_exists__diff,axiom,
% 0.30/0.46 ! [P: set_variable_real > $o] :
% 0.30/0.46 ( ( ? [S2: set_variable_real] : ( P @ ( uminus430703407e_real @ S2 ) ) )
% 0.30/0.46 = ( ? [X9: set_variable_real] : ( P @ X9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exists_diff
% 0.30/0.46 thf(fact_91_exists__diff,axiom,
% 0.30/0.46 ! [P: set_variable > $o] :
% 0.30/0.46 ( ( ? [S2: set_variable] : ( P @ ( uminus1851247844riable @ S2 ) ) )
% 0.30/0.46 = ( ? [X9: set_variable] : ( P @ X9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exists_diff
% 0.30/0.46 thf(fact_92_uminus__Pair,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( uminus501400228e_real @ ( produc86945893e_real @ A3 @ B2 ) )
% 0.30/0.46 = ( produc86945893e_real @ ( uminus430703407e_real @ A3 ) @ ( uminus430703407e_real @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_Pair
% 0.30/0.46 thf(fact_93_uminus__Pair,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable] :
% 0.30/0.46 ( ( uminus2115124697riable @ ( produc544095770riable @ A3 @ B2 ) )
% 0.30/0.46 = ( produc544095770riable @ ( uminus430703407e_real @ A3 ) @ ( uminus1851247844riable @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_Pair
% 0.30/0.46 thf(fact_94_uminus__Pair,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable_real] :
% 0.30/0.46 ( ( uminus7300697e_real @ ( produc1400669210e_real @ A3 @ B2 ) )
% 0.30/0.46 = ( produc1400669210e_real @ ( uminus1851247844riable @ A3 ) @ ( uminus430703407e_real @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_Pair
% 0.30/0.46 thf(fact_95_uminus__Pair,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( uminus269410190riable @ ( produc1766592463riable @ A3 @ B2 ) )
% 0.30/0.46 = ( produc1766592463riable @ ( uminus1851247844riable @ A3 ) @ ( uminus1851247844riable @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % uminus_Pair
% 0.30/0.46 thf(fact_96_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: set_variable,X22: option_game,Y1: set_variable,Y22: option_game] :
% 0.30/0.46 ( ( ( produc1149443391n_game @ X1 @ X22 )
% 0.30/0.46 = ( produc1149443391n_game @ Y1 @ Y22 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_97_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: option_game,A4: set_variable,B3: option_game] :
% 0.30/0.46 ( ( ( produc1149443391n_game @ A3 @ B2 )
% 0.30/0.46 = ( produc1149443391n_game @ A4 @ B3 ) )
% 0.30/0.46 = ( ( A3 = A4 )
% 0.30/0.46 & ( B2 = B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_98_subset__antisym,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ( ord_le282106107riable @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_99_subset__antisym,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_100_subsetI,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ! [X8: variable] :
% 0.30/0.46 ( ( member_variable @ X8 @ A )
% 0.30/0.46 => ( member_variable @ X8 @ B ) )
% 0.30/0.46 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_101_subsetI,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ! [X8: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X8 @ A )
% 0.30/0.46 => ( member_variable_real @ X8 @ B ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_102_compl__le__compl__iff,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( uminus1851247844riable @ X2 ) @ ( uminus1851247844riable @ Y ) )
% 0.30/0.46 = ( ord_le282106107riable @ Y @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_compl_iff
% 0.30/0.46 thf(fact_103_compl__le__compl__iff,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ X2 ) @ ( uminus430703407e_real @ Y ) )
% 0.30/0.46 = ( ord_le1113654598e_real @ Y @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_compl_iff
% 0.30/0.46 thf(fact_104_Compl__subset__Compl__iff,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
% 0.30/0.46 = ( ord_le282106107riable @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_subset_Compl_iff
% 0.30/0.46 thf(fact_105_Compl__subset__Compl__iff,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
% 0.30/0.46 = ( ord_le1113654598e_real @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_subset_Compl_iff
% 0.30/0.46 thf(fact_106_Compl__anti__mono,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_anti_mono
% 0.30/0.46 thf(fact_107_Compl__anti__mono,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Compl_anti_mono
% 0.30/0.46 thf(fact_108_prod_Ocollapse,axiom,
% 0.30/0.46 ! [Prod: produc1078154247n_game] :
% 0.30/0.46 ( ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) )
% 0.30/0.46 = Prod ) ).
% 0.30/0.46
% 0.30/0.46 % prod.collapse
% 0.30/0.46 thf(fact_109_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc1078154247n_game] :
% 0.30/0.46 ? [X8: set_variable,Y2: option_game] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc1149443391n_game @ X8 @ Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_110_prod__cases,axiom,
% 0.30/0.46 ! [P: produc1078154247n_game > $o,P2: produc1078154247n_game] :
% 0.30/0.46 ( ! [A5: set_variable,B4: option_game] : ( P @ ( produc1149443391n_game @ A5 @ B4 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_111_Pair__inject,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: option_game,A4: set_variable,B3: option_game] :
% 0.30/0.46 ( ( ( produc1149443391n_game @ A3 @ B2 )
% 0.30/0.46 = ( produc1149443391n_game @ A4 @ B3 ) )
% 0.30/0.46 => ~ ( ( A3 = A4 )
% 0.30/0.46 => ( B2 != B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_112_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc1078154247n_game] :
% 0.30/0.46 ~ ! [A5: set_variable,B4: option_game] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc1149443391n_game @ A5 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_113_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc1078154247n_game > $o,Prod: produc1078154247n_game] :
% 0.30/0.46 ( ! [A5: set_variable,B4: option_game] : ( P @ ( produc1149443391n_game @ A5 @ B4 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_114_Collect__mono__iff,axiom,
% 0.30/0.46 ! [P: variable > $o,Q: variable > $o] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 0.30/0.46 = ( ! [X3: variable] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_115_Collect__mono__iff,axiom,
% 0.30/0.46 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) )
% 0.30/0.46 = ( ! [X3: variable > real] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_116_set__eq__subset,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A2 @ B5 )
% 0.30/0.46 & ( ord_le282106107riable @ B5 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_117_set__eq__subset,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A2 @ B5 )
% 0.30/0.46 & ( ord_le1113654598e_real @ B5 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_118_subset__trans,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ( ord_le282106107riable @ B @ C2 )
% 0.30/0.46 => ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_119_subset__trans,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real,C2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B @ C2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ A @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_120_Collect__mono,axiom,
% 0.30/0.46 ! [P: variable > $o,Q: variable > $o] :
% 0.30/0.46 ( ! [X8: variable] :
% 0.30/0.46 ( ( P @ X8 )
% 0.30/0.46 => ( Q @ X8 ) )
% 0.30/0.46 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_121_Collect__mono,axiom,
% 0.30/0.46 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/0.46 ( ! [X8: variable > real] :
% 0.30/0.46 ( ( P @ X8 )
% 0.30/0.46 => ( Q @ X8 ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_122_subset__refl,axiom,
% 0.30/0.46 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_123_subset__refl,axiom,
% 0.30/0.46 ! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_124_subset__iff,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/0.46 ! [T: variable] :
% 0.30/0.46 ( ( member_variable @ T @ A2 )
% 0.30/0.46 => ( member_variable @ T @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_125_subset__iff,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/0.46 ! [T: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ T @ A2 )
% 0.30/0.46 => ( member_variable_real @ T @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_126_equalityD2,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ord_le282106107riable @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_127_equalityD2,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ord_le1113654598e_real @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_128_equalityD1,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_129_equalityD1,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ord_le1113654598e_real @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_130_subset__eq,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/0.46 ! [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A2 )
% 0.30/0.46 => ( member_variable @ X3 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_131_subset__eq,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/0.46 ! [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ A2 )
% 0.30/0.46 => ( member_variable_real @ X3 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_132_equalityE,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ~ ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_133_equalityE,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ~ ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ~ ( ord_le1113654598e_real @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_134_subsetD,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,C: variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ( member_variable @ C @ A )
% 0.30/0.46 => ( member_variable @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_135_subsetD,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real,C: variable > real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ( member_variable_real @ C @ A )
% 0.30/0.46 => ( member_variable_real @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_136_in__mono,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,X2: variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ( member_variable @ X2 @ A )
% 0.30/0.46 => ( member_variable @ X2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_137_in__mono,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real,X2: variable > real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ( member_variable_real @ X2 @ A )
% 0.30/0.46 => ( member_variable_real @ X2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_138_Collect__subset,axiom,
% 0.30/0.46 ! [A: set_variable,P: variable > $o] :
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 @ A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_subset
% 0.30/0.46 thf(fact_139_Collect__subset,axiom,
% 0.30/0.46 ! [A: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 @ A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_subset
% 0.30/0.46 thf(fact_140_fst__eqD,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: option_game,A3: set_variable] :
% 0.30/0.46 ( ( ( produc893821739n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/0.46 = A3 )
% 0.30/0.46 => ( X2 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_eqD
% 0.30/0.46 thf(fact_141_fst__conv,axiom,
% 0.30/0.46 ! [X1: set_variable,X22: option_game] :
% 0.30/0.46 ( ( produc893821739n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.30/0.46 = X1 ) ).
% 0.30/0.46
% 0.30/0.46 % fst_conv
% 0.30/0.46 thf(fact_142_snd__conv,axiom,
% 0.30/0.46 ! [X1: set_variable,X22: option_game] :
% 0.30/0.46 ( ( produc293487213n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.30/0.46 = X22 ) ).
% 0.30/0.46
% 0.30/0.46 % snd_conv
% 0.30/0.46 thf(fact_143_snd__eqD,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: option_game,A3: option_game] :
% 0.30/0.46 ( ( ( produc293487213n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/0.46 = A3 )
% 0.30/0.46 => ( Y = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_eqD
% 0.30/0.46 thf(fact_144_compl__le__swap2,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( uminus1851247844riable @ Y ) @ X2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( uminus1851247844riable @ X2 ) @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_swap2
% 0.30/0.46 thf(fact_145_compl__le__swap2,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ Y ) @ X2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ X2 ) @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_swap2
% 0.30/0.46 thf(fact_146_compl__le__swap1,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ Y @ ( uminus1851247844riable @ X2 ) )
% 0.30/0.46 => ( ord_le282106107riable @ X2 @ ( uminus1851247844riable @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_swap1
% 0.30/0.46 thf(fact_147_compl__le__swap1,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ Y @ ( uminus430703407e_real @ X2 ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ X2 @ ( uminus430703407e_real @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_le_swap1
% 0.30/0.46 thf(fact_148_compl__mono,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/0.46 => ( ord_le282106107riable @ ( uminus1851247844riable @ Y ) @ ( uminus1851247844riable @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_mono
% 0.30/0.46 thf(fact_149_compl__mono,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ Y ) @ ( uminus430703407e_real @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % compl_mono
% 0.30/0.46 thf(fact_150_fst__pair,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: option_game] :
% 0.30/0.46 ( ( produc893821739n_game @ ( produc1149443391n_game @ A3 @ B2 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % fst_pair
% 0.30/0.46 thf(fact_151_snd__pair,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: option_game] :
% 0.30/0.46 ( ( produc293487213n_game @ ( produc1149443391n_game @ A3 @ B2 ) )
% 0.30/0.46 = B2 ) ).
% 0.30/0.46
% 0.30/0.46 % snd_pair
% 0.30/0.46 thf(fact_152_surjective__pairing,axiom,
% 0.30/0.46 ! [T2: produc1078154247n_game] :
% 0.30/0.46 ( T2
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ T2 ) @ ( produc293487213n_game @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % surjective_pairing
% 0.30/0.46 thf(fact_153_prod_Oexhaust__sel,axiom,
% 0.30/0.46 ! [Prod: produc1078154247n_game] :
% 0.30/0.46 ( Prod
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.exhaust_sel
% 0.30/0.46 thf(fact_154_conjI__realizer,axiom,
% 0.30/0.46 ! [P: set_variable > $o,P2: set_variable,Q: option_game > $o,Q2: option_game] :
% 0.30/0.46 ( ( P @ P2 )
% 0.30/0.46 => ( ( Q @ Q2 )
% 0.30/0.46 => ( ( P @ ( produc893821739n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) )
% 0.30/0.46 & ( Q @ ( produc293487213n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conjI_realizer
% 0.30/0.46 thf(fact_155_exI__realizer,axiom,
% 0.30/0.46 ! [P: option_game > set_variable > $o,Y: option_game,X2: set_variable] :
% 0.30/0.46 ( ( P @ Y @ X2 )
% 0.30/0.46 => ( P @ ( produc293487213n_game @ ( produc1149443391n_game @ X2 @ Y ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ X2 @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exI_realizer
% 0.30/0.46 thf(fact_156_Uvariation__mon,axiom,
% 0.30/0.46 ! [U: set_variable,V: set_variable,Omega: variable > real,Nu: variable > real] :
% 0.30/0.46 ( ( ord_le282106107riable @ U @ V )
% 0.30/0.46 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/0.46 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Uvariation_mon
% 0.30/0.46 thf(fact_157_usubstappp__fst__mon,axiom,
% 0.30/0.46 ! [U: set_variable,V: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.30/0.46 ( ( ord_le282106107riable @ U @ V )
% 0.30/0.46 => ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_fst_mon
% 0.30/0.46 thf(fact_158_usubst__taboos__mon,axiom,
% 0.30/0.46 ! [U: set_variable,Sigma: produc1418842292n_game,Alpha: game] : ( ord_le282106107riable @ U @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubst_taboos_mon
% 0.30/0.46 thf(fact_159_usubstappp__dual,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/0.46 ( ( uSubst516392814stappp @ Sigma @ U @ ( dual @ Alpha ) )
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_dual
% 0.30/0.46 thf(fact_160_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.46 ! [P: set_variable > option_game > $o,X2: set_variable,Y: option_game,A3: produc1078154247n_game] :
% 0.30/0.46 ( ( P @ X2 @ Y )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 = ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/0.46 => ( P @ ( produc893821739n_game @ A3 ) @ ( produc293487213n_game @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.46 thf(fact_161_usubstappp_Osimps_I7_J,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/0.46 ( ( uSubst516392814stappp @ Sigma @ U @ ( dual @ Alpha ) )
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp.simps(7)
% 0.30/0.46 thf(fact_162_usubstappp_Osimps_I6_J,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/0.46 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp.simps(6)
% 0.30/0.46 thf(fact_163_usubstappp__loop,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/0.46 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.30/0.46 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_loop
% 0.30/0.46 thf(fact_164_order__refl,axiom,
% 0.30/0.46 ! [X2: set_variable] : ( ord_le282106107riable @ X2 @ X2 ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_165_order__refl,axiom,
% 0.30/0.46 ! [X2: set_variable_real] : ( ord_le1113654598e_real @ X2 @ X2 ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_166_monotone,axiom,
% 0.30/0.46 ! [X: set_variable_real,Y4: set_variable_real,I: denotational_interp,Alpha: game] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X @ Y4 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( denota1245701238me_sem @ I @ Alpha @ X ) @ ( denota1245701238me_sem @ I @ Alpha @ Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % monotone
% 0.30/0.46 thf(fact_167_less__eq__set__def,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/0.46 ( ord_le1407353162able_o
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 )
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_set_def
% 0.30/0.46 thf(fact_168_less__eq__set__def,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/0.46 ( ord_le1354144447real_o
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A2 )
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_set_def
% 0.30/0.46 thf(fact_169_Loopo__undef,axiom,
% 0.30/0.46 ! [Alpha: option_game] :
% 0.30/0.46 ( ( ( uSubst23177304_Loopo @ Alpha )
% 0.30/0.46 = none_game )
% 0.30/0.46 = ( Alpha = none_game ) ) ).
% 0.30/0.46
% 0.30/0.46 % Loopo_undef
% 0.30/0.46 thf(fact_170_Dualo__undef,axiom,
% 0.30/0.46 ! [Alpha: option_game] :
% 0.30/0.46 ( ( ( uSubst1916713664_Dualo @ Alpha )
% 0.30/0.46 = none_game )
% 0.30/0.46 = ( Alpha = none_game ) ) ).
% 0.30/0.46
% 0.30/0.46 % Dualo_undef
% 0.30/0.46 thf(fact_171_Loopo_Osimps_I2_J,axiom,
% 0.30/0.46 ( ( uSubst23177304_Loopo @ none_game )
% 0.30/0.46 = none_game ) ).
% 0.30/0.46
% 0.30/0.46 % Loopo.simps(2)
% 0.30/0.46 thf(fact_172_Dualo_Osimps_I2_J,axiom,
% 0.30/0.46 ( ( uSubst1916713664_Dualo @ none_game )
% 0.30/0.46 = none_game ) ).
% 0.30/0.46
% 0.30/0.46 % Dualo.simps(2)
% 0.30/0.46 thf(fact_173_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( A3 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_174_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( A3 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_175_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B6 @ A6 )
% 0.30/0.46 & ( ord_le282106107riable @ A6 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_176_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B6 @ A6 )
% 0.30/0.46 & ( ord_le1113654598e_real @ A6 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_177_dual__order_Otrans,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le282106107riable @ C @ B2 )
% 0.30/0.46 => ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_178_dual__order_Otrans,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ C @ B2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_179_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_180_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A3: set_variable_real] : ( ord_le1113654598e_real @ A3 @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_181_order__trans,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/0.46 => ( ( ord_le282106107riable @ Y @ Z2 )
% 0.30/0.46 => ( ord_le282106107riable @ X2 @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_182_order__trans,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real,Z2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ Y @ Z2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ X2 @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_183_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( A3 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_184_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( A3 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_185_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( B2 = C )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_186_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( B2 = C )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_187_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( A3 = B2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_188_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( A3 = B2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_189_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A6 @ B6 )
% 0.30/0.46 & ( ord_le282106107riable @ B6 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_190_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A6 @ B6 )
% 0.30/0.46 & ( ord_le1113654598e_real @ B6 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_191_antisym__conv,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/0.46 = ( X2 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_192_antisym__conv,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/0.46 = ( X2 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_193_order_Otrans,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_194_order_Otrans,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_195_eq__refl,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( X2 = Y )
% 0.30/0.46 => ( ord_le282106107riable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_196_eq__refl,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ( X2 = Y )
% 0.30/0.46 => ( ord_le1113654598e_real @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_197_antisym,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/0.46 => ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/0.46 => ( X2 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_198_antisym,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/0.46 => ( X2 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_199_eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X3: set_variable,Y5: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X3 @ Y5 )
% 0.30/0.46 & ( ord_le282106107riable @ Y5 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_200_eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X3: set_variable_real,Y5: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X3 @ Y5 )
% 0.30/0.46 & ( ord_le1113654598e_real @ Y5 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_201_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_202_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_203_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_204_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_205_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A3: set_variable,F: set_variable > set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_206_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A3: set_variable_real,F: set_variable > set_variable_real,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_207_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A3: set_variable,F: set_variable_real > set_variable,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_208_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A3: set_variable_real,F: set_variable_real > set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_209_order__subst2,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ ( F @ B2 ) @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_210_order__subst2,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ ( F @ B2 ) @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_211_order__subst2,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ ( F @ B2 ) @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_212_order__subst2,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ ( F @ B2 ) @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_213_order__subst1,axiom,
% 0.30/0.46 ! [A3: set_variable,F: set_variable > set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_214_order__subst1,axiom,
% 0.30/0.46 ! [A3: set_variable,F: set_variable_real > set_variable,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_215_order__subst1,axiom,
% 0.30/0.46 ! [A3: set_variable_real,F: set_variable > set_variable_real,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_216_order__subst1,axiom,
% 0.30/0.46 ! [A3: set_variable_real,F: set_variable_real > set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_217_subset__CollectI,axiom,
% 0.30/0.46 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 0.30/0.46 ( ( ord_le282106107riable @ B @ A )
% 0.30/0.46 => ( ! [X8: variable] :
% 0.30/0.46 ( ( member_variable @ X8 @ B )
% 0.30/0.46 => ( ( Q @ X8 )
% 0.30/0.46 => ( P @ X8 ) ) )
% 0.30/0.46 => ( ord_le282106107riable
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ B )
% 0.30/0.46 & ( Q @ X3 ) ) )
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_CollectI
% 0.30/0.46 thf(fact_218_subset__CollectI,axiom,
% 0.30/0.46 ! [B: set_variable_real,A: set_variable_real,Q: ( variable > real ) > $o,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/0.46 => ( ! [X8: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X8 @ B )
% 0.30/0.46 => ( ( Q @ X8 )
% 0.30/0.46 => ( P @ X8 ) ) )
% 0.30/0.46 => ( ord_le1113654598e_real
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ B )
% 0.30/0.46 & ( Q @ X3 ) ) )
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_CollectI
% 0.30/0.46 thf(fact_219_subset__Collect__iff,axiom,
% 0.30/0.46 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 0.30/0.46 ( ( ord_le282106107riable @ B @ A )
% 0.30/0.46 => ( ( ord_le282106107riable @ B
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) ) )
% 0.30/0.46 = ( ! [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ B )
% 0.30/0.46 => ( P @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_iff
% 0.30/0.46 thf(fact_220_subset__Collect__iff,axiom,
% 0.30/0.46 ! [B: set_variable_real,A: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) ) ) )
% 0.30/0.46 = ( ! [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ B )
% 0.30/0.46 => ( P @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_iff
% 0.30/0.46 thf(fact_221_sndI,axiom,
% 0.30/0.46 ! [X2: produc1078154247n_game,Y: set_variable,Z2: option_game] :
% 0.30/0.46 ( ( X2
% 0.30/0.46 = ( produc1149443391n_game @ Y @ Z2 ) )
% 0.30/0.46 => ( ( produc293487213n_game @ X2 )
% 0.30/0.46 = Z2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sndI
% 0.30/0.46 thf(fact_222_eq__snd__iff,axiom,
% 0.30/0.46 ! [B2: option_game,P2: produc1078154247n_game] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 = ( produc293487213n_game @ P2 ) )
% 0.30/0.46 = ( ? [A6: set_variable] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc1149443391n_game @ A6 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_snd_iff
% 0.30/0.46 thf(fact_223_eq__fst__iff,axiom,
% 0.30/0.46 ! [A3: set_variable,P2: produc1078154247n_game] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( produc893821739n_game @ P2 ) )
% 0.30/0.46 = ( ? [B6: option_game] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc1149443391n_game @ A3 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_fst_iff
% 0.30/0.46 thf(fact_224_fstI,axiom,
% 0.30/0.46 ! [X2: produc1078154247n_game,Y: set_variable,Z2: option_game] :
% 0.30/0.46 ( ( X2
% 0.30/0.46 = ( produc1149443391n_game @ Y @ Z2 ) )
% 0.30/0.46 => ( ( produc893821739n_game @ X2 )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % fstI
% 0.30/0.46 thf(fact_225_pred__subset__eq,axiom,
% 0.30/0.46 ! [R: set_variable,S3: set_variable] :
% 0.30/0.46 ( ( ord_le1407353162able_o
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ R )
% 0.30/0.46 @ ^ [X3: variable] : ( member_variable @ X3 @ S3 ) )
% 0.30/0.46 = ( ord_le282106107riable @ R @ S3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq
% 0.30/0.46 thf(fact_226_pred__subset__eq,axiom,
% 0.30/0.46 ! [R: set_variable_real,S3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1354144447real_o
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ R )
% 0.30/0.46 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ S3 ) )
% 0.30/0.46 = ( ord_le1113654598e_real @ R @ S3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq
% 0.30/0.46 thf(fact_227_Collect__restrict,axiom,
% 0.30/0.46 ! [X: set_variable,P: variable > $o] :
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ X )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 @ X ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_restrict
% 0.30/0.46 thf(fact_228_Collect__restrict,axiom,
% 0.30/0.46 ! [X: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ X )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 @ X ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_restrict
% 0.30/0.46 thf(fact_229_subrelI,axiom,
% 0.30/0.46 ! [R2: set_Pr166476775n_game,S4: set_Pr166476775n_game] :
% 0.30/0.46 ( ! [X8: set_variable,Y2: option_game] :
% 0.30/0.46 ( ( member171223600n_game @ ( produc1149443391n_game @ X8 @ Y2 ) @ R2 )
% 0.30/0.46 => ( member171223600n_game @ ( produc1149443391n_game @ X8 @ Y2 ) @ S4 ) )
% 0.30/0.46 => ( ord_le17855367n_game @ R2 @ S4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subrelI
% 0.30/0.46 thf(fact_230_ssubst__Pair__rhs,axiom,
% 0.30/0.46 ! [R2: set_variable,S4: option_game,R: set_Pr166476775n_game,S5: option_game] :
% 0.30/0.46 ( ( member171223600n_game @ ( produc1149443391n_game @ R2 @ S4 ) @ R )
% 0.30/0.46 => ( ( S5 = S4 )
% 0.30/0.46 => ( member171223600n_game @ ( produc1149443391n_game @ R2 @ S5 ) @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ssubst_Pair_rhs
% 0.30/0.46 thf(fact_231_pred__subset__eq2,axiom,
% 0.30/0.46 ! [R: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 0.30/0.46 ( ( ord_le2134856704game_o
% 0.30/0.46 @ ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ R )
% 0.30/0.46 @ ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ S3 ) )
% 0.30/0.46 = ( ord_le17855367n_game @ R @ S3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq2
% 0.30/0.46 thf(fact_232_pred__equals__eq2,axiom,
% 0.30/0.46 ! [R: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 0.30/0.46 ( ( ( ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ R ) )
% 0.30/0.46 = ( ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ S3 ) ) )
% 0.30/0.46 = ( R = S3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_equals_eq2
% 0.30/0.46 thf(fact_233_prop__restrict,axiom,
% 0.30/0.46 ! [X2: variable,Z3: set_variable,X: set_variable,P: variable > $o] :
% 0.30/0.46 ( ( member_variable @ X2 @ Z3 )
% 0.30/0.46 => ( ( ord_le282106107riable @ Z3
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ X )
% 0.30/0.46 & ( P @ X3 ) ) ) )
% 0.30/0.46 => ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prop_restrict
% 0.30/0.46 thf(fact_234_prop__restrict,axiom,
% 0.30/0.46 ! [X2: variable > real,Z3: set_variable_real,X: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/0.46 ( ( member_variable_real @ X2 @ Z3 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ Z3
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( member_variable_real @ X3 @ X )
% 0.30/0.46 & ( P @ X3 ) ) ) )
% 0.30/0.46 => ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prop_restrict
% 0.30/0.46 thf(fact_235_conj__subset__def,axiom,
% 0.30/0.46 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 0.30/0.46 ( ( ord_le282106107riable @ A
% 0.30/0.46 @ ( collect_variable
% 0.30/0.46 @ ^ [X3: variable] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 & ( Q @ X3 ) ) ) )
% 0.30/0.46 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 0.30/0.46 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conj_subset_def
% 0.30/0.46 thf(fact_236_conj__subset__def,axiom,
% 0.30/0.46 ! [A: set_variable_real,P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A
% 0.30/0.46 @ ( collec633296133e_real
% 0.30/0.46 @ ^ [X3: variable > real] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 & ( Q @ X3 ) ) ) )
% 0.30/0.46 = ( ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ P ) )
% 0.30/0.46 & ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ Q ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conj_subset_def
% 0.30/0.46 thf(fact_237_prod_Oswap__def,axiom,
% 0.30/0.46 ( produc345397471riable
% 0.30/0.46 = ( ^ [P3: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ P3 ) @ ( produc884810027riable @ P3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.swap_def
% 0.30/0.46 thf(fact_238_prod_Oswap__def,axiom,
% 0.30/0.46 ( produc354409183n_game
% 0.30/0.46 = ( ^ [P3: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ P3 ) @ ( produc893821739n_game @ P3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.swap_def
% 0.30/0.46 thf(fact_239_swap__simp,axiom,
% 0.30/0.46 ! [X2: option_game,Y: set_variable] :
% 0.30/0.46 ( ( produc345397471riable @ ( produc1140431679riable @ X2 @ Y ) )
% 0.30/0.46 = ( produc1149443391n_game @ Y @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % swap_simp
% 0.30/0.46 thf(fact_240_swap__simp,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: option_game] :
% 0.30/0.46 ( ( produc354409183n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/0.46 = ( produc1140431679riable @ Y @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % swap_simp
% 0.30/0.46 thf(fact_241_snd__swap,axiom,
% 0.30/0.46 ! [X2: produc1078154247n_game] :
% 0.30/0.46 ( ( produc284475501riable @ ( produc354409183n_game @ X2 ) )
% 0.30/0.46 = ( produc893821739n_game @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_swap
% 0.30/0.46 thf(fact_242_snd__swap,axiom,
% 0.30/0.46 ! [X2: produc735959047riable] :
% 0.30/0.46 ( ( produc293487213n_game @ ( produc345397471riable @ X2 ) )
% 0.30/0.46 = ( produc884810027riable @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % snd_swap
% 0.30/0.46 thf(fact_243_fst__swap,axiom,
% 0.30/0.46 ! [X2: produc735959047riable] :
% 0.30/0.46 ( ( produc893821739n_game @ ( produc345397471riable @ X2 ) )
% 0.30/0.46 = ( produc284475501riable @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_swap
% 0.30/0.46 thf(fact_244_fst__swap,axiom,
% 0.30/0.46 ! [X2: produc1078154247n_game] :
% 0.30/0.46 ( ( produc884810027riable @ ( produc354409183n_game @ X2 ) )
% 0.30/0.46 = ( produc293487213n_game @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fst_swap
% 0.30/0.46 thf(fact_245_usubstappp__choice,axiom,
% 0.30/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.30/0.46 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.30/0.46 = ( produc1149443391n_game @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1484167963hoiceo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % usubstappp_choice
% 0.30/0.46 thf(fact_246_sup_Oidem,axiom,
% 0.30/0.46 ! [A3: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A3 @ A3 )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % sup.idem
% 0.30/0.46 thf(fact_247_sup__idem,axiom,
% 0.30/0.46 ! [X2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ X2 @ X2 )
% 0.30/0.46 = X2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_idem
% 0.30/0.46 thf(fact_248_sup_Oleft__idem,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ A3 @ B2 ) )
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.left_idem
% 0.30/0.46 thf(fact_249_sup__left__idem,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) )
% 0.30/0.46 = ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_left_idem
% 0.30/0.46 thf(fact_250_sup_Oright__idem,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A3 @ B2 ) @ B2 )
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.right_idem
% 0.30/0.46 thf(fact_251_UnCI,axiom,
% 0.30/0.46 ! [C: variable > real,B: set_variable_real,A: set_variable_real] :
% 0.30/0.46 ( ( ~ ( member_variable_real @ C @ B )
% 0.30/0.46 => ( member_variable_real @ C @ A ) )
% 0.30/0.46 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_252_UnCI,axiom,
% 0.30/0.46 ! [C: variable,B: set_variable,A: set_variable] :
% 0.30/0.46 ( ( ~ ( member_variable @ C @ B )
% 0.30/0.46 => ( member_variable @ C @ A ) )
% 0.30/0.46 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_253_sup_Obounded__iff,axiom,
% 0.30/0.46 ! [B2: set_variable,C: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 )
% 0.30/0.46 = ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 & ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.bounded_iff
% 0.30/0.46 thf(fact_254_sup_Obounded__iff,axiom,
% 0.30/0.46 ! [B2: set_variable_real,C: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 )
% 0.30/0.46 = ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 & ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.bounded_iff
% 0.30/0.46 thf(fact_255_le__sup__iff,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/0.46 = ( ( ord_le282106107riable @ X2 @ Z2 )
% 0.30/0.46 & ( ord_le282106107riable @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_sup_iff
% 0.30/0.46 thf(fact_256_le__sup__iff,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real,Z2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ X2 @ Y ) @ Z2 )
% 0.30/0.46 = ( ( ord_le1113654598e_real @ X2 @ Z2 )
% 0.30/0.46 & ( ord_le1113654598e_real @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_sup_iff
% 0.30/0.46 thf(fact_257_Un__subset__iff,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C2 )
% 0.30/0.46 = ( ( ord_le282106107riable @ A @ C2 )
% 0.30/0.46 & ( ord_le282106107riable @ B @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_subset_iff
% 0.30/0.46 thf(fact_258_Un__subset__iff,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real,C2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C2 )
% 0.30/0.46 = ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/0.46 & ( ord_le1113654598e_real @ B @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_subset_iff
% 0.30/0.46 thf(fact_259_subset__Un__eq,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A2 @ B5 )
% 0.30/0.46 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Un_eq
% 0.30/0.46 thf(fact_260_subset__Un__eq,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/0.46 ( ( sup_su1685293586e_real @ A2 @ B5 )
% 0.30/0.46 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Un_eq
% 0.30/0.46 thf(fact_261_subset__UnE,axiom,
% 0.30/0.46 ! [C2: set_variable,A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/0.46 => ~ ! [A7: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A7 @ A )
% 0.30/0.46 => ! [B7: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B7 @ B )
% 0.30/0.46 => ( C2
% 0.30/0.46 != ( sup_sup_set_variable @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_UnE
% 0.30/0.46 thf(fact_262_subset__UnE,axiom,
% 0.30/0.46 ! [C2: set_variable_real,A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ C2 @ ( sup_su1685293586e_real @ A @ B ) )
% 0.30/0.46 => ~ ! [A7: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A7 @ A )
% 0.30/0.46 => ! [B7: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B7 @ B )
% 0.30/0.46 => ( C2
% 0.30/0.46 != ( sup_su1685293586e_real @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_UnE
% 0.30/0.46 thf(fact_263_Un__absorb2,axiom,
% 0.30/0.46 ! [B: set_variable,A: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B @ A )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb2
% 0.30/0.46 thf(fact_264_Un__absorb2,axiom,
% 0.30/0.46 ! [B: set_variable_real,A: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb2
% 0.30/0.46 thf(fact_265_Un__absorb1,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ B )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb1
% 0.30/0.46 thf(fact_266_Un__absorb1,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb1
% 0.30/0.46 thf(fact_267_Un__upper2,axiom,
% 0.30/0.46 ! [B: set_variable,A: set_variable] : ( ord_le282106107riable @ B @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper2
% 0.30/0.46 thf(fact_268_Un__upper2,axiom,
% 0.30/0.46 ! [B: set_variable_real,A: set_variable_real] : ( ord_le1113654598e_real @ B @ ( sup_su1685293586e_real @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper2
% 0.30/0.46 thf(fact_269_Un__upper1,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper1
% 0.30/0.46 thf(fact_270_Un__upper1,axiom,
% 0.30/0.46 ! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper1
% 0.30/0.46 thf(fact_271_Un__least,axiom,
% 0.30/0.46 ! [A: set_variable,C2: set_variable,B: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ C2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B @ C2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_least
% 0.30/0.46 thf(fact_272_Un__least,axiom,
% 0.30/0.46 ! [A: set_variable_real,C2: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B @ C2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_least
% 0.30/0.46 thf(fact_273_Un__mono,axiom,
% 0.30/0.46 ! [A: set_variable,C2: set_variable,B: set_variable,D: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A @ C2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B @ D )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ ( sup_sup_set_variable @ C2 @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_mono
% 0.30/0.46 thf(fact_274_Un__mono,axiom,
% 0.30/0.46 ! [A: set_variable_real,C2: set_variable_real,B: set_variable_real,D: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B @ D )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ ( sup_su1685293586e_real @ C2 @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_mono
% 0.30/0.46 thf(fact_275_sup_OcoboundedI2,axiom,
% 0.30/0.46 ! [C: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ C @ B2 )
% 0.30/0.46 => ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI2
% 0.30/0.46 thf(fact_276_sup_OcoboundedI2,axiom,
% 0.30/0.46 ! [C: set_variable_real,B2: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ C @ B2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ C @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI2
% 0.30/0.46 thf(fact_277_sup_OcoboundedI1,axiom,
% 0.30/0.46 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ C @ A3 )
% 0.30/0.46 => ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI1
% 0.30/0.46 thf(fact_278_sup_OcoboundedI1,axiom,
% 0.30/0.46 ! [C: set_variable_real,A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/0.46 => ( ord_le1113654598e_real @ C @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI1
% 0.30/0.46 thf(fact_279_sup_Oabsorb__iff2,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A6 @ B6 )
% 0.30/0.46 = B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff2
% 0.30/0.46 thf(fact_280_sup_Oabsorb__iff2,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/0.46 ( ( sup_su1685293586e_real @ A6 @ B6 )
% 0.30/0.46 = B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff2
% 0.30/0.46 thf(fact_281_sup_Oabsorb__iff1,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [B6: set_variable,A6: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A6 @ B6 )
% 0.30/0.46 = A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff1
% 0.30/0.46 thf(fact_282_sup_Oabsorb__iff1,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [B6: set_variable_real,A6: set_variable_real] :
% 0.30/0.46 ( ( sup_su1685293586e_real @ A6 @ B6 )
% 0.30/0.46 = A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff1
% 0.30/0.46 thf(fact_283_sup_Ocobounded2,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable] : ( ord_le282106107riable @ B2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded2
% 0.30/0.46 thf(fact_284_sup_Ocobounded2,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real] : ( ord_le1113654598e_real @ B2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded2
% 0.30/0.46 thf(fact_285_sup_Ocobounded1,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ A3 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded1
% 0.30/0.46 thf(fact_286_sup_Ocobounded1,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real] : ( ord_le1113654598e_real @ A3 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded1
% 0.30/0.46 thf(fact_287_sup_Oorder__iff,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [B6: set_variable,A6: set_variable] :
% 0.30/0.46 ( A6
% 0.30/0.46 = ( sup_sup_set_variable @ A6 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.order_iff
% 0.30/0.46 thf(fact_288_sup_Oorder__iff,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [B6: set_variable_real,A6: set_variable_real] :
% 0.30/0.46 ( A6
% 0.30/0.46 = ( sup_su1685293586e_real @ A6 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.order_iff
% 0.30/0.46 thf(fact_289_sup_OboundedI,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le282106107riable @ C @ A3 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedI
% 0.30/0.46 thf(fact_290_sup_OboundedI,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real,C: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedI
% 0.30/0.46 thf(fact_291_sup_OboundedE,axiom,
% 0.30/0.46 ! [B2: set_variable,C: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 )
% 0.30/0.46 => ~ ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ~ ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedE
% 0.30/0.46 thf(fact_292_sup_OboundedE,axiom,
% 0.30/0.46 ! [B2: set_variable_real,C: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 )
% 0.30/0.46 => ~ ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ~ ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedE
% 0.30/0.46 thf(fact_293_sup__absorb2,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/0.46 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb2
% 0.30/0.46 thf(fact_294_sup__absorb2,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb2
% 0.30/0.46 thf(fact_295_sup__absorb1,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/0.46 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/0.46 = X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb1
% 0.30/0.46 thf(fact_296_sup__absorb1,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/0.46 = X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb1
% 0.30/0.46 thf(fact_297_sup_Oabsorb2,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A3 @ B2 )
% 0.30/0.46 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb2
% 0.30/0.46 thf(fact_298_sup_Oabsorb2,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ A3 @ B2 )
% 0.30/0.46 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb2
% 0.30/0.46 thf(fact_299_sup_Oabsorb1,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A3 @ B2 )
% 0.30/0.46 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb1
% 0.30/0.46 thf(fact_300_sup_Oabsorb1,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ A3 @ B2 )
% 0.30/0.46 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb1
% 0.30/0.46 thf(fact_301_sup__unique,axiom,
% 0.30/0.46 ! [F: set_variable > set_variable > set_variable,X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ! [X8: set_variable,Y2: set_variable] : ( ord_le282106107riable @ X8 @ ( F @ X8 @ Y2 ) )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable] : ( ord_le282106107riable @ Y2 @ ( F @ X8 @ Y2 ) )
% 0.30/0.46 => ( ! [X8: set_variable,Y2: set_variable,Z4: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ Y2 @ X8 )
% 0.30/0.46 => ( ( ord_le282106107riable @ Z4 @ X8 )
% 0.30/0.46 => ( ord_le282106107riable @ ( F @ Y2 @ Z4 ) @ X8 ) ) )
% 0.30/0.46 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/0.46 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_unique
% 0.30/0.46 thf(fact_302_sup__unique,axiom,
% 0.30/0.46 ! [F: set_variable_real > set_variable_real > set_variable_real,X2: set_variable_real,Y: set_variable_real] :
% 0.30/0.46 ( ! [X8: set_variable_real,Y2: set_variable_real] : ( ord_le1113654598e_real @ X8 @ ( F @ X8 @ Y2 ) )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real] : ( ord_le1113654598e_real @ Y2 @ ( F @ X8 @ Y2 ) )
% 0.30/0.46 => ( ! [X8: set_variable_real,Y2: set_variable_real,Z4: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ Y2 @ X8 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ Z4 @ X8 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( F @ Y2 @ Z4 ) @ X8 ) ) )
% 0.30/0.46 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/0.46 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_unique
% 0.30/0.46 thf(fact_303_sup_OorderI,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ B2 ) )
% 0.30/0.46 => ( ord_le282106107riable @ B2 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderI
% 0.30/0.46 thf(fact_304_sup_OorderI,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( sup_su1685293586e_real @ A3 @ B2 ) )
% 0.30/0.46 => ( ord_le1113654598e_real @ B2 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderI
% 0.30/0.46 thf(fact_305_sup_OorderE,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderE
% 0.30/0.46 thf(fact_306_sup_OorderE,axiom,
% 0.30/0.46 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderE
% 0.30/0.46 thf(fact_307_le__iff__sup,axiom,
% 0.30/0.46 ( ord_le282106107riable
% 0.30/0.46 = ( ^ [X3: set_variable,Y5: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ X3 @ Y5 )
% 0.30/0.46 = Y5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_sup
% 0.30/0.46 thf(fact_308_le__iff__sup,axiom,
% 0.30/0.46 ( ord_le1113654598e_real
% 0.30/0.46 = ( ^ [X3: set_variable_real,Y5: set_variable_real] :
% 0.30/0.46 ( ( sup_su1685293586e_real @ X3 @ Y5 )
% 0.30/0.46 = Y5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_sup
% 0.30/0.46 thf(fact_309_sup__least,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ Z2 @ X2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ Y @ Z2 ) @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_least
% 0.30/0.46 thf(fact_310_sup__least,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real,Z2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ Z2 @ X2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ Y @ Z2 ) @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_least
% 0.30/0.46 thf(fact_311_sup__mono,axiom,
% 0.30/0.46 ! [A3: set_variable,C: set_variable,B2: set_variable,D2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ C )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ D2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ ( sup_sup_set_variable @ C @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_mono
% 0.30/0.46 thf(fact_312_sup__mono,axiom,
% 0.30/0.46 ! [A3: set_variable_real,C: set_variable_real,B2: set_variable_real,D2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ C )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ D2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ ( sup_su1685293586e_real @ C @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_mono
% 0.30/0.46 thf(fact_313_sup_Omono,axiom,
% 0.30/0.46 ! [C: set_variable,A3: set_variable,D2: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ C @ A3 )
% 0.30/0.46 => ( ( ord_le282106107riable @ D2 @ B2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ C @ D2 ) @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.mono
% 0.30/0.46 thf(fact_314_sup_Omono,axiom,
% 0.30/0.46 ! [C: set_variable_real,A3: set_variable_real,D2: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ D2 @ B2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ C @ D2 ) @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.mono
% 0.30/0.46 thf(fact_315_le__supI2,axiom,
% 0.30/0.46 ! [X2: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ B2 )
% 0.30/0.46 => ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI2
% 0.30/0.46 thf(fact_316_le__supI2,axiom,
% 0.30/0.46 ! [X2: set_variable_real,B2: set_variable_real,A3: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ B2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI2
% 0.30/0.46 thf(fact_317_le__supI1,axiom,
% 0.30/0.46 ! [X2: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ X2 @ A3 )
% 0.30/0.46 => ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI1
% 0.30/0.46 thf(fact_318_le__supI1,axiom,
% 0.30/0.46 ! [X2: set_variable_real,A3: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ X2 @ A3 )
% 0.30/0.46 => ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI1
% 0.30/0.46 thf(fact_319_sup__ge2,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge2
% 0.30/0.46 thf(fact_320_sup__ge2,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] : ( ord_le1113654598e_real @ Y @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge2
% 0.30/0.46 thf(fact_321_sup__ge1,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] : ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge1
% 0.30/0.46 thf(fact_322_sup__ge1,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] : ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge1
% 0.30/0.46 thf(fact_323_le__supI,axiom,
% 0.30/0.46 ! [A3: set_variable,X2: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ A3 @ X2 )
% 0.30/0.46 => ( ( ord_le282106107riable @ B2 @ X2 )
% 0.30/0.46 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI
% 0.30/0.46 thf(fact_324_le__supI,axiom,
% 0.30/0.46 ! [A3: set_variable_real,X2: set_variable_real,B2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ A3 @ X2 )
% 0.30/0.46 => ( ( ord_le1113654598e_real @ B2 @ X2 )
% 0.30/0.46 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI
% 0.30/0.46 thf(fact_325_le__supE,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,X2: set_variable] :
% 0.30/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ X2 )
% 0.30/0.46 => ~ ( ( ord_le282106107riable @ A3 @ X2 )
% 0.30/0.46 => ~ ( ord_le282106107riable @ B2 @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supE
% 0.30/0.46 thf(fact_326_le__supE,axiom,
% 0.30/0.46 ! [A3: set_variable_real,B2: set_variable_real,X2: set_variable_real] :
% 0.30/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ X2 )
% 0.30/0.46 => ~ ( ( ord_le1113654598e_real @ A3 @ X2 )
% 0.30/0.46 => ~ ( ord_le1113654598e_real @ B2 @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supE
% 0.30/0.46 thf(fact_327_inf__sup__ord_I3_J,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] : ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(3)
% 0.30/0.46 thf(fact_328_inf__sup__ord_I3_J,axiom,
% 0.30/0.46 ! [X2: set_variable_real,Y: set_variable_real] : ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(3)
% 0.30/0.46 thf(fact_329_inf__sup__ord_I4_J,axiom,
% 0.30/0.46 ! [Y: set_variable,X2: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(4)
% 0.30/0.46 thf(fact_330_inf__sup__ord_I4_J,axiom,
% 0.30/0.46 ! [Y: set_variable_real,X2: set_variable_real] : ( ord_le1113654598e_real @ Y @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(4)
% 0.30/0.46 thf(fact_331_inf__sup__aci_I8_J,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) )
% 0.30/0.46 = ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(8)
% 0.30/0.46 thf(fact_332_inf__sup__aci_I7_J,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) )
% 0.30/0.46 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X2 @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(7)
% 0.30/0.46 thf(fact_333_inf__sup__aci_I6_J,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/0.46 = ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(6)
% 0.30/0.46 thf(fact_334_inf__sup__aci_I5_J,axiom,
% 0.30/0.46 ( sup_sup_set_variable
% 0.30/0.46 = ( ^ [X3: set_variable,Y5: set_variable] : ( sup_sup_set_variable @ Y5 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(5)
% 0.30/0.46 thf(fact_335_UnE,axiom,
% 0.30/0.46 ! [C: variable > real,A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) )
% 0.30/0.46 => ( ~ ( member_variable_real @ C @ A )
% 0.30/0.46 => ( member_variable_real @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_336_UnE,axiom,
% 0.30/0.46 ! [C: variable,A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/0.46 => ( ~ ( member_variable @ C @ A )
% 0.30/0.46 => ( member_variable @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_337_UnI1,axiom,
% 0.30/0.46 ! [C: variable > real,A: set_variable_real,B: set_variable_real] :
% 0.30/0.46 ( ( member_variable_real @ C @ A )
% 0.30/0.46 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_338_UnI1,axiom,
% 0.30/0.46 ! [C: variable,A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( member_variable @ C @ A )
% 0.30/0.46 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_339_UnI2,axiom,
% 0.30/0.46 ! [C: variable > real,B: set_variable_real,A: set_variable_real] :
% 0.30/0.46 ( ( member_variable_real @ C @ B )
% 0.30/0.46 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_340_UnI2,axiom,
% 0.30/0.46 ! [C: variable,B: set_variable,A: set_variable] :
% 0.30/0.46 ( ( member_variable @ C @ B )
% 0.30/0.46 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_341_bex__Un,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.30/0.46 ( ( ? [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 = ( ? [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A )
% 0.30/0.46 & ( P @ X3 ) )
% 0.30/0.46 | ? [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ B )
% 0.30/0.46 & ( P @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_342_ball__Un,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.30/0.46 ( ( ! [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/0.46 => ( P @ X3 ) ) )
% 0.30/0.46 = ( ! [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ A )
% 0.30/0.46 => ( P @ X3 ) )
% 0.30/0.46 & ! [X3: variable] :
% 0.30/0.46 ( ( member_variable @ X3 @ B )
% 0.30/0.46 => ( P @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_343_Un__assoc,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C2 )
% 0.30/0.46 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_344_Un__absorb,axiom,
% 0.30/0.46 ! [A: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_345_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/0.46 = ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_346_Un__left__commute,axiom,
% 0.30/0.46 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C2 ) )
% 0.30/0.46 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_347_boolean__algebra__cancel_Osup1,axiom,
% 0.30/0.46 ! [A: set_variable,K: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( sup_sup_set_variable @ K @ A3 ) )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A @ B2 )
% 0.30/0.46 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.sup1
% 0.30/0.46 thf(fact_348_boolean__algebra__cancel_Osup2,axiom,
% 0.30/0.46 ! [B: set_variable,K: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/0.46 ( ( B
% 0.30/0.46 = ( sup_sup_set_variable @ K @ B2 ) )
% 0.30/0.46 => ( ( sup_sup_set_variable @ A3 @ B )
% 0.30/0.46 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.sup2
% 0.30/0.46 thf(fact_349_sup_Oassoc,axiom,
% 0.30/0.46 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A3 @ B2 ) @ C )
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ B2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.assoc
% 0.30/0.46 thf(fact_350_sup__assoc,axiom,
% 0.30/0.46 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/0.46 = ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_assoc
% 0.30/0.46 thf(fact_351_sup_Ocommute,axiom,
% 0.30/0.46 ( sup_sup_set_variable
% 0.30/0.46 = ( ^ [A6: set_variable,B6: set_variable] : ( sup_sup_set_variable @ B6 @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.commute
% 0.30/0.46 thf(fact_352_sup__commute,axiom,
% 0.30/0.46 ( sup_sup_set_variable
% 0.30/0.46 = ( ^ [X3: set_variable,Y5: set_variable] : ( sup_sup_set_variable @ Y5 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_commute
% 0.30/0.46 thf(fact_353_sup_Oleft__commute,axiom,
% 0.30/0.46 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/0.46 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A3 @ C ) )
% 0.30/0.46 = ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ B2 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.left_commute
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
% 0.30/0.46 = ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.30/1.50 ---- Embedded in THF ---
% 0.30/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.51 %%% Generated on Tue Feb 24 08:30:20 EST 2026
% 0.30/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.51 %%% Logic specification used:
% 0.30/1.51 %%% thf(spec, logic, $$dhol).
% 0.30/1.51
% 0.30/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2DTF28368.p
% See solution above
% 0.30/1.51 ------------------------
% 0.30/1.55 ---- Cleaned THF ---
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.30/1.55 produc1418842292n_game: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/1.55 produc2038871085e_real: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/1.55 produc1794985442e_real: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/1.55 produc1755325794riable: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/1.55 set_Pr166476775n_game: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/1.55 produc1078154247n_game: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/1.55 produc735959047riable: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/1.55 produc432717079riable: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.55 set_variable_real: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/1.55 option_game: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.30/1.55 denotational_interp: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.55 set_variable: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Syntax__Ovariable,type,
% 0.30/1.55 variable: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Syntax__Ogame,type,
% 0.30/1.55 game: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(ty_n_t__Real__Oreal,type,
% 0.30/1.55 real: $tType ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.30/1.55 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Denotational__Semantics_Ogame__sem,type,
% 0.30/1.55 denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 0.30/1.55 uminus970116630real_o: ( ( variable > real ) > $o ) > ( variable > real ) > $o ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J,type,
% 0.30/1.55 uminus679091071game_o: ( produc1078154247n_game > $o ) > produc1078154247n_game > $o ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.30/1.55 uminus1666842273able_o: ( variable > $o ) > variable > $o ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001_Eo,type,
% 0.30/1.55 uminus_uminus_o: $o > $o ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/1.55 uminus501400228e_real: produc2038871085e_real > produc2038871085e_real ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/1.55 uminus2115124697riable: produc1755325794riable > produc1755325794riable ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.30/1.55 uminus7300697e_real: produc1794985442e_real > produc1794985442e_real ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.30/1.55 uminus269410190riable: produc432717079riable > produc432717079riable ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.55 uminus430703407e_real: set_variable_real > set_variable_real ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/1.55 uminus2030647006n_game: set_Pr166476775n_game > set_Pr166476775n_game ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.55 uminus1851247844riable: set_variable > set_variable ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.55 sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.55 sup_sup_set_variable: set_variable > set_variable > set_variable ).
% 0.30/1.55
% 0.30/1.55 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.30/1.56 none_game: option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.30/1.56 the_game: option_game > game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 0.30/1.56 ord_le1354144447real_o: ( ( variable > real ) > $o ) > ( ( variable > real ) > $o ) > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
% 0.30/1.56 ord_le2134856704game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.30/1.56 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.30/1.56 ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc1140431679riable: option_game > set_variable > produc735959047riable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc86945893e_real: set_variable_real > set_variable_real > produc2038871085e_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc544095770riable: set_variable_real > set_variable > produc1755325794riable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/1.56 produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc1400669210e_real: set_variable > set_variable_real > produc1794985442e_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc1766592463riable: set_variable > set_variable > produc432717079riable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc884810027riable: produc735959047riable > option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc702045265e_real: produc2038871085e_real > set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc944271878riable: produc1755325794riable > set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/1.56 produc893821739n_game: produc1078154247n_game > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc1800845318e_real: produc1794985442e_real > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc1300679611riable: produc432717079riable > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc284475501riable: produc735959047riable > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc220849299e_real: produc2038871085e_real > set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc1192298056riable: produc1755325794riable > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/1.56 produc293487213n_game: produc1078154247n_game > option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.30/1.56 produc2048871496e_real: produc1794985442e_real > set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc319712253riable: produc432717079riable > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.30/1.56 produc345397471riable: produc735959047riable > produc1078154247n_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.30/1.56 produc354409183n_game: produc1078154247n_game > produc735959047riable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Set_OCollect_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.30/1.56 collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/1.56 collec1702522994n_game: ( produc1078154247n_game > $o ) > set_Pr166476775n_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.30/1.56 collect_variable: ( variable > $o ) > set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Syntax_OSkip,type,
% 0.30/1.56 skip: game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Syntax_Ogame_OChoice,type,
% 0.30/1.56 choice: game > game > game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Syntax_Ogame_ODual,type,
% 0.30/1.56 dual: game > game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_Syntax_Ogame_OLoop,type,
% 0.30/1.56 loop: game > game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OChoiceo,type,
% 0.30/1.56 uSubst1484167963hoiceo: option_game > option_game > option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODualo,type,
% 0.30/1.56 uSubst1916713664_Dualo: option_game > option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OLoopo,type,
% 0.30/1.56 uSubst23177304_Loopo: option_game > option_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Oadjoint,type,
% 0.30/1.56 uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappp,type,
% 0.30/1.56 uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_member_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.30/1.56 member_variable_real: ( variable > real ) > set_variable_real > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.30/1.56 member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.30/1.56 member_variable: variable > set_variable > $o ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v_I,type,
% 0.30/1.56 i: denotational_interp ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v_U,type,
% 0.30/1.56 u: set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v_Ua____,type,
% 0.30/1.56 ua: set_variable ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v_Xa____,type,
% 0.30/1.56 xa: set_variable_real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060alpha_062_H_H____,type,
% 0.30/1.56 alpha: game ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060nu_062,type,
% 0.30/1.56 nu: variable > real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060nu_062_H____,type,
% 0.30/1.56 nu2: variable > real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060omega_062,type,
% 0.30/1.56 omega: variable > real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060omega_062_H____,type,
% 0.30/1.56 omega2: variable > real ).
% 0.30/1.56
% 0.30/1.56 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.30/1.56 sigma: produc1418842292n_game ).
% 0.30/1.56
% 0.30/1.56 thf(fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,axiom,
% 0.30/1.56 ! [X: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/1.56 = ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_1_IH_092_060alpha_062,axiom,
% 0.30/1.56 ! [X: set_variable_real] :
% 0.30/1.56 ( ( denota1419872369iation @ nu2 @ omega2 @ ua )
% 0.30/1.56 => ( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/1.56 = ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_2_uv,axiom,
% 0.30/1.56 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.30/1.56
% 0.30/1.56 thf(fact_3_snd__uminus,axiom,
% 0.30/1.56 ! [X2: produc432717079riable] :
% 0.30/1.56 ( ( produc319712253riable @ ( uminus269410190riable @ X2 ) )
% 0.30/1.56 = ( uminus1851247844riable @ ( produc319712253riable @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_4_snd__uminus,axiom,
% 0.30/1.56 ! [X2: produc1794985442e_real] :
% 0.30/1.56 ( ( produc2048871496e_real @ ( uminus7300697e_real @ X2 ) )
% 0.30/1.56 = ( uminus430703407e_real @ ( produc2048871496e_real @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_5_snd__uminus,axiom,
% 0.30/1.56 ! [X2: produc1755325794riable] :
% 0.30/1.56 ( ( produc1192298056riable @ ( uminus2115124697riable @ X2 ) )
% 0.30/1.56 = ( uminus1851247844riable @ ( produc1192298056riable @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_6_snd__uminus,axiom,
% 0.30/1.56 ! [X2: produc2038871085e_real] :
% 0.30/1.56 ( ( produc220849299e_real @ ( uminus501400228e_real @ X2 ) )
% 0.30/1.56 = ( uminus430703407e_real @ ( produc220849299e_real @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_7_def,axiom,
% 0.30/1.56 ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( dual @ alpha ) ) )
% 0.30/1.56 != none_game ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_8_ComplI,axiom,
% 0.30/1.56 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/1.56 ( ~ ( member171223600n_game @ C @ A )
% 0.30/1.56 => ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_9_ComplI,axiom,
% 0.30/1.56 ! [C: variable,A: set_variable] :
% 0.30/1.56 ( ~ ( member_variable @ C @ A )
% 0.30/1.56 => ( member_variable @ C @ ( uminus1851247844riable @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_10_ComplI,axiom,
% 0.30/1.56 ! [C: variable > real,A: set_variable_real] :
% 0.30/1.56 ( ~ ( member_variable_real @ C @ A )
% 0.30/1.56 => ( member_variable_real @ C @ ( uminus430703407e_real @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_11_Compl__iff,axiom,
% 0.30/1.56 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/1.56 ( ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) )
% 0.30/1.56 = ( ~ ( member171223600n_game @ C @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_12_Compl__iff,axiom,
% 0.30/1.56 ! [C: variable,A: set_variable] :
% 0.30/1.56 ( ( member_variable @ C @ ( uminus1851247844riable @ A ) )
% 0.30/1.56 = ( ~ ( member_variable @ C @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_13_Compl__iff,axiom,
% 0.30/1.56 ! [C: variable > real,A: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ C @ ( uminus430703407e_real @ A ) )
% 0.30/1.56 = ( ~ ( member_variable_real @ C @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_14_Compl__eq__Compl__iff,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ( uminus1851247844riable @ A )
% 0.30/1.56 = ( uminus1851247844riable @ B ) )
% 0.30/1.56 = ( A = B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_15_Compl__eq__Compl__iff,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ( uminus430703407e_real @ A )
% 0.30/1.56 = ( uminus430703407e_real @ B ) )
% 0.30/1.56 = ( A = B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_16_uminus__apply,axiom,
% 0.30/1.56 ( uminus1666842273able_o
% 0.30/1.56 = ( ^ [A2: variable > $o,X3: variable] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_17_uminus__apply,axiom,
% 0.30/1.56 ( uminus970116630real_o
% 0.30/1.56 = ( ^ [A2: ( variable > real ) > $o,X3: variable > real] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_18_double__compl,axiom,
% 0.30/1.56 ! [X2: variable > $o] :
% 0.30/1.56 ( ( uminus1666842273able_o @ ( uminus1666842273able_o @ X2 ) )
% 0.30/1.56 = X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_19_double__compl,axiom,
% 0.30/1.56 ! [X2: ( variable > real ) > $o] :
% 0.30/1.56 ( ( uminus970116630real_o @ ( uminus970116630real_o @ X2 ) )
% 0.30/1.56 = X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_20_double__compl,axiom,
% 0.30/1.56 ! [X2: set_variable_real] :
% 0.30/1.56 ( ( uminus430703407e_real @ ( uminus430703407e_real @ X2 ) )
% 0.30/1.56 = X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_21_double__compl,axiom,
% 0.30/1.56 ! [X2: set_variable] :
% 0.30/1.56 ( ( uminus1851247844riable @ ( uminus1851247844riable @ X2 ) )
% 0.30/1.56 = X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_22_vaouter,axiom,
% 0.30/1.56 denota1419872369iation @ nu @ omega @ u ).
% 0.30/1.56
% 0.30/1.56 thf(fact_23_compl__eq__compl__iff,axiom,
% 0.30/1.56 ! [X2: variable > $o,Y: variable > $o] :
% 0.30/1.56 ( ( ( uminus1666842273able_o @ X2 )
% 0.30/1.56 = ( uminus1666842273able_o @ Y ) )
% 0.30/1.56 = ( X2 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_24_compl__eq__compl__iff,axiom,
% 0.30/1.56 ! [X2: ( variable > real ) > $o,Y: ( variable > real ) > $o] :
% 0.30/1.56 ( ( ( uminus970116630real_o @ X2 )
% 0.30/1.56 = ( uminus970116630real_o @ Y ) )
% 0.30/1.56 = ( X2 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_25_compl__eq__compl__iff,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( ( uminus430703407e_real @ X2 )
% 0.30/1.56 = ( uminus430703407e_real @ Y ) )
% 0.30/1.56 = ( X2 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_26_compl__eq__compl__iff,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( ( uminus1851247844riable @ X2 )
% 0.30/1.56 = ( uminus1851247844riable @ Y ) )
% 0.30/1.56 = ( X2 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_27_usubstappp__det,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,V: set_variable] :
% 0.30/1.56 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_28_fun__Compl__def,axiom,
% 0.30/1.56 ( uminus1666842273able_o
% 0.30/1.56 = ( ^ [A2: variable > $o,X3: variable] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_29_fun__Compl__def,axiom,
% 0.30/1.56 ( uminus970116630real_o
% 0.30/1.56 = ( ^ [A2: ( variable > real ) > $o,X3: variable > real] : ( uminus_uminus_o @ ( A2 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_30_double__complement,axiom,
% 0.30/1.56 ! [A: set_variable_real] :
% 0.30/1.56 ( ( uminus430703407e_real @ ( uminus430703407e_real @ A ) )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_31_double__complement,axiom,
% 0.30/1.56 ! [A: set_variable] :
% 0.30/1.56 ( ( uminus1851247844riable @ ( uminus1851247844riable @ A ) )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_32_ComplD,axiom,
% 0.30/1.56 ! [C: produc1078154247n_game,A: set_Pr166476775n_game] :
% 0.30/1.56 ( ( member171223600n_game @ C @ ( uminus2030647006n_game @ A ) )
% 0.30/1.56 => ~ ( member171223600n_game @ C @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_33_ComplD,axiom,
% 0.30/1.56 ! [C: variable > real,A: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ C @ ( uminus430703407e_real @ A ) )
% 0.30/1.56 => ~ ( member_variable_real @ C @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_34_ComplD,axiom,
% 0.30/1.56 ! [C: variable,A: set_variable] :
% 0.30/1.56 ( ( member_variable @ C @ ( uminus1851247844riable @ A ) )
% 0.30/1.56 => ~ ( member_variable @ C @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_35_game__sem_Osimps_I7_J,axiom,
% 0.30/1.56 ! [I: denotational_interp,Alpha: game] :
% 0.30/1.56 ( ( denota1245701238me_sem @ I @ ( dual @ Alpha ) )
% 0.30/1.56 = ( ^ [X4: set_variable_real] : ( uminus430703407e_real @ ( denota1245701238me_sem @ I @ Alpha @ ( uminus430703407e_real @ X4 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_36_Dual_OIH,axiom,
% 0.30/1.56 ! [Nu: variable > real,Omega: variable > real,X: set_variable_real] :
% 0.30/1.56 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( denota1419872369iation @ Nu @ Omega @ ua )
% 0.30/1.56 => ( ( member_variable_real @ Nu @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X ) )
% 0.30/1.56 = ( member_variable_real @ Nu @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ Omega ) @ alpha @ X ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_37_game_Oinject_I7_J,axiom,
% 0.30/1.56 ! [X7: game,Y7: game] :
% 0.30/1.56 ( ( ( dual @ X7 )
% 0.30/1.56 = ( dual @ Y7 ) )
% 0.30/1.56 = ( X7 = Y7 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_38_Dual_Oprems_I2_J,axiom,
% 0.30/1.56 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.30/1.56
% 0.30/1.56 thf(fact_39_option_Oexpand,axiom,
% 0.30/1.56 ! [Option: option_game,Option2: option_game] :
% 0.30/1.56 ( ( ( Option = none_game )
% 0.30/1.56 = ( Option2 = none_game ) )
% 0.30/1.56 => ( ( ( Option != none_game )
% 0.30/1.56 => ( ( Option2 != none_game )
% 0.30/1.56 => ( ( the_game @ Option )
% 0.30/1.56 = ( the_game @ Option2 ) ) ) )
% 0.30/1.56 => ( Option = Option2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_40_usubst__game__loop,axiom,
% 0.30/1.56 ! [Nu: variable > real,Omega: variable > real,U: set_variable,Sigma: produc1418842292n_game,Alpha: game,I: denotational_interp,X: set_variable_real] :
% 0.30/1.56 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 0.30/1.56 => ( ! [Nu2: variable > real,Omega2: variable > real,X5: set_variable_real] :
% 0.30/1.56 ( ( denota1419872369iation @ Nu2 @ Omega2 @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( member_variable_real @ Nu2 @ ( denota1245701238me_sem @ I @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) @ X5 ) )
% 0.30/1.56 = ( member_variable_real @ Nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ Sigma @ I @ Omega2 ) @ Alpha @ X5 ) ) ) ) )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( member_variable_real @ Nu @ ( denota1245701238me_sem @ I @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) ) ) @ X ) )
% 0.30/1.56 = ( member_variable_real @ Nu @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ Sigma @ I @ Omega ) @ ( loop @ Alpha ) @ X ) ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_41_Uvariation__def,axiom,
% 0.30/1.56 ( denota1419872369iation
% 0.30/1.56 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 0.30/1.56 ! [I2: variable] :
% 0.30/1.56 ( ~ ( member_variable @ I2 @ U2 )
% 0.30/1.56 => ( ( Nu3 @ I2 )
% 0.30/1.56 = ( Nu4 @ I2 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_42_Uvariation__sym,axiom,
% 0.30/1.56 ( denota1419872369iation
% 0.30/1.56 = ( ^ [Omega3: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_43_Uvariation__refl,axiom,
% 0.30/1.56 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_44_Uvariation__sym__rel,axiom,
% 0.30/1.56 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 0.30/1.56 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/1.56 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_45_usubstappp__choice__conv,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.30/1.56 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) )
% 0.30/1.56 != none_game ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_46_game_Oinject_I6_J,axiom,
% 0.30/1.56 ! [X6: game,Y6: game] :
% 0.30/1.56 ( ( ( loop @ X6 )
% 0.30/1.56 = ( loop @ Y6 ) )
% 0.30/1.56 = ( X6 = Y6 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_47_game_Oinject_I4_J,axiom,
% 0.30/1.56 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 0.30/1.56 ( ( ( choice @ X41 @ X42 )
% 0.30/1.56 = ( choice @ Y41 @ Y42 ) )
% 0.30/1.56 = ( ( X41 = Y41 )
% 0.30/1.56 & ( X42 = Y42 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_48_fst__uminus,axiom,
% 0.30/1.56 ! [X2: produc432717079riable] :
% 0.30/1.56 ( ( produc1300679611riable @ ( uminus269410190riable @ X2 ) )
% 0.30/1.56 = ( uminus1851247844riable @ ( produc1300679611riable @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_49_fst__uminus,axiom,
% 0.30/1.56 ! [X2: produc1794985442e_real] :
% 0.30/1.56 ( ( produc1800845318e_real @ ( uminus7300697e_real @ X2 ) )
% 0.30/1.56 = ( uminus1851247844riable @ ( produc1800845318e_real @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_50_fst__uminus,axiom,
% 0.30/1.56 ! [X2: produc1755325794riable] :
% 0.30/1.56 ( ( produc944271878riable @ ( uminus2115124697riable @ X2 ) )
% 0.30/1.56 = ( uminus430703407e_real @ ( produc944271878riable @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_51_fst__uminus,axiom,
% 0.30/1.56 ! [X2: produc2038871085e_real] :
% 0.30/1.56 ( ( produc702045265e_real @ ( uminus501400228e_real @ X2 ) )
% 0.30/1.56 = ( uminus430703407e_real @ ( produc702045265e_real @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_52_Uvariation__univ,axiom,
% 0.30/1.56 ! [Nu: variable > real,Nu5: variable > real] :
% 0.30/1.56 ( denota1419872369iation @ Nu @ Nu5
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] : $true ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_53_game_Odistinct_I39_J,axiom,
% 0.30/1.56 ! [X41: game,X42: game,X6: game] :
% 0.30/1.56 ( ( choice @ X41 @ X42 )
% 0.30/1.56 != ( loop @ X6 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_54_uminus__set__def,axiom,
% 0.30/1.56 ( uminus2030647006n_game
% 0.30/1.56 = ( ^ [A2: set_Pr166476775n_game] :
% 0.30/1.56 ( collec1702522994n_game
% 0.30/1.56 @ ( uminus679091071game_o
% 0.30/1.56 @ ^ [X3: produc1078154247n_game] : ( member171223600n_game @ X3 @ A2 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_55_uminus__set__def,axiom,
% 0.30/1.56 ( uminus430703407e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real] :
% 0.30/1.56 ( collec633296133e_real
% 0.30/1.56 @ ( uminus970116630real_o
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A2 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_56_uminus__set__def,axiom,
% 0.30/1.56 ( uminus1851247844riable
% 0.30/1.56 = ( ^ [A2: set_variable] :
% 0.30/1.56 ( collect_variable
% 0.30/1.56 @ ( uminus1666842273able_o
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_57_Collect__neg__eq,axiom,
% 0.30/1.56 ! [P: ( variable > real ) > $o] :
% 0.30/1.56 ( ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ~ ( P @ X3 ) )
% 0.30/1.56 = ( uminus430703407e_real @ ( collec633296133e_real @ P ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_58_Collect__neg__eq,axiom,
% 0.30/1.56 ! [P: variable > $o] :
% 0.30/1.56 ( ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ~ ( P @ X3 ) )
% 0.30/1.56 = ( uminus1851247844riable @ ( collect_variable @ P ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_59_Compl__eq,axiom,
% 0.30/1.56 ( uminus2030647006n_game
% 0.30/1.56 = ( ^ [A2: set_Pr166476775n_game] :
% 0.30/1.56 ( collec1702522994n_game
% 0.30/1.56 @ ^ [X3: produc1078154247n_game] :
% 0.30/1.56 ~ ( member171223600n_game @ X3 @ A2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_60_Compl__eq,axiom,
% 0.30/1.56 ( uminus430703407e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real] :
% 0.30/1.56 ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ~ ( member_variable_real @ X3 @ A2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_61_Compl__eq,axiom,
% 0.30/1.56 ( uminus1851247844riable
% 0.30/1.56 = ( ^ [A2: set_variable] :
% 0.30/1.56 ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ~ ( member_variable @ X3 @ A2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_62_game_Odistinct_I51_J,axiom,
% 0.30/1.56 ! [X6: game,X7: game] :
% 0.30/1.56 ( ( loop @ X6 )
% 0.30/1.56 != ( dual @ X7 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_63_game_Odistinct_I41_J,axiom,
% 0.30/1.56 ! [X41: game,X42: game,X7: game] :
% 0.30/1.56 ( ( choice @ X41 @ X42 )
% 0.30/1.56 != ( dual @ X7 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_64_usubstappp__loop__conv,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/1.56 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.30/1.56 != none_game ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_65_mem__Collect__eq,axiom,
% 0.30/1.56 ! [A3: produc1078154247n_game,P: produc1078154247n_game > $o] :
% 0.30/1.56 ( ( member171223600n_game @ A3 @ ( collec1702522994n_game @ P ) )
% 0.30/1.56 = ( P @ A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_66_mem__Collect__eq,axiom,
% 0.30/1.56 ! [A3: variable > real,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ( member_variable_real @ A3 @ ( collec633296133e_real @ P ) )
% 0.30/1.56 = ( P @ A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_67_mem__Collect__eq,axiom,
% 0.30/1.56 ! [A3: variable,P: variable > $o] :
% 0.30/1.56 ( ( member_variable @ A3 @ ( collect_variable @ P ) )
% 0.30/1.56 = ( P @ A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_68_Collect__mem__eq,axiom,
% 0.30/1.56 ! [A: set_Pr166476775n_game] :
% 0.30/1.56 ( ( collec1702522994n_game
% 0.30/1.56 @ ^ [X3: produc1078154247n_game] : ( member171223600n_game @ X3 @ A ) )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_69_Collect__mem__eq,axiom,
% 0.30/1.56 ! [A: set_variable_real] :
% 0.30/1.56 ( ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A ) )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_70_Collect__mem__eq,axiom,
% 0.30/1.56 ! [A: set_variable] :
% 0.30/1.56 ( ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ A ) )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_71_Collect__cong,axiom,
% 0.30/1.56 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/1.56 ( ! [X8: variable > real] :
% 0.30/1.56 ( ( P @ X8 )
% 0.30/1.56 = ( Q @ X8 ) )
% 0.30/1.56 => ( ( collec633296133e_real @ P )
% 0.30/1.56 = ( collec633296133e_real @ Q ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_72_Collect__cong,axiom,
% 0.30/1.56 ! [P: variable > $o,Q: variable > $o] :
% 0.30/1.56 ( ! [X8: variable] :
% 0.30/1.56 ( ( P @ X8 )
% 0.30/1.56 = ( Q @ X8 ) )
% 0.30/1.56 => ( ( collect_variable @ P )
% 0.30/1.56 = ( collect_variable @ Q ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_73_skip__id,axiom,
% 0.30/1.56 ! [I: denotational_interp,X: set_variable_real] :
% 0.30/1.56 ( ( denota1245701238me_sem @ I @ skip @ X )
% 0.30/1.56 = X ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_74_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc432717079riable,Q2: produc432717079riable] :
% 0.30/1.56 ( ( ( produc1300679611riable @ P2 )
% 0.30/1.56 = ( produc1300679611riable @ Q2 ) )
% 0.30/1.56 => ( ( ( produc319712253riable @ P2 )
% 0.30/1.56 = ( produc319712253riable @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_75_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc1794985442e_real,Q2: produc1794985442e_real] :
% 0.30/1.56 ( ( ( produc1800845318e_real @ P2 )
% 0.30/1.56 = ( produc1800845318e_real @ Q2 ) )
% 0.30/1.56 => ( ( ( produc2048871496e_real @ P2 )
% 0.30/1.56 = ( produc2048871496e_real @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_76_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc1755325794riable,Q2: produc1755325794riable] :
% 0.30/1.56 ( ( ( produc944271878riable @ P2 )
% 0.30/1.56 = ( produc944271878riable @ Q2 ) )
% 0.30/1.56 => ( ( ( produc1192298056riable @ P2 )
% 0.30/1.56 = ( produc1192298056riable @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_77_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc2038871085e_real,Q2: produc2038871085e_real] :
% 0.30/1.56 ( ( ( produc702045265e_real @ P2 )
% 0.30/1.56 = ( produc702045265e_real @ Q2 ) )
% 0.30/1.56 => ( ( ( produc220849299e_real @ P2 )
% 0.30/1.56 = ( produc220849299e_real @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_78_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc735959047riable,Q2: produc735959047riable] :
% 0.30/1.56 ( ( ( produc884810027riable @ P2 )
% 0.30/1.56 = ( produc884810027riable @ Q2 ) )
% 0.30/1.56 => ( ( ( produc284475501riable @ P2 )
% 0.30/1.56 = ( produc284475501riable @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_79_prod__eqI,axiom,
% 0.30/1.56 ! [P2: produc1078154247n_game,Q2: produc1078154247n_game] :
% 0.30/1.56 ( ( ( produc893821739n_game @ P2 )
% 0.30/1.56 = ( produc893821739n_game @ Q2 ) )
% 0.30/1.56 => ( ( ( produc293487213n_game @ P2 )
% 0.30/1.56 = ( produc293487213n_game @ Q2 ) )
% 0.30/1.56 => ( P2 = Q2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_80_exE__realizer_H,axiom,
% 0.30/1.56 ! [P: set_variable_real > set_variable_real > $o,P2: produc2038871085e_real] :
% 0.30/1.56 ( ( P @ ( produc220849299e_real @ P2 ) @ ( produc702045265e_real @ P2 ) )
% 0.30/1.56 => ~ ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_81_exE__realizer_H,axiom,
% 0.30/1.56 ! [P: set_variable > option_game > $o,P2: produc735959047riable] :
% 0.30/1.56 ( ( P @ ( produc284475501riable @ P2 ) @ ( produc884810027riable @ P2 ) )
% 0.30/1.56 => ~ ! [X8: option_game,Y2: set_variable] :
% 0.30/1.56 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_82_exE__realizer_H,axiom,
% 0.30/1.56 ! [P: option_game > set_variable > $o,P2: produc1078154247n_game] :
% 0.30/1.56 ( ( P @ ( produc293487213n_game @ P2 ) @ ( produc893821739n_game @ P2 ) )
% 0.30/1.56 => ~ ! [X8: set_variable,Y2: option_game] :
% 0.30/1.56 ~ ( P @ Y2 @ X8 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_83_prod_Oexpand,axiom,
% 0.30/1.56 ! [Prod: produc1078154247n_game,Prod2: produc1078154247n_game] :
% 0.30/1.56 ( ( ( ( produc893821739n_game @ Prod )
% 0.30/1.56 = ( produc893821739n_game @ Prod2 ) )
% 0.30/1.56 & ( ( produc293487213n_game @ Prod )
% 0.30/1.56 = ( produc293487213n_game @ Prod2 ) ) )
% 0.30/1.56 => ( Prod = Prod2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_84_prod__eq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: produc1078154247n_game,Z: produc1078154247n_game] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [S: produc1078154247n_game,T: produc1078154247n_game] :
% 0.30/1.56 ( ( ( produc893821739n_game @ S )
% 0.30/1.56 = ( produc893821739n_game @ T ) )
% 0.30/1.56 & ( ( produc293487213n_game @ S )
% 0.30/1.56 = ( produc293487213n_game @ T ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_85_uminus__prod__def,axiom,
% 0.30/1.56 ( uminus501400228e_real
% 0.30/1.56 = ( ^ [X3: produc2038871085e_real] : ( produc86945893e_real @ ( uminus430703407e_real @ ( produc702045265e_real @ X3 ) ) @ ( uminus430703407e_real @ ( produc220849299e_real @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_86_uminus__prod__def,axiom,
% 0.30/1.56 ( uminus2115124697riable
% 0.30/1.56 = ( ^ [X3: produc1755325794riable] : ( produc544095770riable @ ( uminus430703407e_real @ ( produc944271878riable @ X3 ) ) @ ( uminus1851247844riable @ ( produc1192298056riable @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_87_uminus__prod__def,axiom,
% 0.30/1.56 ( uminus7300697e_real
% 0.30/1.56 = ( ^ [X3: produc1794985442e_real] : ( produc1400669210e_real @ ( uminus1851247844riable @ ( produc1800845318e_real @ X3 ) ) @ ( uminus430703407e_real @ ( produc2048871496e_real @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_88_uminus__prod__def,axiom,
% 0.30/1.56 ( uminus269410190riable
% 0.30/1.56 = ( ^ [X3: produc432717079riable] : ( produc1766592463riable @ ( uminus1851247844riable @ ( produc1300679611riable @ X3 ) ) @ ( uminus1851247844riable @ ( produc319712253riable @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_89_usubstappp__antimon,axiom,
% 0.30/1.56 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.30/1.56 ( ( ord_le282106107riable @ V @ U )
% 0.30/1.56 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 != none_game )
% 0.30/1.56 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.30/1.56 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_90_exists__diff,axiom,
% 0.30/1.56 ! [P: set_variable_real > $o] :
% 0.30/1.56 ( ( ? [S2: set_variable_real] : ( P @ ( uminus430703407e_real @ S2 ) ) )
% 0.30/1.56 = ( ? [X9: set_variable_real] : ( P @ X9 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_91_exists__diff,axiom,
% 0.30/1.56 ! [P: set_variable > $o] :
% 0.30/1.56 ( ( ? [S2: set_variable] : ( P @ ( uminus1851247844riable @ S2 ) ) )
% 0.30/1.56 = ( ? [X9: set_variable] : ( P @ X9 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_92_uminus__Pair,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( uminus501400228e_real @ ( produc86945893e_real @ A3 @ B2 ) )
% 0.30/1.56 = ( produc86945893e_real @ ( uminus430703407e_real @ A3 ) @ ( uminus430703407e_real @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_93_uminus__Pair,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable] :
% 0.30/1.56 ( ( uminus2115124697riable @ ( produc544095770riable @ A3 @ B2 ) )
% 0.30/1.56 = ( produc544095770riable @ ( uminus430703407e_real @ A3 ) @ ( uminus1851247844riable @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_94_uminus__Pair,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable_real] :
% 0.30/1.56 ( ( uminus7300697e_real @ ( produc1400669210e_real @ A3 @ B2 ) )
% 0.30/1.56 = ( produc1400669210e_real @ ( uminus1851247844riable @ A3 ) @ ( uminus430703407e_real @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_95_uminus__Pair,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( uminus269410190riable @ ( produc1766592463riable @ A3 @ B2 ) )
% 0.30/1.56 = ( produc1766592463riable @ ( uminus1851247844riable @ A3 ) @ ( uminus1851247844riable @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_96_prod_Oinject,axiom,
% 0.30/1.56 ! [X1: set_variable,X22: option_game,Y1: set_variable,Y22: option_game] :
% 0.30/1.56 ( ( ( produc1149443391n_game @ X1 @ X22 )
% 0.30/1.56 = ( produc1149443391n_game @ Y1 @ Y22 ) )
% 0.30/1.56 = ( ( X1 = Y1 )
% 0.30/1.56 & ( X22 = Y22 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_97_old_Oprod_Oinject,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: option_game,A4: set_variable,B3: option_game] :
% 0.30/1.56 ( ( ( produc1149443391n_game @ A3 @ B2 )
% 0.30/1.56 = ( produc1149443391n_game @ A4 @ B3 ) )
% 0.30/1.56 = ( ( A3 = A4 )
% 0.30/1.56 & ( B2 = B3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_98_subset__antisym,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ( ord_le282106107riable @ B @ A )
% 0.30/1.56 => ( A = B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_99_subset__antisym,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B @ A )
% 0.30/1.56 => ( A = B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_100_subsetI,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ! [X8: variable] :
% 0.30/1.56 ( ( member_variable @ X8 @ A )
% 0.30/1.56 => ( member_variable @ X8 @ B ) )
% 0.30/1.56 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_101_subsetI,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ! [X8: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X8 @ A )
% 0.30/1.56 => ( member_variable_real @ X8 @ B ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_102_compl__le__compl__iff,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( uminus1851247844riable @ X2 ) @ ( uminus1851247844riable @ Y ) )
% 0.30/1.56 = ( ord_le282106107riable @ Y @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_103_compl__le__compl__iff,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ X2 ) @ ( uminus430703407e_real @ Y ) )
% 0.30/1.56 = ( ord_le1113654598e_real @ Y @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_104_Compl__subset__Compl__iff,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( uminus1851247844riable @ A ) @ ( uminus1851247844riable @ B ) )
% 0.30/1.56 = ( ord_le282106107riable @ B @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_105_Compl__subset__Compl__iff,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ A ) @ ( uminus430703407e_real @ B ) )
% 0.30/1.56 = ( ord_le1113654598e_real @ B @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_106_Compl__anti__mono,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ord_le282106107riable @ ( uminus1851247844riable @ B ) @ ( uminus1851247844riable @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_107_Compl__anti__mono,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ B ) @ ( uminus430703407e_real @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_108_prod_Ocollapse,axiom,
% 0.30/1.56 ! [Prod: produc1078154247n_game] :
% 0.30/1.56 ( ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) )
% 0.30/1.56 = Prod ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_109_surj__pair,axiom,
% 0.30/1.56 ! [P2: produc1078154247n_game] :
% 0.30/1.56 ? [X8: set_variable,Y2: option_game] :
% 0.30/1.56 ( P2
% 0.30/1.56 = ( produc1149443391n_game @ X8 @ Y2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_110_prod__cases,axiom,
% 0.30/1.56 ! [P: produc1078154247n_game > $o,P2: produc1078154247n_game] :
% 0.30/1.56 ( ! [A5: set_variable,B4: option_game] : ( P @ ( produc1149443391n_game @ A5 @ B4 ) )
% 0.30/1.56 => ( P @ P2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_111_Pair__inject,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: option_game,A4: set_variable,B3: option_game] :
% 0.30/1.56 ( ( ( produc1149443391n_game @ A3 @ B2 )
% 0.30/1.56 = ( produc1149443391n_game @ A4 @ B3 ) )
% 0.30/1.56 => ~ ( ( A3 = A4 )
% 0.30/1.56 => ( B2 != B3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_112_old_Oprod_Oexhaust,axiom,
% 0.30/1.56 ! [Y: produc1078154247n_game] :
% 0.30/1.56 ~ ! [A5: set_variable,B4: option_game] :
% 0.30/1.56 ( Y
% 0.30/1.56 != ( produc1149443391n_game @ A5 @ B4 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_113_old_Oprod_Oinducts,axiom,
% 0.30/1.56 ! [P: produc1078154247n_game > $o,Prod: produc1078154247n_game] :
% 0.30/1.56 ( ! [A5: set_variable,B4: option_game] : ( P @ ( produc1149443391n_game @ A5 @ B4 ) )
% 0.30/1.56 => ( P @ Prod ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_114_Collect__mono__iff,axiom,
% 0.30/1.56 ! [P: variable > $o,Q: variable > $o] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 0.30/1.56 = ( ! [X3: variable] :
% 0.30/1.56 ( ( P @ X3 )
% 0.30/1.56 => ( Q @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_115_Collect__mono__iff,axiom,
% 0.30/1.56 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) )
% 0.30/1.56 = ( ! [X3: variable > real] :
% 0.30/1.56 ( ( P @ X3 )
% 0.30/1.56 => ( Q @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_116_set__eq__subset,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A2 @ B5 )
% 0.30/1.56 & ( ord_le282106107riable @ B5 @ A2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_117_set__eq__subset,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A2 @ B5 )
% 0.30/1.56 & ( ord_le1113654598e_real @ B5 @ A2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_118_subset__trans,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ( ord_le282106107riable @ B @ C2 )
% 0.30/1.56 => ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_119_subset__trans,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real,C2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B @ C2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ A @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_120_Collect__mono,axiom,
% 0.30/1.56 ! [P: variable > $o,Q: variable > $o] :
% 0.30/1.56 ( ! [X8: variable] :
% 0.30/1.56 ( ( P @ X8 )
% 0.30/1.56 => ( Q @ X8 ) )
% 0.30/1.56 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_121_Collect__mono,axiom,
% 0.30/1.56 ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/1.56 ( ! [X8: variable > real] :
% 0.30/1.56 ( ( P @ X8 )
% 0.30/1.56 => ( Q @ X8 ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_122_subset__refl,axiom,
% 0.30/1.56 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_123_subset__refl,axiom,
% 0.30/1.56 ! [A: set_variable_real] : ( ord_le1113654598e_real @ A @ A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_124_subset__iff,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/1.56 ! [T: variable] :
% 0.30/1.56 ( ( member_variable @ T @ A2 )
% 0.30/1.56 => ( member_variable @ T @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_125_subset__iff,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/1.56 ! [T: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ T @ A2 )
% 0.30/1.56 => ( member_variable_real @ T @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_126_equalityD2,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ( ord_le282106107riable @ B @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_127_equalityD2,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ( ord_le1113654598e_real @ B @ A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_128_equalityD1,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_129_equalityD1,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ( ord_le1113654598e_real @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_130_subset__eq,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/1.56 ! [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A2 )
% 0.30/1.56 => ( member_variable @ X3 @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_131_subset__eq,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/1.56 ! [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ A2 )
% 0.30/1.56 => ( member_variable_real @ X3 @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_132_equalityE,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ~ ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_133_equalityE,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( A = B )
% 0.30/1.56 => ~ ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ~ ( ord_le1113654598e_real @ B @ A ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_134_subsetD,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,C: variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ( member_variable @ C @ A )
% 0.30/1.56 => ( member_variable @ C @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_135_subsetD,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real,C: variable > real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ( member_variable_real @ C @ A )
% 0.30/1.56 => ( member_variable_real @ C @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_136_in__mono,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,X2: variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ( member_variable @ X2 @ A )
% 0.30/1.56 => ( member_variable @ X2 @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_137_in__mono,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real,X2: variable > real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ( member_variable_real @ X2 @ A )
% 0.30/1.56 => ( member_variable_real @ X2 @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_138_Collect__subset,axiom,
% 0.30/1.56 ! [A: set_variable,P: variable > $o] :
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) )
% 0.30/1.56 @ A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_139_Collect__subset,axiom,
% 0.30/1.56 ! [A: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) )
% 0.30/1.56 @ A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_140_fst__eqD,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: option_game,A3: set_variable] :
% 0.30/1.56 ( ( ( produc893821739n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/1.56 = A3 )
% 0.30/1.56 => ( X2 = A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_141_fst__conv,axiom,
% 0.30/1.56 ! [X1: set_variable,X22: option_game] :
% 0.30/1.56 ( ( produc893821739n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.30/1.56 = X1 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_142_snd__conv,axiom,
% 0.30/1.56 ! [X1: set_variable,X22: option_game] :
% 0.30/1.56 ( ( produc293487213n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.30/1.56 = X22 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_143_snd__eqD,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: option_game,A3: option_game] :
% 0.30/1.56 ( ( ( produc293487213n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/1.56 = A3 )
% 0.30/1.56 => ( Y = A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_144_compl__le__swap2,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( uminus1851247844riable @ Y ) @ X2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( uminus1851247844riable @ X2 ) @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_145_compl__le__swap2,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ Y ) @ X2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ X2 ) @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_146_compl__le__swap1,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ Y @ ( uminus1851247844riable @ X2 ) )
% 0.30/1.56 => ( ord_le282106107riable @ X2 @ ( uminus1851247844riable @ Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_147_compl__le__swap1,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ Y @ ( uminus430703407e_real @ X2 ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ X2 @ ( uminus430703407e_real @ Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_148_compl__mono,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/1.56 => ( ord_le282106107riable @ ( uminus1851247844riable @ Y ) @ ( uminus1851247844riable @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_149_compl__mono,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( uminus430703407e_real @ Y ) @ ( uminus430703407e_real @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_150_fst__pair,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: option_game] :
% 0.30/1.56 ( ( produc893821739n_game @ ( produc1149443391n_game @ A3 @ B2 ) )
% 0.30/1.56 = A3 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_151_snd__pair,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: option_game] :
% 0.30/1.56 ( ( produc293487213n_game @ ( produc1149443391n_game @ A3 @ B2 ) )
% 0.30/1.56 = B2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_152_surjective__pairing,axiom,
% 0.30/1.56 ! [T2: produc1078154247n_game] :
% 0.30/1.56 ( T2
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ T2 ) @ ( produc293487213n_game @ T2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_153_prod_Oexhaust__sel,axiom,
% 0.30/1.56 ! [Prod: produc1078154247n_game] :
% 0.30/1.56 ( Prod
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_154_conjI__realizer,axiom,
% 0.30/1.56 ! [P: set_variable > $o,P2: set_variable,Q: option_game > $o,Q2: option_game] :
% 0.30/1.56 ( ( P @ P2 )
% 0.30/1.56 => ( ( Q @ Q2 )
% 0.30/1.56 => ( ( P @ ( produc893821739n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) )
% 0.30/1.56 & ( Q @ ( produc293487213n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_155_exI__realizer,axiom,
% 0.30/1.56 ! [P: option_game > set_variable > $o,Y: option_game,X2: set_variable] :
% 0.30/1.56 ( ( P @ Y @ X2 )
% 0.30/1.56 => ( P @ ( produc293487213n_game @ ( produc1149443391n_game @ X2 @ Y ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ X2 @ Y ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_156_Uvariation__mon,axiom,
% 0.30/1.56 ! [U: set_variable,V: set_variable,Omega: variable > real,Nu: variable > real] :
% 0.30/1.56 ( ( ord_le282106107riable @ U @ V )
% 0.30/1.56 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.30/1.56 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_157_usubstappp__fst__mon,axiom,
% 0.30/1.56 ! [U: set_variable,V: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.30/1.56 ( ( ord_le282106107riable @ U @ V )
% 0.30/1.56 => ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_158_usubst__taboos__mon,axiom,
% 0.30/1.56 ! [U: set_variable,Sigma: produc1418842292n_game,Alpha: game] : ( ord_le282106107riable @ U @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_159_usubstappp__dual,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/1.56 ( ( uSubst516392814stappp @ Sigma @ U @ ( dual @ Alpha ) )
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_160_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/1.56 ! [P: set_variable > option_game > $o,X2: set_variable,Y: option_game,A3: produc1078154247n_game] :
% 0.30/1.56 ( ( P @ X2 @ Y )
% 0.30/1.56 => ( ( A3
% 0.30/1.56 = ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/1.56 => ( P @ ( produc893821739n_game @ A3 ) @ ( produc293487213n_game @ A3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_161_usubstappp_Osimps_I7_J,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/1.56 ( ( uSubst516392814stappp @ Sigma @ U @ ( dual @ Alpha ) )
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst1916713664_Dualo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_162_usubstappp_Osimps_I6_J,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/1.56 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_163_usubstappp__loop,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.30/1.56 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.30/1.56 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_164_order__refl,axiom,
% 0.30/1.56 ! [X2: set_variable] : ( ord_le282106107riable @ X2 @ X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_165_order__refl,axiom,
% 0.30/1.56 ! [X2: set_variable_real] : ( ord_le1113654598e_real @ X2 @ X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_166_monotone,axiom,
% 0.30/1.56 ! [X: set_variable_real,Y4: set_variable_real,I: denotational_interp,Alpha: game] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X @ Y4 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( denota1245701238me_sem @ I @ Alpha @ X ) @ ( denota1245701238me_sem @ I @ Alpha @ Y4 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_167_less__eq__set__def,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/1.56 ( ord_le1407353162able_o
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 )
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_168_less__eq__set__def,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/1.56 ( ord_le1354144447real_o
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ A2 )
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ B5 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_169_Loopo__undef,axiom,
% 0.30/1.56 ! [Alpha: option_game] :
% 0.30/1.56 ( ( ( uSubst23177304_Loopo @ Alpha )
% 0.30/1.56 = none_game )
% 0.30/1.56 = ( Alpha = none_game ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_170_Dualo__undef,axiom,
% 0.30/1.56 ! [Alpha: option_game] :
% 0.30/1.56 ( ( ( uSubst1916713664_Dualo @ Alpha )
% 0.30/1.56 = none_game )
% 0.30/1.56 = ( Alpha = none_game ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_171_Loopo_Osimps_I2_J,axiom,
% 0.30/1.56 ( ( uSubst23177304_Loopo @ none_game )
% 0.30/1.56 = none_game ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_172_Dualo_Osimps_I2_J,axiom,
% 0.30/1.56 ( ( uSubst1916713664_Dualo @ none_game )
% 0.30/1.56 = none_game ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_173_dual__order_Oantisym,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( A3 = B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_174_dual__order_Oantisym,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( A3 = B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_175_dual__order_Oeq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B6 @ A6 )
% 0.30/1.56 & ( ord_le282106107riable @ A6 @ B6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_176_dual__order_Oeq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B6 @ A6 )
% 0.30/1.56 & ( ord_le1113654598e_real @ A6 @ B6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_177_dual__order_Otrans,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le282106107riable @ C @ B2 )
% 0.30/1.56 => ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_178_dual__order_Otrans,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ C @ B2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_179_dual__order_Orefl,axiom,
% 0.30/1.56 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_180_dual__order_Orefl,axiom,
% 0.30/1.56 ! [A3: set_variable_real] : ( ord_le1113654598e_real @ A3 @ A3 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_181_order__trans,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/1.56 => ( ( ord_le282106107riable @ Y @ Z2 )
% 0.30/1.56 => ( ord_le282106107riable @ X2 @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_182_order__trans,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real,Z2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ Y @ Z2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ X2 @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_183_order__class_Oorder_Oantisym,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( A3 = B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_184_order__class_Oorder_Oantisym,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( A3 = B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_185_ord__le__eq__trans,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( B2 = C )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_186_ord__le__eq__trans,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( B2 = C )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_187_ord__eq__le__trans,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( A3 = B2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_188_ord__eq__le__trans,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( A3 = B2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_189_order__class_Oorder_Oeq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A6 @ B6 )
% 0.30/1.56 & ( ord_le282106107riable @ B6 @ A6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_190_order__class_Oorder_Oeq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A6 @ B6 )
% 0.30/1.56 & ( ord_le1113654598e_real @ B6 @ A6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_191_antisym__conv,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/1.56 = ( X2 = Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_192_antisym__conv,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/1.56 = ( X2 = Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_193_order_Otrans,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_194_order_Otrans,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_195_eq__refl,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( X2 = Y )
% 0.30/1.56 => ( ord_le282106107riable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_196_eq__refl,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( X2 = Y )
% 0.30/1.56 => ( ord_le1113654598e_real @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_197_antisym,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/1.56 => ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/1.56 => ( X2 = Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_198_antisym,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/1.56 => ( X2 = Y ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_199_eq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable,Z: set_variable] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [X3: set_variable,Y5: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X3 @ Y5 )
% 0.30/1.56 & ( ord_le282106107riable @ Y5 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_200_eq__iff,axiom,
% 0.30/1.56 ( ( ^ [Y3: set_variable_real,Z: set_variable_real] : ( Y3 = Z ) )
% 0.30/1.56 = ( ^ [X3: set_variable_real,Y5: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X3 @ Y5 )
% 0.30/1.56 & ( ord_le1113654598e_real @ Y5 @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_201_ord__le__eq__subst,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ( F @ B2 )
% 0.30/1.56 = C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_202_ord__le__eq__subst,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ( F @ B2 )
% 0.30/1.56 = C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_203_ord__le__eq__subst,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ( F @ B2 )
% 0.30/1.56 = C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_204_ord__le__eq__subst,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ( F @ B2 )
% 0.30/1.56 = C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_205_ord__eq__le__subst,axiom,
% 0.30/1.56 ! [A3: set_variable,F: set_variable > set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_206_ord__eq__le__subst,axiom,
% 0.30/1.56 ! [A3: set_variable_real,F: set_variable > set_variable_real,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_207_ord__eq__le__subst,axiom,
% 0.30/1.56 ! [A3: set_variable,F: set_variable_real > set_variable,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_208_ord__eq__le__subst,axiom,
% 0.30/1.56 ! [A3: set_variable_real,F: set_variable_real > set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_209_order__subst2,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ ( F @ B2 ) @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_210_order__subst2,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,F: set_variable > set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ ( F @ B2 ) @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_211_order__subst2,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ ( F @ B2 ) @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_212_order__subst2,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,F: set_variable_real > set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ ( F @ B2 ) @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_213_order__subst1,axiom,
% 0.30/1.56 ! [A3: set_variable,F: set_variable > set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_214_order__subst1,axiom,
% 0.30/1.56 ! [A3: set_variable,F: set_variable_real > set_variable,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_215_order__subst1,axiom,
% 0.30/1.56 ! [A3: set_variable_real,F: set_variable > set_variable_real,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_216_order__subst1,axiom,
% 0.30/1.56 ! [A3: set_variable_real,F: set_variable_real > set_variable_real,B2: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ ( F @ B2 ) )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ C )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X8 @ Y2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ X8 ) @ ( F @ Y2 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_217_subset__CollectI,axiom,
% 0.30/1.56 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 0.30/1.56 ( ( ord_le282106107riable @ B @ A )
% 0.30/1.56 => ( ! [X8: variable] :
% 0.30/1.56 ( ( member_variable @ X8 @ B )
% 0.30/1.56 => ( ( Q @ X8 )
% 0.30/1.56 => ( P @ X8 ) ) )
% 0.30/1.56 => ( ord_le282106107riable
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ B )
% 0.30/1.56 & ( Q @ X3 ) ) )
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_218_subset__CollectI,axiom,
% 0.30/1.56 ! [B: set_variable_real,A: set_variable_real,Q: ( variable > real ) > $o,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/1.56 => ( ! [X8: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X8 @ B )
% 0.30/1.56 => ( ( Q @ X8 )
% 0.30/1.56 => ( P @ X8 ) ) )
% 0.30/1.56 => ( ord_le1113654598e_real
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ B )
% 0.30/1.56 & ( Q @ X3 ) ) )
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_219_subset__Collect__iff,axiom,
% 0.30/1.56 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 0.30/1.56 ( ( ord_le282106107riable @ B @ A )
% 0.30/1.56 => ( ( ord_le282106107riable @ B
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) ) )
% 0.30/1.56 = ( ! [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ B )
% 0.30/1.56 => ( P @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_220_subset__Collect__iff,axiom,
% 0.30/1.56 ! [B: set_variable_real,A: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) ) ) )
% 0.30/1.56 = ( ! [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ B )
% 0.30/1.56 => ( P @ X3 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_221_sndI,axiom,
% 0.30/1.56 ! [X2: produc1078154247n_game,Y: set_variable,Z2: option_game] :
% 0.30/1.56 ( ( X2
% 0.30/1.56 = ( produc1149443391n_game @ Y @ Z2 ) )
% 0.30/1.56 => ( ( produc293487213n_game @ X2 )
% 0.30/1.56 = Z2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_222_eq__snd__iff,axiom,
% 0.30/1.56 ! [B2: option_game,P2: produc1078154247n_game] :
% 0.30/1.56 ( ( B2
% 0.30/1.56 = ( produc293487213n_game @ P2 ) )
% 0.30/1.56 = ( ? [A6: set_variable] :
% 0.30/1.56 ( P2
% 0.30/1.56 = ( produc1149443391n_game @ A6 @ B2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_223_eq__fst__iff,axiom,
% 0.30/1.56 ! [A3: set_variable,P2: produc1078154247n_game] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( produc893821739n_game @ P2 ) )
% 0.30/1.56 = ( ? [B6: option_game] :
% 0.30/1.56 ( P2
% 0.30/1.56 = ( produc1149443391n_game @ A3 @ B6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_224_fstI,axiom,
% 0.30/1.56 ! [X2: produc1078154247n_game,Y: set_variable,Z2: option_game] :
% 0.30/1.56 ( ( X2
% 0.30/1.56 = ( produc1149443391n_game @ Y @ Z2 ) )
% 0.30/1.56 => ( ( produc893821739n_game @ X2 )
% 0.30/1.56 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_225_pred__subset__eq,axiom,
% 0.30/1.56 ! [R: set_variable,S3: set_variable] :
% 0.30/1.56 ( ( ord_le1407353162able_o
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ R )
% 0.30/1.56 @ ^ [X3: variable] : ( member_variable @ X3 @ S3 ) )
% 0.30/1.56 = ( ord_le282106107riable @ R @ S3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_226_pred__subset__eq,axiom,
% 0.30/1.56 ! [R: set_variable_real,S3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1354144447real_o
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ R )
% 0.30/1.56 @ ^ [X3: variable > real] : ( member_variable_real @ X3 @ S3 ) )
% 0.30/1.56 = ( ord_le1113654598e_real @ R @ S3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_227_Collect__restrict,axiom,
% 0.30/1.56 ! [X: set_variable,P: variable > $o] :
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ X )
% 0.30/1.56 & ( P @ X3 ) ) )
% 0.30/1.56 @ X ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_228_Collect__restrict,axiom,
% 0.30/1.56 ! [X: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ X )
% 0.30/1.56 & ( P @ X3 ) ) )
% 0.30/1.56 @ X ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_229_subrelI,axiom,
% 0.30/1.56 ! [R2: set_Pr166476775n_game,S4: set_Pr166476775n_game] :
% 0.30/1.56 ( ! [X8: set_variable,Y2: option_game] :
% 0.30/1.56 ( ( member171223600n_game @ ( produc1149443391n_game @ X8 @ Y2 ) @ R2 )
% 0.30/1.56 => ( member171223600n_game @ ( produc1149443391n_game @ X8 @ Y2 ) @ S4 ) )
% 0.30/1.56 => ( ord_le17855367n_game @ R2 @ S4 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_230_ssubst__Pair__rhs,axiom,
% 0.30/1.56 ! [R2: set_variable,S4: option_game,R: set_Pr166476775n_game,S5: option_game] :
% 0.30/1.56 ( ( member171223600n_game @ ( produc1149443391n_game @ R2 @ S4 ) @ R )
% 0.30/1.56 => ( ( S5 = S4 )
% 0.30/1.56 => ( member171223600n_game @ ( produc1149443391n_game @ R2 @ S5 ) @ R ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_231_pred__subset__eq2,axiom,
% 0.30/1.56 ! [R: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 0.30/1.56 ( ( ord_le2134856704game_o
% 0.30/1.56 @ ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ R )
% 0.30/1.56 @ ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ S3 ) )
% 0.30/1.56 = ( ord_le17855367n_game @ R @ S3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_232_pred__equals__eq2,axiom,
% 0.30/1.56 ! [R: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 0.30/1.56 ( ( ( ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ R ) )
% 0.30/1.56 = ( ^ [X3: set_variable,Y5: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y5 ) @ S3 ) ) )
% 0.30/1.56 = ( R = S3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_233_prop__restrict,axiom,
% 0.30/1.56 ! [X2: variable,Z3: set_variable,X: set_variable,P: variable > $o] :
% 0.30/1.56 ( ( member_variable @ X2 @ Z3 )
% 0.30/1.56 => ( ( ord_le282106107riable @ Z3
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ X )
% 0.30/1.56 & ( P @ X3 ) ) ) )
% 0.30/1.56 => ( P @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_234_prop__restrict,axiom,
% 0.30/1.56 ! [X2: variable > real,Z3: set_variable_real,X: set_variable_real,P: ( variable > real ) > $o] :
% 0.30/1.56 ( ( member_variable_real @ X2 @ Z3 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ Z3
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( member_variable_real @ X3 @ X )
% 0.30/1.56 & ( P @ X3 ) ) ) )
% 0.30/1.56 => ( P @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_235_conj__subset__def,axiom,
% 0.30/1.56 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 0.30/1.56 ( ( ord_le282106107riable @ A
% 0.30/1.56 @ ( collect_variable
% 0.30/1.56 @ ^ [X3: variable] :
% 0.30/1.56 ( ( P @ X3 )
% 0.30/1.56 & ( Q @ X3 ) ) ) )
% 0.30/1.56 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 0.30/1.56 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_236_conj__subset__def,axiom,
% 0.30/1.56 ! [A: set_variable_real,P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A
% 0.30/1.56 @ ( collec633296133e_real
% 0.30/1.56 @ ^ [X3: variable > real] :
% 0.30/1.56 ( ( P @ X3 )
% 0.30/1.56 & ( Q @ X3 ) ) ) )
% 0.30/1.56 = ( ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ P ) )
% 0.30/1.56 & ( ord_le1113654598e_real @ A @ ( collec633296133e_real @ Q ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_237_prod_Oswap__def,axiom,
% 0.30/1.56 ( produc345397471riable
% 0.30/1.56 = ( ^ [P3: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ P3 ) @ ( produc884810027riable @ P3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_238_prod_Oswap__def,axiom,
% 0.30/1.56 ( produc354409183n_game
% 0.30/1.56 = ( ^ [P3: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ P3 ) @ ( produc893821739n_game @ P3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_239_swap__simp,axiom,
% 0.30/1.56 ! [X2: option_game,Y: set_variable] :
% 0.30/1.56 ( ( produc345397471riable @ ( produc1140431679riable @ X2 @ Y ) )
% 0.30/1.56 = ( produc1149443391n_game @ Y @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_240_swap__simp,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: option_game] :
% 0.30/1.56 ( ( produc354409183n_game @ ( produc1149443391n_game @ X2 @ Y ) )
% 0.30/1.56 = ( produc1140431679riable @ Y @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_241_snd__swap,axiom,
% 0.30/1.56 ! [X2: produc1078154247n_game] :
% 0.30/1.56 ( ( produc284475501riable @ ( produc354409183n_game @ X2 ) )
% 0.30/1.56 = ( produc893821739n_game @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_242_snd__swap,axiom,
% 0.30/1.56 ! [X2: produc735959047riable] :
% 0.30/1.56 ( ( produc293487213n_game @ ( produc345397471riable @ X2 ) )
% 0.30/1.56 = ( produc884810027riable @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_243_fst__swap,axiom,
% 0.30/1.56 ! [X2: produc735959047riable] :
% 0.30/1.56 ( ( produc893821739n_game @ ( produc345397471riable @ X2 ) )
% 0.30/1.56 = ( produc284475501riable @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_244_fst__swap,axiom,
% 0.30/1.56 ! [X2: produc1078154247n_game] :
% 0.30/1.56 ( ( produc884810027riable @ ( produc354409183n_game @ X2 ) )
% 0.30/1.56 = ( produc293487213n_game @ X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_245_usubstappp__choice,axiom,
% 0.30/1.56 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.30/1.56 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.30/1.56 = ( produc1149443391n_game @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) ) ) @ ( uSubst1484167963hoiceo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_246_sup_Oidem,axiom,
% 0.30/1.56 ! [A3: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A3 @ A3 )
% 0.30/1.56 = A3 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_247_sup__idem,axiom,
% 0.30/1.56 ! [X2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ X2 @ X2 )
% 0.30/1.56 = X2 ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_248_sup_Oleft__idem,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ A3 @ B2 ) )
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_249_sup__left__idem,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) )
% 0.30/1.56 = ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_250_sup_Oright__idem,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A3 @ B2 ) @ B2 )
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_251_UnCI,axiom,
% 0.30/1.56 ! [C: variable > real,B: set_variable_real,A: set_variable_real] :
% 0.30/1.56 ( ( ~ ( member_variable_real @ C @ B )
% 0.30/1.56 => ( member_variable_real @ C @ A ) )
% 0.30/1.56 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_252_UnCI,axiom,
% 0.30/1.56 ! [C: variable,B: set_variable,A: set_variable] :
% 0.30/1.56 ( ( ~ ( member_variable @ C @ B )
% 0.30/1.56 => ( member_variable @ C @ A ) )
% 0.30/1.56 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_253_sup_Obounded__iff,axiom,
% 0.30/1.56 ! [B2: set_variable,C: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 )
% 0.30/1.56 = ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 & ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_254_sup_Obounded__iff,axiom,
% 0.30/1.56 ! [B2: set_variable_real,C: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 )
% 0.30/1.56 = ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 & ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_255_le__sup__iff,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/1.56 = ( ( ord_le282106107riable @ X2 @ Z2 )
% 0.30/1.56 & ( ord_le282106107riable @ Y @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_256_le__sup__iff,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real,Z2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ X2 @ Y ) @ Z2 )
% 0.30/1.56 = ( ( ord_le1113654598e_real @ X2 @ Z2 )
% 0.30/1.56 & ( ord_le1113654598e_real @ Y @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_257_Un__subset__iff,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C2 )
% 0.30/1.56 = ( ( ord_le282106107riable @ A @ C2 )
% 0.30/1.56 & ( ord_le282106107riable @ B @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_258_Un__subset__iff,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real,C2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C2 )
% 0.30/1.56 = ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/1.56 & ( ord_le1113654598e_real @ B @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_259_subset__Un__eq,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [A2: set_variable,B5: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A2 @ B5 )
% 0.30/1.56 = B5 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_260_subset__Un__eq,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [A2: set_variable_real,B5: set_variable_real] :
% 0.30/1.56 ( ( sup_su1685293586e_real @ A2 @ B5 )
% 0.30/1.56 = B5 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_261_subset__UnE,axiom,
% 0.30/1.56 ! [C2: set_variable,A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/1.56 => ~ ! [A7: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A7 @ A )
% 0.30/1.56 => ! [B7: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B7 @ B )
% 0.30/1.56 => ( C2
% 0.30/1.56 != ( sup_sup_set_variable @ A7 @ B7 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_262_subset__UnE,axiom,
% 0.30/1.56 ! [C2: set_variable_real,A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ C2 @ ( sup_su1685293586e_real @ A @ B ) )
% 0.30/1.56 => ~ ! [A7: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A7 @ A )
% 0.30/1.56 => ! [B7: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B7 @ B )
% 0.30/1.56 => ( C2
% 0.30/1.56 != ( sup_su1685293586e_real @ A7 @ B7 ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_263_Un__absorb2,axiom,
% 0.30/1.56 ! [B: set_variable,A: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B @ A )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A @ B )
% 0.30/1.56 = A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_264_Un__absorb2,axiom,
% 0.30/1.56 ! [B: set_variable_real,A: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B @ A )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ A @ B )
% 0.30/1.56 = A ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_265_Un__absorb1,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ B )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A @ B )
% 0.30/1.56 = B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_266_Un__absorb1,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ B )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ A @ B )
% 0.30/1.56 = B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_267_Un__upper2,axiom,
% 0.30/1.56 ! [B: set_variable,A: set_variable] : ( ord_le282106107riable @ B @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_268_Un__upper2,axiom,
% 0.30/1.56 ! [B: set_variable_real,A: set_variable_real] : ( ord_le1113654598e_real @ B @ ( sup_su1685293586e_real @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_269_Un__upper1,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_270_Un__upper1,axiom,
% 0.30/1.56 ! [A: set_variable_real,B: set_variable_real] : ( ord_le1113654598e_real @ A @ ( sup_su1685293586e_real @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_271_Un__least,axiom,
% 0.30/1.56 ! [A: set_variable,C2: set_variable,B: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ C2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B @ C2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_272_Un__least,axiom,
% 0.30/1.56 ! [A: set_variable_real,C2: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B @ C2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_273_Un__mono,axiom,
% 0.30/1.56 ! [A: set_variable,C2: set_variable,B: set_variable,D: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A @ C2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B @ D )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ ( sup_sup_set_variable @ C2 @ D ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_274_Un__mono,axiom,
% 0.30/1.56 ! [A: set_variable_real,C2: set_variable_real,B: set_variable_real,D: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A @ C2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B @ D )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A @ B ) @ ( sup_su1685293586e_real @ C2 @ D ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_275_sup_OcoboundedI2,axiom,
% 0.30/1.56 ! [C: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ C @ B2 )
% 0.30/1.56 => ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_276_sup_OcoboundedI2,axiom,
% 0.30/1.56 ! [C: set_variable_real,B2: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ C @ B2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ C @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_277_sup_OcoboundedI1,axiom,
% 0.30/1.56 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ C @ A3 )
% 0.30/1.56 => ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_278_sup_OcoboundedI1,axiom,
% 0.30/1.56 ! [C: set_variable_real,A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/1.56 => ( ord_le1113654598e_real @ C @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_279_sup_Oabsorb__iff2,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [A6: set_variable,B6: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A6 @ B6 )
% 0.30/1.56 = B6 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_280_sup_Oabsorb__iff2,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [A6: set_variable_real,B6: set_variable_real] :
% 0.30/1.56 ( ( sup_su1685293586e_real @ A6 @ B6 )
% 0.30/1.56 = B6 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_281_sup_Oabsorb__iff1,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [B6: set_variable,A6: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A6 @ B6 )
% 0.30/1.56 = A6 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_282_sup_Oabsorb__iff1,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [B6: set_variable_real,A6: set_variable_real] :
% 0.30/1.56 ( ( sup_su1685293586e_real @ A6 @ B6 )
% 0.30/1.56 = A6 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_283_sup_Ocobounded2,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable] : ( ord_le282106107riable @ B2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_284_sup_Ocobounded2,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real] : ( ord_le1113654598e_real @ B2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_285_sup_Ocobounded1,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ A3 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_286_sup_Ocobounded1,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real] : ( ord_le1113654598e_real @ A3 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_287_sup_Oorder__iff,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [B6: set_variable,A6: set_variable] :
% 0.30/1.56 ( A6
% 0.30/1.56 = ( sup_sup_set_variable @ A6 @ B6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_288_sup_Oorder__iff,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [B6: set_variable_real,A6: set_variable_real] :
% 0.30/1.56 ( A6
% 0.30/1.56 = ( sup_su1685293586e_real @ A6 @ B6 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_289_sup_OboundedI,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le282106107riable @ C @ A3 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_290_sup_OboundedI,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real,C: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_291_sup_OboundedE,axiom,
% 0.30/1.56 ! [B2: set_variable,C: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C ) @ A3 )
% 0.30/1.56 => ~ ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ~ ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_292_sup_OboundedE,axiom,
% 0.30/1.56 ! [B2: set_variable_real,C: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ B2 @ C ) @ A3 )
% 0.30/1.56 => ~ ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ~ ( ord_le1113654598e_real @ C @ A3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_293_sup__absorb2,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ Y )
% 0.30/1.56 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/1.56 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_294_sup__absorb2,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ Y )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/1.56 = Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_295_sup__absorb1,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/1.56 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/1.56 = X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_296_sup__absorb1,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/1.56 = X2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_297_sup_Oabsorb2,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A3 @ B2 )
% 0.30/1.56 = B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_298_sup_Oabsorb2,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ B2 )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ A3 @ B2 )
% 0.30/1.56 = B2 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_299_sup_Oabsorb1,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A3 @ B2 )
% 0.30/1.56 = A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_300_sup_Oabsorb1,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ A3 @ B2 )
% 0.30/1.56 = A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_301_sup__unique,axiom,
% 0.30/1.56 ! [F: set_variable > set_variable > set_variable,X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ! [X8: set_variable,Y2: set_variable] : ( ord_le282106107riable @ X8 @ ( F @ X8 @ Y2 ) )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable] : ( ord_le282106107riable @ Y2 @ ( F @ X8 @ Y2 ) )
% 0.30/1.56 => ( ! [X8: set_variable,Y2: set_variable,Z4: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ Y2 @ X8 )
% 0.30/1.56 => ( ( ord_le282106107riable @ Z4 @ X8 )
% 0.30/1.56 => ( ord_le282106107riable @ ( F @ Y2 @ Z4 ) @ X8 ) ) )
% 0.30/1.56 => ( ( sup_sup_set_variable @ X2 @ Y )
% 0.30/1.56 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_302_sup__unique,axiom,
% 0.30/1.56 ! [F: set_variable_real > set_variable_real > set_variable_real,X2: set_variable_real,Y: set_variable_real] :
% 0.30/1.56 ( ! [X8: set_variable_real,Y2: set_variable_real] : ( ord_le1113654598e_real @ X8 @ ( F @ X8 @ Y2 ) )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real] : ( ord_le1113654598e_real @ Y2 @ ( F @ X8 @ Y2 ) )
% 0.30/1.56 => ( ! [X8: set_variable_real,Y2: set_variable_real,Z4: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ Y2 @ X8 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ Z4 @ X8 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( F @ Y2 @ Z4 ) @ X8 ) ) )
% 0.30/1.56 => ( ( sup_su1685293586e_real @ X2 @ Y )
% 0.30/1.56 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_303_sup_OorderI,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ B2 ) )
% 0.30/1.56 => ( ord_le282106107riable @ B2 @ A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_304_sup_OorderI,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( A3
% 0.30/1.56 = ( sup_su1685293586e_real @ A3 @ B2 ) )
% 0.30/1.56 => ( ord_le1113654598e_real @ B2 @ A3 ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_305_sup_OorderE,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.30/1.56 => ( A3
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_306_sup_OorderE,axiom,
% 0.30/1.56 ! [B2: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ B2 @ A3 )
% 0.30/1.56 => ( A3
% 0.30/1.56 = ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_307_le__iff__sup,axiom,
% 0.30/1.56 ( ord_le282106107riable
% 0.30/1.56 = ( ^ [X3: set_variable,Y5: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ X3 @ Y5 )
% 0.30/1.56 = Y5 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_308_le__iff__sup,axiom,
% 0.30/1.56 ( ord_le1113654598e_real
% 0.30/1.56 = ( ^ [X3: set_variable_real,Y5: set_variable_real] :
% 0.30/1.56 ( ( sup_su1685293586e_real @ X3 @ Y5 )
% 0.30/1.56 = Y5 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_309_sup__least,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ Y @ X2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ Z2 @ X2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ Y @ Z2 ) @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_310_sup__least,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real,Z2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ Y @ X2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ Z2 @ X2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ Y @ Z2 ) @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_311_sup__mono,axiom,
% 0.30/1.56 ! [A3: set_variable,C: set_variable,B2: set_variable,D2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ C )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ D2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ ( sup_sup_set_variable @ C @ D2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_312_sup__mono,axiom,
% 0.30/1.56 ! [A3: set_variable_real,C: set_variable_real,B2: set_variable_real,D2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ C )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ D2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ ( sup_su1685293586e_real @ C @ D2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_313_sup_Omono,axiom,
% 0.30/1.56 ! [C: set_variable,A3: set_variable,D2: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ C @ A3 )
% 0.30/1.56 => ( ( ord_le282106107riable @ D2 @ B2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ C @ D2 ) @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_314_sup_Omono,axiom,
% 0.30/1.56 ! [C: set_variable_real,A3: set_variable_real,D2: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ C @ A3 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ D2 @ B2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ C @ D2 ) @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_315_le__supI2,axiom,
% 0.30/1.56 ! [X2: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ B2 )
% 0.30/1.56 => ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_316_le__supI2,axiom,
% 0.30/1.56 ! [X2: set_variable_real,B2: set_variable_real,A3: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ B2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_317_le__supI1,axiom,
% 0.30/1.56 ! [X2: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ X2 @ A3 )
% 0.30/1.56 => ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_318_le__supI1,axiom,
% 0.30/1.56 ! [X2: set_variable_real,A3: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ X2 @ A3 )
% 0.30/1.56 => ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ A3 @ B2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_319_sup__ge2,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_320_sup__ge2,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] : ( ord_le1113654598e_real @ Y @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_321_sup__ge1,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] : ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_322_sup__ge1,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] : ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_323_le__supI,axiom,
% 0.30/1.56 ! [A3: set_variable,X2: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ A3 @ X2 )
% 0.30/1.56 => ( ( ord_le282106107riable @ B2 @ X2 )
% 0.30/1.56 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_324_le__supI,axiom,
% 0.30/1.56 ! [A3: set_variable_real,X2: set_variable_real,B2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ A3 @ X2 )
% 0.30/1.56 => ( ( ord_le1113654598e_real @ B2 @ X2 )
% 0.30/1.56 => ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_325_le__supE,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,X2: set_variable] :
% 0.30/1.56 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A3 @ B2 ) @ X2 )
% 0.30/1.56 => ~ ( ( ord_le282106107riable @ A3 @ X2 )
% 0.30/1.56 => ~ ( ord_le282106107riable @ B2 @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_326_le__supE,axiom,
% 0.30/1.56 ! [A3: set_variable_real,B2: set_variable_real,X2: set_variable_real] :
% 0.30/1.56 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ A3 @ B2 ) @ X2 )
% 0.30/1.56 => ~ ( ( ord_le1113654598e_real @ A3 @ X2 )
% 0.30/1.56 => ~ ( ord_le1113654598e_real @ B2 @ X2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_327_inf__sup__ord_I3_J,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] : ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_328_inf__sup__ord_I3_J,axiom,
% 0.30/1.56 ! [X2: set_variable_real,Y: set_variable_real] : ( ord_le1113654598e_real @ X2 @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_329_inf__sup__ord_I4_J,axiom,
% 0.30/1.56 ! [Y: set_variable,X2: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_330_inf__sup__ord_I4_J,axiom,
% 0.30/1.56 ! [Y: set_variable_real,X2: set_variable_real] : ( ord_le1113654598e_real @ Y @ ( sup_su1685293586e_real @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_331_inf__sup__aci_I8_J,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ X2 @ Y ) )
% 0.30/1.56 = ( sup_sup_set_variable @ X2 @ Y ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_332_inf__sup__aci_I7_J,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) )
% 0.30/1.56 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X2 @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_333_inf__sup__aci_I6_J,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/1.56 = ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_334_inf__sup__aci_I5_J,axiom,
% 0.30/1.56 ( sup_sup_set_variable
% 0.30/1.56 = ( ^ [X3: set_variable,Y5: set_variable] : ( sup_sup_set_variable @ Y5 @ X3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_335_UnE,axiom,
% 0.30/1.56 ! [C: variable > real,A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) )
% 0.30/1.56 => ( ~ ( member_variable_real @ C @ A )
% 0.30/1.56 => ( member_variable_real @ C @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_336_UnE,axiom,
% 0.30/1.56 ! [C: variable,A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/1.56 => ( ~ ( member_variable @ C @ A )
% 0.30/1.56 => ( member_variable @ C @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_337_UnI1,axiom,
% 0.30/1.56 ! [C: variable > real,A: set_variable_real,B: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ C @ A )
% 0.30/1.56 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_338_UnI1,axiom,
% 0.30/1.56 ! [C: variable,A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( member_variable @ C @ A )
% 0.30/1.56 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_339_UnI2,axiom,
% 0.30/1.56 ! [C: variable > real,B: set_variable_real,A: set_variable_real] :
% 0.30/1.56 ( ( member_variable_real @ C @ B )
% 0.30/1.56 => ( member_variable_real @ C @ ( sup_su1685293586e_real @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_340_UnI2,axiom,
% 0.30/1.56 ! [C: variable,B: set_variable,A: set_variable] :
% 0.30/1.56 ( ( member_variable @ C @ B )
% 0.30/1.56 => ( member_variable @ C @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_341_bex__Un,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.30/1.56 ( ( ? [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/1.56 & ( P @ X3 ) ) )
% 0.30/1.56 = ( ? [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A )
% 0.30/1.56 & ( P @ X3 ) )
% 0.30/1.56 | ? [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ B )
% 0.30/1.56 & ( P @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_342_ball__Un,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.30/1.56 ( ( ! [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/1.56 => ( P @ X3 ) ) )
% 0.30/1.56 = ( ! [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ A )
% 0.30/1.56 => ( P @ X3 ) )
% 0.30/1.56 & ! [X3: variable] :
% 0.30/1.56 ( ( member_variable @ X3 @ B )
% 0.30/1.56 => ( P @ X3 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_343_Un__assoc,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C2 )
% 0.30/1.56 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_344_Un__absorb,axiom,
% 0.30/1.56 ! [A: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A @ A )
% 0.30/1.56 = A ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_345_Un__left__absorb,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
% 0.30/1.56 = ( sup_sup_set_variable @ A @ B ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_346_Un__left__commute,axiom,
% 0.30/1.56 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C2 ) )
% 0.30/1.56 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_347_boolean__algebra__cancel_Osup1,axiom,
% 0.30/1.56 ! [A: set_variable,K: set_variable,A3: set_variable,B2: set_variable] :
% 0.30/1.56 ( ( A
% 0.30/1.56 = ( sup_sup_set_variable @ K @ A3 ) )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A @ B2 )
% 0.30/1.56 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_348_boolean__algebra__cancel_Osup2,axiom,
% 0.30/1.56 ! [B: set_variable,K: set_variable,B2: set_variable,A3: set_variable] :
% 0.30/1.56 ( ( B
% 0.30/1.56 = ( sup_sup_set_variable @ K @ B2 ) )
% 0.30/1.56 => ( ( sup_sup_set_variable @ A3 @ B )
% 0.30/1.56 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_349_sup_Oassoc,axiom,
% 0.30/1.56 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A3 @ B2 ) @ C )
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ B2 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_350_sup__assoc,axiom,
% 0.30/1.56 ! [X2: set_variable,Y: set_variable,Z2: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X2 @ Y ) @ Z2 )
% 0.30/1.56 = ( sup_sup_set_variable @ X2 @ ( sup_sup_set_variable @ Y @ Z2 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_351_sup_Ocommute,axiom,
% 0.30/1.56 ( sup_sup_set_variable
% 0.30/1.56 = ( ^ [A6: set_variable,B6: set_variable] : ( sup_sup_set_variable @ B6 @ A6 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_352_sup__commute,axiom,
% 0.30/1.56 ( sup_sup_set_variable
% 0.30/1.56 = ( ^ [X3: set_variable,Y5: set_variable] : ( sup_sup_set_variable @ Y5 @ X3 ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(fact_353_sup_Oleft__commute,axiom,
% 0.30/1.56 ! [B2: set_variable,A3: set_variable,C: set_variable] :
% 0.30/1.56 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A3 @ C ) )
% 0.30/1.56 = ( sup_sup_set_variable @ A3 @ ( sup_sup_set_variable @ B2 @ C ) ) ) ).
% 0.30/1.56
% 0.30/1.56 thf(conj_0,conjecture,
% 0.30/1.56 ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
% 0.30/1.56 = ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ) ).
% 0.30/1.56 ------------------------
% 0.30/1.58 % (28473)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/18Mi)
% 0.30/1.58 % (28472)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_28368 for (2999ds/275Mi)
% 0.30/1.58 % (28470)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/2Mi)
% 0.30/1.58 % (28467)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/183Mi)
% 0.30/1.58 % (28468)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_28368 for (2999ds/4Mi)
% 0.30/1.58 % (28470)Instruction limit reached!
% 0.30/1.58 % (28470)------------------------------
% 0.30/1.58 % (28470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (28470)Termination reason: Unknown
% 0.30/1.58 % (28470)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (28470)Memory used [KB]: 1407
% 0.30/1.58 % (28470)Time elapsed: 0.002 s
% 0.30/1.58 % (28470)Instructions burned: 2 (million)
% 0.30/1.58 % (28470)------------------------------
% 0.30/1.58 % (28470)------------------------------
% 0.30/1.58 % (28468)Instruction limit reached!
% 0.30/1.58 % (28468)------------------------------
% 0.30/1.58 % (28468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (28468)Termination reason: Unknown
% 0.30/1.58 % (28468)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (28468)Memory used [KB]: 1535
% 0.30/1.58 % (28468)Time elapsed: 0.003 s
% 0.30/1.58 % (28468)Instructions burned: 6 (million)
% 0.30/1.58 % (28468)------------------------------
% 0.30/1.58 % (28468)------------------------------
% 0.30/1.59 % (28473)Instruction limit reached!
% 0.30/1.59 % (28473)------------------------------
% 0.30/1.59 % (28473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (28473)Termination reason: Unknown
% 0.30/1.59 % (28473)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (28473)Memory used [KB]: 1791
% 0.30/1.59 % (28473)Time elapsed: 0.007 s
% 0.30/1.59 % (28473)Instructions burned: 18 (million)
% 0.30/1.59 % (28473)------------------------------
% 0.30/1.59 % (28473)------------------------------
% 0.30/1.59 % (28469)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_28368 for (2999ds/27Mi)
% 0.30/1.59 % (28471)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_28368 for (2999ds/2Mi)
% 0.30/1.59 % (28471)Instruction limit reached!
% 0.30/1.59 % (28471)------------------------------
% 0.30/1.59 % (28471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (28471)Termination reason: Unknown
% 0.30/1.59 % (28471)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (28471)Memory used [KB]: 1407
% 0.30/1.59 % (28471)Time elapsed: 0.004 s
% 0.30/1.59 % (28471)Instructions burned: 3 (million)
% 0.30/1.59 % (28471)------------------------------
% 0.30/1.59 % (28471)------------------------------
% 0.30/1.59 % (28474)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/3Mi)
% 0.30/1.59 % (28475)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_28368 for (2999ds/37Mi)
% 0.30/1.59 % (28474)Instruction limit reached!
% 0.30/1.59 % (28474)------------------------------
% 0.30/1.59 % (28474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (28474)Termination reason: Unknown
% 0.30/1.59 % (28474)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (28474)Memory used [KB]: 1407
% 0.30/1.59 % (28474)Time elapsed: 0.003 s
% 0.30/1.59 % (28474)Instructions burned: 4 (million)
% 0.30/1.59 % (28474)------------------------------
% 0.30/1.59 % (28474)------------------------------
% 0.30/1.59 % (28476)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_28368 for (2999ds/15Mi)
% 2.95/1.60 % (28476)Instruction limit reached!
% 2.95/1.60 % (28476)------------------------------
% 2.95/1.60 % (28476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (28476)Termination reason: Unknown
% 2.95/1.60 % (28476)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (28476)Memory used [KB]: 1663
% 2.95/1.60 % (28476)Time elapsed: 0.006 s
% 2.95/1.60 % (28476)Instructions burned: 16 (million)
% 2.95/1.60 % (28476)------------------------------
% 2.95/1.60 % (28476)------------------------------
% 2.95/1.60 % (28478)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_28368 for (2999ds/1041Mi)
% 2.95/1.60 % (28475)Instruction limit reached!
% 2.95/1.60 % (28475)------------------------------
% 2.95/1.60 % (28475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (28475)Termination reason: Unknown
% 2.95/1.60 % (28475)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (28475)Memory used [KB]: 2174
% 2.95/1.60 % (28475)Time elapsed: 0.013 s
% 2.95/1.60 % (28475)Instructions burned: 38 (million)
% 2.95/1.60 % (28475)------------------------------
% 2.95/1.60 % (28475)------------------------------
% 2.95/1.60 % (28469)Instruction limit reached!
% 2.95/1.60 % (28469)------------------------------
% 2.95/1.60 % (28469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (28469)Termination reason: Unknown
% 2.95/1.60 % (28469)Termination phase: Property scanning
% 2.95/1.60
% 2.95/1.60 % (28469)Memory used [KB]: 1791
% 2.95/1.60 % (28469)Time elapsed: 0.019 s
% 2.95/1.60 % (28469)Instructions burned: 28 (million)
% 2.95/1.60 % (28469)------------------------------
% 2.95/1.60 % (28469)------------------------------
% 2.95/1.61 % (28477)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_28368 for (2999ds/3Mi)
% 2.95/1.61 % (28477)Instruction limit reached!
% 2.95/1.61 % (28477)------------------------------
% 2.95/1.61 % (28477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (28477)Termination reason: Unknown
% 2.95/1.61 % (28477)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (28479)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/7Mi)
% 2.95/1.61 % (28477)Memory used [KB]: 1407
% 2.95/1.61 % (28477)Time elapsed: 0.004 s
% 2.95/1.61 % (28477)Instructions burned: 3 (million)
% 2.95/1.61 % (28477)------------------------------
% 2.95/1.61 % (28477)------------------------------
% 2.95/1.61 % (28479)Instruction limit reached!
% 2.95/1.61 % (28479)------------------------------
% 2.95/1.61 % (28479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (28479)Termination reason: Unknown
% 2.95/1.61 % (28479)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (28479)Memory used [KB]: 1535
% 2.95/1.61 % (28479)Time elapsed: 0.003 s
% 2.95/1.61 % (28479)Instructions burned: 7 (million)
% 2.95/1.61 % (28479)------------------------------
% 2.95/1.61 % (28479)------------------------------
% 2.95/1.61 % (28480)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/16Mi)
% 2.95/1.62 % (28480)Instruction limit reached!
% 2.95/1.62 % (28480)------------------------------
% 2.95/1.62 % (28480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (28480)Termination reason: Unknown
% 2.95/1.62 % (28480)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (28480)Memory used [KB]: 1791
% 2.95/1.62 % (28480)Time elapsed: 0.008 s
% 2.95/1.62 % (28480)Instructions burned: 18 (million)
% 2.95/1.62 % (28480)------------------------------
% 2.95/1.62 % (28480)------------------------------
% 2.95/1.62 % (28483)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/7Mi)
% 2.95/1.62 % (28481)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_28368 for (2999ds/3Mi)
% 2.95/1.62 % (28483)Instruction limit reached!
% 2.95/1.62 % (28483)------------------------------
% 2.95/1.62 % (28483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (28483)Termination reason: Unknown
% 2.95/1.62 % (28483)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (28483)Memory used [KB]: 1535
% 2.95/1.62 % (28483)Time elapsed: 0.003 s
% 2.95/1.62 % (28483)Instructions burned: 7 (million)
% 2.95/1.62 % (28483)------------------------------
% 2.95/1.62 % (28483)------------------------------
% 2.95/1.62 % (28481)Instruction limit reached!
% 2.95/1.62 % (28481)------------------------------
% 2.95/1.62 % (28481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (28481)Termination reason: Unknown
% 2.95/1.62 % (28481)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (28481)Memory used [KB]: 1407
% 2.95/1.62 % (28481)Time elapsed: 0.004 s
% 2.95/1.62 % (28481)Instructions burned: 3 (million)
% 2.95/1.62 % (28481)------------------------------
% 2.95/1.62 % (28481)------------------------------
% 2.95/1.63 % (28482)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_28368 for (2999ds/3Mi)
% 2.95/1.63 % (28482)Instruction limit reached!
% 2.95/1.63 % (28482)------------------------------
% 2.95/1.63 % (28482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (28482)Termination reason: Unknown
% 2.95/1.63 % (28482)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (28482)Memory used [KB]: 1407
% 2.95/1.63 % (28482)Time elapsed: 0.004 s
% 2.95/1.63 % (28482)Instructions burned: 3 (million)
% 2.95/1.63 % (28482)------------------------------
% 2.95/1.63 % (28482)------------------------------
% 2.95/1.63 % (28484)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/3Mi)
% 2.95/1.63 % (28484)Instruction limit reached!
% 2.95/1.63 % (28484)------------------------------
% 2.95/1.63 % (28484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (28484)Termination reason: Unknown
% 2.95/1.63 % (28484)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (28484)Memory used [KB]: 1407
% 2.95/1.63 % (28484)Time elapsed: 0.003 s
% 2.95/1.63 % (28484)Instructions burned: 4 (million)
% 2.95/1.63 % (28484)------------------------------
% 2.95/1.63 % (28484)------------------------------
% 2.95/1.63 % (28485)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/4Mi)
% 2.95/1.63 % (28485)Instruction limit reached!
% 2.95/1.63 % (28485)------------------------------
% 2.95/1.63 % (28485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (28485)Termination reason: Unknown
% 2.95/1.63 % (28485)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (28485)Memory used [KB]: 1407
% 2.95/1.63 % (28485)Time elapsed: 0.002 s
% 2.95/1.63 % (28485)Instructions burned: 4 (million)
% 2.95/1.63 % (28485)------------------------------
% 2.95/1.63 % (28485)------------------------------
% 2.95/1.64 % (28467)Instruction limit reached!
% 2.95/1.64 % (28467)------------------------------
% 2.95/1.64 % (28467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (28467)Termination reason: Unknown
% 2.95/1.64 % (28467)Termination phase: Saturation
% 2.95/1.64
% 2.95/1.64 % (28467)Memory used [KB]: 7291
% 2.95/1.64 % (28467)Time elapsed: 0.057 s
% 2.95/1.64 % (28467)Instructions burned: 185 (million)
% 2.95/1.64 % (28467)------------------------------
% 2.95/1.64 % (28467)------------------------------
% 2.95/1.64 % (28488)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/6Mi)
% 2.95/1.64 % (28486)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/18Mi)
% 2.95/1.64 % (28489)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_28368 for (2999ds/902Mi)
% 2.95/1.64 % (28488)Instruction limit reached!
% 2.95/1.64 % (28488)------------------------------
% 2.95/1.64 % (28488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (28488)Termination reason: Unknown
% 2.95/1.64 % (28488)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (28488)Memory used [KB]: 1535
% 2.95/1.64 % (28488)Time elapsed: 0.004 s
% 2.95/1.64 % (28488)Instructions burned: 7 (million)
% 2.95/1.64 % (28488)------------------------------
% 2.95/1.64 % (28488)------------------------------
% 2.95/1.65 % (28487)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/710Mi)
% 2.95/1.65 % (28490)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_28368 for (2999ds/21Mi)
% 2.95/1.65 % (28486)Instruction limit reached!
% 2.95/1.65 % (28486)------------------------------
% 2.95/1.65 % (28486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (28486)Termination reason: Unknown
% 2.95/1.65 % (28486)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (28486)Memory used [KB]: 1791
% 2.95/1.65 % (28486)Time elapsed: 0.013 s
% 2.95/1.65 % (28486)Instructions burned: 19 (million)
% 2.95/1.65 % (28486)------------------------------
% 2.95/1.65 % (28486)------------------------------
% 2.95/1.65 % (28490)Instruction limit reached!
% 2.95/1.65 % (28490)------------------------------
% 2.95/1.65 % (28490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (28490)Termination reason: Unknown
% 2.95/1.65 % (28490)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (28490)Memory used [KB]: 1791
% 2.95/1.65 % (28490)Time elapsed: 0.009 s
% 2.95/1.65 % (28490)Instructions burned: 21 (million)
% 2.95/1.65 % (28490)------------------------------
% 2.95/1.65 % (28490)------------------------------
% 2.95/1.65 % (28491)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/5Mi)
% 2.95/1.66 % (28491)Instruction limit reached!
% 2.95/1.66 % (28491)------------------------------
% 2.95/1.66 % (28491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (28491)Termination reason: Unknown
% 2.95/1.66 % (28491)Termination phase: shuffling
% 2.95/1.66
% 2.95/1.66 % (28491)Memory used [KB]: 1535
% 2.95/1.66 % (28491)Time elapsed: 0.004 s
% 2.95/1.66 % (28491)Instructions burned: 7 (million)
% 2.95/1.66 % (28491)------------------------------
% 2.95/1.66 % (28491)------------------------------
% 2.95/1.66 % (28472)Instruction limit reached!
% 2.95/1.66 % (28472)------------------------------
% 2.95/1.66 % (28472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (28472)Termination reason: Unknown
% 2.95/1.66 % (28472)Termination phase: Saturation
% 2.95/1.66
% 2.95/1.66 % (28472)Memory used [KB]: 7164
% 2.95/1.66 % (28472)Time elapsed: 0.083 s
% 2.95/1.66 % (28472)Instructions burned: 276 (million)
% 2.95/1.66 % (28472)------------------------------
% 2.95/1.66 % (28472)------------------------------
% 2.95/1.66 % (28493)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28368 for (2999ds/377Mi)
% 2.95/1.67 % (28494)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_28368 for (2999ds/779Mi)
% 2.95/1.67 % (28492)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_28368 for (2999ds/6Mi)
% 2.95/1.67 % (28495)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_28368 for (2998ds/19Mi)
% 2.95/1.67 % (28492)Instruction limit reached!
% 2.95/1.67 % (28492)------------------------------
% 2.95/1.67 % (28492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (28492)Termination reason: Unknown
% 2.95/1.67 % (28492)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (28492)Memory used [KB]: 1535
% 2.95/1.67 % (28492)Time elapsed: 0.005 s
% 2.95/1.67 % (28492)Instructions burned: 6 (million)
% 2.95/1.67 % (28492)------------------------------
% 2.95/1.67 % (28492)------------------------------
% 2.95/1.68 % (28495)Instruction limit reached!
% 2.95/1.68 % (28495)------------------------------
% 2.95/1.68 % (28495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.68 % (28495)Termination reason: Unknown
% 2.95/1.68 % (28495)Termination phase: shuffling
% 2.95/1.68
% 2.95/1.68 % (28495)Memory used [KB]: 1791
% 2.95/1.68 % (28495)Time elapsed: 0.007 s
% 2.95/1.68 % (28495)Instructions burned: 22 (million)
% 2.95/1.68 % (28495)------------------------------
% 2.95/1.68 % (28495)------------------------------
% 2.95/1.69 % (28497)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28368 for (2998ds/17Mi)
% 2.95/1.69 % (28496)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28368 for (2998ds/879Mi)
% 2.95/1.69 % (28497)Instruction limit reached!
% 2.95/1.69 % (28497)------------------------------
% 2.95/1.69 % (28497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.69 % (28497)Termination reason: Unknown
% 2.95/1.69 % (28497)Termination phase: shuffling
% 2.95/1.69
% 2.95/1.69 % (28497)Memory used [KB]: 1791
% 2.95/1.69 % (28497)Time elapsed: 0.007 s
% 2.95/1.69 % (28497)Instructions burned: 19 (million)
% 2.95/1.69 % (28497)------------------------------
% 2.95/1.69 % (28497)------------------------------
% 2.95/1.70 % (28498)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28368 for (2998ds/3Mi)
% 2.95/1.70 % (28498)Instruction limit reached!
% 2.95/1.70 % (28498)------------------------------
% 2.95/1.70 % (28498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.70 % (28498)Termination reason: Unknown
% 2.95/1.70 % (28498)Termination phase: shuffling
% 2.95/1.70
% 2.95/1.70 % (28498)Memory used [KB]: 1407
% 2.95/1.70 % (28498)Time elapsed: 0.002 s
% 2.95/1.70 % (28498)Instructions burned: 3 (million)
% 2.95/1.70 % (28498)------------------------------
% 2.95/1.70 % (28498)------------------------------
% 2.95/1.71 % (28499)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28368 for (2998ds/30Mi)
% 2.95/1.72 % (28499)Instruction limit reached!
% 2.95/1.72 % (28499)------------------------------
% 2.95/1.72 % (28499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.72 % (28499)Termination reason: Unknown
% 2.95/1.72 % (28499)Termination phase: Property scanning
% 2.95/1.72
% 2.95/1.72 % (28499)Memory used [KB]: 1918
% 2.95/1.72 % (28499)Time elapsed: 0.011 s
% 2.95/1.72 % (28499)Instructions burned: 32 (million)
% 2.95/1.72 % (28499)------------------------------
% 2.95/1.72 % (28499)------------------------------
% 2.95/1.73 % (28500)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28368 for (2998ds/127Mi)
% 2.95/1.77 % (28500)Instruction limit reached!
% 2.95/1.77 % (28500)------------------------------
% 2.95/1.77 % (28500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.77 % (28500)Termination reason: Unknown
% 2.95/1.77 % (28500)Termination phase: Saturation
% 2.95/1.77
% 2.95/1.77 % (28500)Memory used [KB]: 6780
% 2.95/1.77 % (28500)Time elapsed: 0.035 s
% 2.95/1.77 % (28500)Instructions burned: 127 (million)
% 2.95/1.77 % (28500)------------------------------
% 2.95/1.77 % (28500)------------------------------
% 2.95/1.78 % (28501)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28368 for (2997ds/100Mi)
% 2.95/1.78 % (28493)Instruction limit reached!
% 2.95/1.78 % (28493)------------------------------
% 2.95/1.78 % (28493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.78 % (28493)Termination reason: Unknown
% 2.95/1.78 % (28493)Termination phase: Saturation
% 2.95/1.78
% 2.95/1.78 % (28493)Memory used [KB]: 8059
% 2.95/1.78 % (28493)Time elapsed: 0.122 s
% 2.95/1.78 % (28493)Instructions burned: 377 (million)
% 2.95/1.78 % (28493)------------------------------
% 2.95/1.78 % (28493)------------------------------
% 2.95/1.79 % (28502)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_28368 for (2997ds/3Mi)
% 2.95/1.80 % (28502)Instruction limit reached!
% 2.95/1.80 % (28502)------------------------------
% 2.95/1.80 % (28502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.80 % (28502)Termination reason: Unknown
% 2.95/1.80 % (28502)Termination phase: shuffling
% 2.95/1.80
% 2.95/1.80 % (28502)Memory used [KB]: 1407
% 2.95/1.80 % (28502)Time elapsed: 0.002 s
% 2.95/1.80 % (28502)Instructions burned: 3 (million)
% 2.95/1.80 % (28502)------------------------------
% 2.95/1.80 % (28502)------------------------------
% 2.95/1.80 % (28501)Instruction limit reached!
% 2.95/1.80 % (28501)------------------------------
% 2.95/1.80 % (28501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.80 % (28501)Termination reason: Unknown
% 2.95/1.80 % (28501)Termination phase: Property scanning
% 2.95/1.80
% 2.95/1.80 % (28501)Memory used [KB]: 2302
% 2.95/1.80 % (28501)Time elapsed: 0.027 s
% 2.95/1.80 % (28501)Instructions burned: 102 (million)
% 2.95/1.80 % (28501)------------------------------
% 2.95/1.80 % (28501)------------------------------
% 2.95/1.81 % (28503)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_28368 for (2997ds/20Mi)
% 2.95/1.81 % (28504)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_28368 for (2997ds/86Mi)
% 2.95/1.81 % (28503)Instruction limit reached!
% 2.95/1.81 % (28503)------------------------------
% 2.95/1.81 % (28503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.81 % (28503)Termination reason: Unknown
% 2.95/1.81 % (28503)Termination phase: shuffling
% 2.95/1.81
% 2.95/1.81 % (28503)Memory used [KB]: 1791
% 2.95/1.81 % (28503)Time elapsed: 0.009 s
% 2.95/1.81 % (28503)Instructions burned: 21 (million)
% 2.95/1.81 % (28503)------------------------------
% 2.95/1.81 % (28503)------------------------------
% 2.95/1.81 % (28489)First to succeed.
% 2.95/1.82 % (28489)Refutation found. Thanks to Tanya!
% 2.95/1.82 % SZS status Theorem for DTF2THF_28368
% 2.95/1.82 % SZS output start Proof for DTF2THF_28368
% 2.95/1.82 thf(type_def_5, type, variable: $tType).
% 2.95/1.82 thf(type_def_6, type, real: $tType).
% 2.95/1.82 thf(type_def_8, type, set_variable: $tType).
% 2.95/1.82 thf(type_def_9, type, denotational_interp: $tType).
% 2.95/1.82 thf(type_def_10, type, game: $tType).
% 2.95/1.82 thf(type_def_11, type, set_variable_real: $tType).
% 2.95/1.82 thf(type_def_12, type, produc1078154247n_game: $tType).
% 2.95/1.82 thf(type_def_13, type, produc2038871085e_real: $tType).
% 2.95/1.82 thf(type_def_14, type, produc1755325794riable: $tType).
% 2.95/1.82 thf(type_def_15, type, produc1794985442e_real: $tType).
% 2.95/1.82 thf(type_def_16, type, produc432717079riable: $tType).
% 2.95/1.82 thf(type_def_17, type, set_Pr166476775n_game: $tType).
% 2.95/1.82 thf(type_def_18, type, option_game: $tType).
% 2.95/1.82 thf(type_def_19, type, produc735959047riable: $tType).
% 2.95/1.82 thf(type_def_20, type, produc1418842292n_game: $tType).
% 2.95/1.82 thf(func_def_0, type, produc1418842292n_game: $tType).
% 2.95/1.82 thf(func_def_1, type, produc2038871085e_real: $tType).
% 2.95/1.82 thf(func_def_2, type, produc1794985442e_real: $tType).
% 2.95/1.82 thf(func_def_3, type, produc1755325794riable: $tType).
% 2.95/1.82 thf(func_def_4, type, set_Pr166476775n_game: $tType).
% 2.95/1.82 thf(func_def_5, type, produc1078154247n_game: $tType).
% 2.95/1.82 thf(func_def_6, type, produc735959047riable: $tType).
% 2.95/1.82 thf(func_def_7, type, produc432717079riable: $tType).
% 2.95/1.82 thf(func_def_8, type, set_variable_real: $tType).
% 2.95/1.82 thf(func_def_9, type, option_game: $tType).
% 2.95/1.82 thf(func_def_10, type, denotational_interp: $tType).
% 2.95/1.82 thf(func_def_11, type, set_variable: $tType).
% 2.95/1.82 thf(func_def_12, type, variable: $tType).
% 2.95/1.82 thf(func_def_13, type, game: $tType).
% 2.95/1.82 thf(func_def_14, type, real: $tType).
% 2.95/1.82 thf(func_def_15, type, denota1419872369iation: (variable > real) > (variable > real) > set_variable > $o).
% 2.95/1.82 thf(func_def_16, type, denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real).
% 2.95/1.82 thf(func_def_17, type, uminus970116630real_o: ((variable > real) > $o) > (variable > real) > $o).
% 2.95/1.82 thf(func_def_18, type, uminus679091071game_o: (produc1078154247n_game > $o) > produc1078154247n_game > $o).
% 2.95/1.82 thf(func_def_19, type, uminus1666842273able_o: (variable > $o) > variable > $o).
% 2.95/1.82 thf(func_def_20, type, uminus_uminus_o: $o > $o).
% 2.95/1.82 thf(func_def_21, type, uminus501400228e_real: produc2038871085e_real > produc2038871085e_real).
% 2.95/1.82 thf(func_def_22, type, uminus2115124697riable: produc1755325794riable > produc1755325794riable).
% 2.95/1.82 thf(func_def_23, type, uminus7300697e_real: produc1794985442e_real > produc1794985442e_real).
% 2.95/1.82 thf(func_def_24, type, uminus269410190riable: produc432717079riable > produc432717079riable).
% 2.95/1.82 thf(func_def_25, type, uminus430703407e_real: set_variable_real > set_variable_real).
% 2.95/1.82 thf(func_def_26, type, uminus2030647006n_game: set_Pr166476775n_game > set_Pr166476775n_game).
% 2.95/1.82 thf(func_def_27, type, uminus1851247844riable: set_variable > set_variable).
% 2.95/1.82 thf(func_def_28, type, sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real).
% 2.95/1.82 thf(func_def_29, type, sup_sup_set_variable: set_variable > set_variable > set_variable).
% 2.95/1.82 thf(func_def_30, type, none_game: option_game).
% 2.95/1.82 thf(func_def_31, type, the_game: option_game > game).
% 2.95/1.82 thf(func_def_32, type, ord_le1354144447real_o: ((variable > real) > $o) > ((variable > real) > $o) > $o).
% 2.95/1.82 thf(func_def_33, type, ord_le2134856704game_o: (set_variable > option_game > $o) > (set_variable > option_game > $o) > $o).
% 2.95/1.82 thf(func_def_34, type, ord_le1407353162able_o: (variable > $o) > (variable > $o) > $o).
% 2.95/1.82 thf(func_def_35, type, ord_le1113654598e_real: set_variable_real > set_variable_real > $o).
% 2.95/1.82 thf(func_def_36, type, ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o).
% 2.95/1.82 thf(func_def_37, type, ord_le282106107riable: set_variable > set_variable > $o).
% 2.95/1.82 thf(func_def_38, type, produc1140431679riable: option_game > set_variable > produc735959047riable).
% 2.95/1.82 thf(func_def_39, type, produc86945893e_real: set_variable_real > set_variable_real > produc2038871085e_real).
% 2.95/1.82 thf(func_def_40, type, produc544095770riable: set_variable_real > set_variable > produc1755325794riable).
% 2.95/1.82 thf(func_def_41, type, produc1149443391n_game: set_variable > option_game > produc1078154247n_game).
% 2.95/1.82 thf(func_def_42, type, produc1400669210e_real: set_variable > set_variable_real > produc1794985442e_real).
% 2.95/1.82 thf(func_def_43, type, produc1766592463riable: set_variable > set_variable > produc432717079riable).
% 2.95/1.82 thf(func_def_44, type, produc884810027riable: produc735959047riable > option_game).
% 2.95/1.82 thf(func_def_45, type, produc702045265e_real: produc2038871085e_real > set_variable_real).
% 2.95/1.82 thf(func_def_46, type, produc944271878riable: produc1755325794riable > set_variable_real).
% 2.95/1.82 thf(func_def_47, type, produc893821739n_game: produc1078154247n_game > set_variable).
% 2.95/1.82 thf(func_def_48, type, produc1800845318e_real: produc1794985442e_real > set_variable).
% 2.95/1.82 thf(func_def_49, type, produc1300679611riable: produc432717079riable > set_variable).
% 2.95/1.82 thf(func_def_50, type, produc284475501riable: produc735959047riable > set_variable).
% 2.95/1.82 thf(func_def_51, type, produc220849299e_real: produc2038871085e_real > set_variable_real).
% 2.95/1.82 thf(func_def_52, type, produc1192298056riable: produc1755325794riable > set_variable).
% 2.95/1.82 thf(func_def_53, type, produc293487213n_game: produc1078154247n_game > option_game).
% 2.95/1.82 thf(func_def_54, type, produc2048871496e_real: produc1794985442e_real > set_variable_real).
% 2.95/1.82 thf(func_def_55, type, produc319712253riable: produc432717079riable > set_variable).
% 2.95/1.82 thf(func_def_56, type, produc345397471riable: produc735959047riable > produc1078154247n_game).
% 2.95/1.82 thf(func_def_57, type, produc354409183n_game: produc1078154247n_game > produc735959047riable).
% 2.95/1.82 thf(func_def_58, type, collec633296133e_real: ((variable > real) > $o) > set_variable_real).
% 2.95/1.82 thf(func_def_59, type, collec1702522994n_game: (produc1078154247n_game > $o) > set_Pr166476775n_game).
% 2.95/1.82 thf(func_def_60, type, collect_variable: (variable > $o) > set_variable).
% 2.95/1.82 thf(func_def_61, type, skip: game).
% 2.95/1.82 thf(func_def_62, type, choice: game > game > game).
% 2.95/1.82 thf(func_def_63, type, dual: game > game).
% 2.95/1.82 thf(func_def_64, type, loop: game > game).
% 2.95/1.82 thf(func_def_65, type, uSubst1484167963hoiceo: option_game > option_game > option_game).
% 2.95/1.82 thf(func_def_66, type, uSubst1916713664_Dualo: option_game > option_game).
% 2.95/1.82 thf(func_def_67, type, uSubst23177304_Loopo: option_game > option_game).
% 2.95/1.82 thf(func_def_68, type, uSubst1599435252djoint: produc1418842292n_game > denotational_interp > (variable > real) > denotational_interp).
% 2.95/1.82 thf(func_def_69, type, uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game).
% 2.95/1.82 thf(func_def_70, type, member_variable_real: (variable > real) > set_variable_real > $o).
% 2.95/1.82 thf(func_def_71, type, member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o).
% 2.95/1.82 thf(func_def_72, type, member_variable: variable > set_variable > $o).
% 2.95/1.82 thf(func_def_73, type, i: denotational_interp).
% 2.95/1.82 thf(func_def_74, type, u: set_variable).
% 2.95/1.82 thf(func_def_75, type, ua: set_variable).
% 2.95/1.82 thf(func_def_76, type, xa: set_variable_real).
% 2.95/1.82 thf(func_def_77, type, alpha: game).
% 2.95/1.82 thf(func_def_78, type, nu: variable > real).
% 2.95/1.82 thf(func_def_79, type, nu2: variable > real).
% 2.95/1.82 thf(func_def_80, type, omega: variable > real).
% 2.95/1.82 thf(func_def_81, type, omega2: variable > real).
% 2.95/1.82 thf(func_def_82, type, sigma: produc1418842292n_game).
% 2.95/1.82 thf(func_def_96, type, sK0: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_97, type, sK1: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_98, type, sK2: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_99, type, sK3: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_100, type, sK4: produc1078154247n_game > set_variable).
% 2.95/1.82 thf(func_def_101, type, sK5: produc1078154247n_game > option_game).
% 2.95/1.82 thf(func_def_102, type, sK6: (variable > $o) > set_variable > variable).
% 2.95/1.82 thf(func_def_103, type, sK7: set_variable > (variable > $o) > variable).
% 2.95/1.82 thf(func_def_104, type, sK8: set_variable > (variable > $o) > set_variable > variable).
% 2.95/1.82 thf(func_def_105, type, sK9: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_106, type, sK10: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_107, type, sK11: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_108, type, sK12: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_109, type, sK13: (set_variable > option_game > $o) > set_variable).
% 2.95/1.82 thf(func_def_110, type, sK14: (set_variable > option_game > $o) > option_game).
% 2.95/1.82 thf(func_def_111, type, sK15: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_112, type, sK16: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_113, type, sK17: (produc1078154247n_game > $o) > option_game).
% 2.95/1.82 thf(func_def_114, type, sK18: (produc1078154247n_game > $o) > set_variable).
% 2.95/1.82 thf(func_def_115, type, sK19: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_116, type, sK20: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_117, type, sK21: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_118, type, sK22: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_119, type, sK23: ((variable > real) > $o) > ((variable > real) > $o) > variable > real).
% 2.95/1.82 thf(func_def_120, type, sK24: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_121, type, sK25: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_122, type, sK26: (variable > $o) > (variable > $o) > variable).
% 2.95/1.82 thf(func_def_123, type, sK27: (option_game > set_variable > $o) > option_game).
% 2.95/1.82 thf(func_def_124, type, sK28: (option_game > set_variable > $o) > set_variable).
% 2.95/1.82 thf(func_def_125, type, sK29: produc1078154247n_game > option_game > set_variable).
% 2.95/1.82 thf(func_def_126, type, sK30: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_127, type, sK31: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_128, type, sK32: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_129, type, sK33: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_130, type, sK34: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_131, type, sK35: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_132, type, sK36: (set_variable_real > set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_133, type, sK37: produc1078154247n_game > option_game).
% 2.95/1.82 thf(func_def_134, type, sK38: produc1078154247n_game > set_variable).
% 2.95/1.82 thf(func_def_135, type, sK39: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_136, type, sK40: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_137, type, sK41: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_138, type, sK42: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_139, type, sK43: (variable > $o) > set_variable > variable).
% 2.95/1.82 thf(func_def_140, type, sK44: (variable > $o) > (variable > $o) > variable).
% 2.95/1.82 thf(func_def_141, type, sK45: set_variable_real > ((variable > real) > $o) > variable > real).
% 2.95/1.82 thf(func_def_142, type, sK46: (variable > $o) > set_variable > set_variable > variable).
% 2.95/1.82 thf(func_def_143, type, sK47: (variable > $o) > set_variable > variable).
% 2.95/1.82 thf(func_def_144, type, sK48: (variable > $o) > set_variable > variable).
% 2.95/1.82 thf(func_def_145, type, sK49: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_146, type, sK50: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_147, type, sK51: set_variable > set_variable > variable).
% 2.95/1.82 thf(func_def_148, type, sK52: (variable > $o) > set_variable > (variable > $o) > variable).
% 2.95/1.82 thf(func_def_149, type, sK53: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_150, type, sK54: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_151, type, sK55: (produc1078154247n_game > $o) > option_game).
% 2.95/1.82 thf(func_def_152, type, sK56: (produc1078154247n_game > $o) > set_variable).
% 2.95/1.82 thf(func_def_153, type, sK57: set_Pr166476775n_game > set_Pr166476775n_game > set_variable).
% 2.95/1.82 thf(func_def_154, type, sK58: set_Pr166476775n_game > set_Pr166476775n_game > option_game).
% 2.95/1.82 thf(func_def_155, type, sK59: (set_variable > $o) > set_variable).
% 2.95/1.82 thf(func_def_156, type, sK60: (set_variable > $o) > set_variable).
% 2.95/1.82 thf(func_def_157, type, sK61: set_variable_real > set_variable_real > variable > real).
% 2.95/1.82 thf(func_def_158, type, sK62: set_variable_real > set_variable_real > set_variable_real > set_variable_real).
% 2.95/1.82 thf(func_def_159, type, sK63: set_variable_real > set_variable_real > set_variable_real > set_variable_real).
% 2.95/1.82 thf(func_def_160, type, sK64: (variable > $o) > (variable > $o) > variable).
% 2.95/1.82 thf(func_def_161, type, sK65: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_162, type, sK66: (set_variable_real > set_variable) > set_variable_real).
% 2.95/1.82 thf(func_def_163, type, sK67: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_164, type, sK68: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_165, type, sK69: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_166, type, sK70: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_167, type, sK71: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_168, type, sK72: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_169, type, sK73: (set_variable > set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_170, type, sK74: (set_variable_real > set_variable_real > $o) > set_variable_real).
% 2.95/1.82 thf(func_def_171, type, sK75: (set_variable_real > set_variable_real > $o) > set_variable_real).
% 2.95/1.82 thf(func_def_172, type, sK76: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_173, type, sK77: (set_variable > set_variable) > set_variable).
% 2.95/1.82 thf(func_def_174, type, sK78: ((variable > real) > $o) > ((variable > real) > $o) > variable > real).
% 2.95/1.82 thf(func_def_175, type, sK79: (set_variable_real > $o) > set_variable_real).
% 2.95/1.82 thf(func_def_176, type, sK80: (set_variable_real > $o) > set_variable_real).
% 2.95/1.82 thf(func_def_177, type, sK81: ((variable > real) > $o) > ((variable > real) > $o) > variable > real).
% 2.95/1.82 thf(func_def_178, type, sK82: set_variable > produc1078154247n_game > option_game).
% 2.95/1.82 thf(func_def_179, type, sK83: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_180, type, sK84: (set_variable > set_variable_real) > set_variable).
% 2.95/1.82 thf(func_def_181, type, sK85: set_variable > set_variable > set_variable > set_variable).
% 2.95/1.82 thf(func_def_182, type, sK86: set_variable > set_variable > set_variable > set_variable).
% 2.95/1.82 thf(func_def_183, type, sK87: produc1418842292n_game > denotational_interp > game > set_variable > variable > real).
% 2.95/1.82 thf(func_def_184, type, sK88: produc1418842292n_game > denotational_interp > game > set_variable > set_variable_real).
% 2.95/1.82 thf(func_def_185, type, sK89: produc1418842292n_game > denotational_interp > game > set_variable > variable > real).
% 2.95/1.82 thf(func_def_186, type, sK90: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_187, type, sK91: (set_variable_real > set_variable_real) > set_variable_real).
% 2.95/1.82 thf(func_def_188, type, sK92: ((variable > real) > $o) > set_variable_real > ((variable > real) > $o) > variable > real).
% 2.95/1.82 thf(func_def_190, type, ph94: !>[X0: $tType]:(X0)).
% 2.95/1.82 thf(f3759,plain,(
% 2.95/1.82 $false),
% 2.95/1.82 inference(avatar_sat_refutation,[status(thm)],[f1977,f1986,f2777,f2788,f2865,f3545,f3575,f3587,f3624,f3660,f3757])).
% 2.95/1.82 thf(f3757,plain,(
% 2.95/1.82 spl93_23 | ~spl93_5),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3742,f2018,f2755])).
% 2.95/1.82 thf(f2755,definition,(
% 2.95/1.82 spl93_23 <=> ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa))))),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_23])],[avatar_definition])).
% 2.95/1.82 thf(f2018,definition,(
% 2.95/1.82 spl93_5 <=> ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa))))),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_5])],[avatar_definition])).
% 2.95/1.82 thf(f3742,plain,(
% 2.95/1.82 ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | ~spl93_5),
% 2.95/1.82 inference(superposition,[status(thm)],[f1512,f2019])).
% 2.95/1.82 thf(f2019,plain,(
% 2.95/1.82 ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | ~spl93_5),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f2018])).
% 2.95/1.82 thf(f1512,plain,(
% 2.95/1.82 ( ! [X0 : set_variable_real] : (((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0)))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1])).
% 2.95/1.82 thf(f1,axiom,(
% 2.95/1.82 ! [X0 : set_variable_real] : ((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0)))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062)).
% 2.95/1.82 thf(f3660,plain,(
% 2.95/1.82 spl93_8 | spl93_7 | ~spl93_3),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3626,f1979,f2027,f2031])).
% 2.95/1.82 thf(f2031,definition,(
% 2.95/1.82 spl93_8 <=> ! [X0 : set_variable] : ((none_game = (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha))) | ($false = (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha))) @ (uminus430703407e_real @ xa))))))),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_8])],[avatar_definition])).
% 2.95/1.82 thf(f2027,definition,(
% 2.95/1.82 spl93_7 <=> ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) = none_game)),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_7])],[avatar_definition])).
% 2.95/1.82 thf(f1979,definition,(
% 2.95/1.82 spl93_3 <=> ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $false)),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_3])],[avatar_definition])).
% 2.95/1.82 thf(f3626,plain,(
% 2.95/1.82 ( ! [X0 : set_variable] : (((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) = none_game) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha))) | ($false = (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha))) @ (uminus430703407e_real @ xa)))))) ) | ~spl93_3),
% 2.95/1.82 inference(superposition,[status(thm)],[f1981,f1651])).
% 2.95/1.82 thf(f1651,plain,(
% 2.95/1.82 ( ! [X2 : set_variable,X3 : set_variable,X0 : game,X1 : produc1418842292n_game] : (((produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0)) = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0)))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1167])).
% 2.95/1.82 thf(f1167,plain,(
% 2.95/1.82 ! [X0 : game,X1 : produc1418842292n_game,X2 : set_variable,X3 : set_variable] : ((none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0))) | ((produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0)) = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0))))),
% 2.95/1.82 inference(flattening,[status(thm)],[f1166])).
% 2.95/1.82 thf(f1166,plain,(
% 2.95/1.82 ! [X0 : game,X1 : produc1418842292n_game,X2 : set_variable,X3 : set_variable] : ((((produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0)) = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0)))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0))))),
% 2.95/1.82 inference(ennf_transformation,[status(thm)],[f994])).
% 2.95/1.82 thf(f994,plain,(
% 2.95/1.82 ! [X0 : game,X1 : produc1418842292n_game,X2 : set_variable,X3 : set_variable] : ((none_game != (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0))) => ((none_game != (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0))) => ((produc293487213n_game @ (uSubst516392814stappp @ X1 @ X3 @ X0)) = (produc293487213n_game @ (uSubst516392814stappp @ X1 @ X2 @ X0)))))),
% 2.95/1.82 inference(rectify,[status(thm)],[f28])).
% 2.95/1.82 thf(f28,axiom,(
% 2.95/1.82 ! [X10 : game,X8 : produc1418842292n_game,X11 : set_variable,X9 : set_variable] : ((none_game != (produc293487213n_game @ (uSubst516392814stappp @ X8 @ X9 @ X10))) => ((none_game != (produc293487213n_game @ (uSubst516392814stappp @ X8 @ X11 @ X10))) => ((produc293487213n_game @ (uSubst516392814stappp @ X8 @ X9 @ X10)) = (produc293487213n_game @ (uSubst516392814stappp @ X8 @ X11 @ X10)))))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_27_usubstappp__det)).
% 2.95/1.82 thf(f1981,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $false) | ~spl93_3),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f1979])).
% 2.95/1.82 thf(f3624,plain,(
% 2.95/1.82 spl93_5 | spl93_1),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3610,f1970,f2018])).
% 2.95/1.82 thf(f1970,definition,(
% 2.95/1.82 spl93_1 <=> ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $true)),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_1])],[avatar_definition])).
% 2.95/1.82 thf(f3610,plain,(
% 2.95/1.82 ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | spl93_1),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f3606])).
% 2.95/1.82 thf(f3606,plain,(
% 2.95/1.82 ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | ($true != $true) | spl93_1),
% 2.95/1.82 inference(superposition,[status(thm)],[f1971,f1563])).
% 2.95/1.82 thf(f1563,plain,(
% 2.95/1.82 ( ! [X0 : variable > real,X1 : set_variable_real] : (($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) | ($true = (member_variable_real @ X0 @ X1))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1296])).
% 2.95/1.82 thf(f1296,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : ((($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) | ($true = (member_variable_real @ X0 @ X1))) & (($true != (member_variable_real @ X0 @ X1)) | ($true != (member_variable_real @ X0 @ (uminus430703407e_real @ X1)))))),
% 2.95/1.82 inference(nnf_transformation,[status(thm)],[f940])).
% 2.95/1.82 thf(f940,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : (($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) <=> ($true != (member_variable_real @ X0 @ X1)))),
% 2.95/1.82 inference(flattening,[status(thm)],[f601])).
% 2.95/1.82 thf(f601,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : (($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) <=> ~($true = (member_variable_real @ X0 @ X1)))),
% 2.95/1.82 inference(fool_elimination,[status(thm)],[f600])).
% 2.95/1.82 thf(f600,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : ((member_variable_real @ X0 @ (uminus430703407e_real @ X1)) = ~(member_variable_real @ X0 @ X1))),
% 2.95/1.82 inference(rectify,[status(thm)],[f14])).
% 2.95/1.82 thf(f14,axiom,(
% 2.95/1.82 ! [X2 : variable > real,X3 : set_variable_real] : ((member_variable_real @ X2 @ (uminus430703407e_real @ X3)) = ~(member_variable_real @ X2 @ X3))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_13_Compl__iff)).
% 2.95/1.82 thf(f1971,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) != $true) | spl93_1),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f1970])).
% 2.95/1.82 thf(f3587,plain,(
% 2.95/1.82 ~spl93_23 | ~spl93_2),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3584,f1974,f2755])).
% 2.95/1.82 thf(f1974,definition,(
% 2.95/1.82 spl93_2 <=> ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $true)),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_2])],[avatar_definition])).
% 2.95/1.82 thf(f3584,plain,(
% 2.95/1.82 ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | ~spl93_2),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f3582])).
% 2.95/1.82 thf(f3582,plain,(
% 2.95/1.82 ($true != $true) | ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | ~spl93_2),
% 2.95/1.82 inference(superposition,[status(thm)],[f1792,f1976])).
% 2.95/1.82 thf(f1976,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $true) | ~spl93_2),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f1974])).
% 2.95/1.82 thf(f1792,plain,(
% 2.95/1.82 ( ! [X0 : variable > real,X1 : set_variable_real] : (($true != (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) | ($true != (member_variable_real @ X0 @ X1))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1201])).
% 2.95/1.82 thf(f1201,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : (($true != (member_variable_real @ X0 @ X1)) | ($true != (member_variable_real @ X0 @ (uminus430703407e_real @ X1))))),
% 2.95/1.82 inference(ennf_transformation,[status(thm)],[f901])).
% 2.95/1.82 thf(f901,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : (($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) => ($true != (member_variable_real @ X0 @ X1)))),
% 2.95/1.82 inference(flattening,[status(thm)],[f375])).
% 2.95/1.82 thf(f375,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : (($true = (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) => ~($true = (member_variable_real @ X0 @ X1)))),
% 2.95/1.82 inference(fool_elimination,[status(thm)],[f374])).
% 2.95/1.82 thf(f374,plain,(
% 2.95/1.82 ! [X0 : variable > real,X1 : set_variable_real] : ((member_variable_real @ X0 @ (uminus430703407e_real @ X1)) => ~(member_variable_real @ X0 @ X1))),
% 2.95/1.82 inference(rectify,[status(thm)],[f34])).
% 2.95/1.82 thf(f34,axiom,(
% 2.95/1.82 ! [X2 : variable > real,X3 : set_variable_real] : ((member_variable_real @ X2 @ (uminus430703407e_real @ X3)) => ~(member_variable_real @ X2 @ X3))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_33_ComplD)).
% 2.95/1.82 thf(f3575,plain,(
% 2.95/1.82 ~spl93_23 | spl93_5),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3574,f2018,f2755])).
% 2.95/1.82 thf(f3574,plain,(
% 2.95/1.82 ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | spl93_5),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f3573])).
% 2.95/1.82 thf(f3573,plain,(
% 2.95/1.82 ($true != $true) | ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | spl93_5),
% 2.95/1.82 inference(forward_demodulation,[status(thm)],[f3562,f1498])).
% 2.95/1.82 thf(f1498,plain,(
% 2.95/1.82 ((denota1419872369iation @ nu2 @ omega2 @ ua) = $true)),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f745])).
% 2.95/1.82 thf(f745,plain,(
% 2.95/1.82 ((denota1419872369iation @ nu2 @ omega2 @ ua) = $true)),
% 2.95/1.82 inference(fool_elimination,[status(thm)],[f744])).
% 2.95/1.82 thf(f744,plain,(
% 2.95/1.82 (denota1419872369iation @ nu2 @ omega2 @ ua)),
% 2.95/1.82 inference(rectify,[status(thm)],[f3])).
% 2.95/1.82 thf(f3,axiom,(
% 2.95/1.82 (denota1419872369iation @ nu2 @ omega2 @ ua)),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_2_uv)).
% 2.95/1.82 thf(f3562,plain,(
% 2.95/1.82 ((denota1419872369iation @ nu2 @ omega2 @ ua) != $true) | ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | spl93_5),
% 2.95/1.82 inference(superposition,[status(thm)],[f2020,f1872])).
% 2.95/1.82 thf(f1872,plain,(
% 2.95/1.82 ( ! [X0 : set_variable_real] : (((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0))) | ((denota1419872369iation @ nu2 @ omega2 @ ua) != $true)) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1194])).
% 2.95/1.82 thf(f1194,plain,(
% 2.95/1.82 ! [X0 : set_variable_real] : (((denota1419872369iation @ nu2 @ omega2 @ ua) != $true) | ((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0))))),
% 2.95/1.82 inference(ennf_transformation,[status(thm)],[f695])).
% 2.95/1.82 thf(f695,plain,(
% 2.95/1.82 ! [X0 : set_variable_real] : (((denota1419872369iation @ nu2 @ omega2 @ ua) = $true) => ((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0))))),
% 2.95/1.82 inference(fool_elimination,[status(thm)],[f694])).
% 2.95/1.82 thf(f694,plain,(
% 2.95/1.82 ! [X0 : set_variable_real] : ((denota1419872369iation @ nu2 @ omega2 @ ua) => ((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0))))),
% 2.95/1.82 inference(rectify,[status(thm)],[f2])).
% 2.95/1.82 thf(f2,axiom,(
% 2.95/1.82 ! [X0 : set_variable_real] : ((denota1419872369iation @ nu2 @ omega2 @ ua) => ((member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ X0)) = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ X0))))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_1_IH_092_060alpha_062)).
% 2.95/1.82 thf(f2020,plain,(
% 2.95/1.82 ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | spl93_5),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f2018])).
% 2.95/1.82 thf(f3545,plain,(
% 2.95/1.82 ~spl93_7 | ~spl93_7),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f3506,f2027,f2027])).
% 2.95/1.82 thf(f3506,plain,(
% 2.95/1.82 ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) != none_game) | ~spl93_7),
% 2.95/1.82 inference(superposition,[status(thm)],[f1813,f3505])).
% 2.95/1.82 thf(f3505,plain,(
% 2.95/1.82 ((uSubst516392814stappp @ sigma @ ua @ alpha) = (uSubst516392814stappp @ sigma @ ua @ (dual @ alpha))) | ~spl93_7),
% 2.95/1.82 inference(forward_demodulation,[status(thm)],[f2859,f2840])).
% 2.95/1.82 thf(f2840,plain,(
% 2.95/1.82 ((uSubst516392814stappp @ sigma @ ua @ alpha) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ none_game)) | ~spl93_7),
% 2.95/1.82 inference(superposition,[status(thm)],[f1787,f2029])).
% 2.95/1.82 thf(f2029,plain,(
% 2.95/1.82 ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) = none_game) | ~spl93_7),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f2027])).
% 2.95/1.82 thf(f1787,plain,(
% 2.95/1.82 ( ! [X0 : produc1078154247n_game] : (((produc1149443391n_game @ (produc893821739n_game @ X0) @ (produc293487213n_game @ X0)) = X0)) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f897])).
% 2.95/1.82 thf(f897,plain,(
% 2.95/1.82 ! [X0 : produc1078154247n_game] : ((produc1149443391n_game @ (produc893821739n_game @ X0) @ (produc293487213n_game @ X0)) = X0)),
% 2.95/1.82 inference(rectify,[status(thm)],[f154])).
% 2.95/1.82 thf(f154,axiom,(
% 2.95/1.82 ! [X43 : produc1078154247n_game] : ((produc1149443391n_game @ (produc893821739n_game @ X43) @ (produc293487213n_game @ X43)) = X43)),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_153_prod_Oexhaust__sel)).
% 2.95/1.82 thf(f2859,plain,(
% 2.95/1.82 ((uSubst516392814stappp @ sigma @ ua @ (dual @ alpha)) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ none_game)) | ~spl93_7),
% 2.95/1.82 inference(forward_demodulation,[status(thm)],[f2828,f1455])).
% 2.95/1.82 thf(f1455,plain,(
% 2.95/1.82 (none_game = (uSubst1916713664_Dualo @ none_game))),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f173])).
% 2.95/1.82 thf(f173,axiom,(
% 2.95/1.82 (none_game = (uSubst1916713664_Dualo @ none_game))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_172_Dualo_Osimps_I2_J)).
% 2.95/1.82 thf(f2828,plain,(
% 2.95/1.82 ((uSubst516392814stappp @ sigma @ ua @ (dual @ alpha)) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ (uSubst1916713664_Dualo @ none_game))) | ~spl93_7),
% 2.95/1.82 inference(superposition,[status(thm)],[f1450,f2029])).
% 2.95/1.82 thf(f1450,plain,(
% 2.95/1.82 ( ! [X2 : game,X0 : produc1418842292n_game,X1 : set_variable] : (((uSubst516392814stappp @ X0 @ X1 @ (dual @ X2)) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ X0 @ X1 @ X2)) @ (uSubst1916713664_Dualo @ (produc293487213n_game @ (uSubst516392814stappp @ X0 @ X1 @ X2)))))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f949])).
% 2.95/1.82 thf(f949,plain,(
% 2.95/1.82 ! [X0 : produc1418842292n_game,X1 : set_variable,X2 : game] : ((uSubst516392814stappp @ X0 @ X1 @ (dual @ X2)) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ X0 @ X1 @ X2)) @ (uSubst1916713664_Dualo @ (produc293487213n_game @ (uSubst516392814stappp @ X0 @ X1 @ X2)))))),
% 2.95/1.82 inference(rectify,[status(thm)],[f160])).
% 2.95/1.82 thf(f160,axiom,(
% 2.95/1.82 ! [X8 : produc1418842292n_game,X9 : set_variable,X10 : game] : ((uSubst516392814stappp @ X8 @ X9 @ (dual @ X10)) = (produc1149443391n_game @ (produc893821739n_game @ (uSubst516392814stappp @ X8 @ X9 @ X10)) @ (uSubst1916713664_Dualo @ (produc293487213n_game @ (uSubst516392814stappp @ X8 @ X9 @ X10)))))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_159_usubstappp__dual)).
% 2.95/1.82 thf(f1813,plain,(
% 2.95/1.82 ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (dual @ alpha))) != none_game)),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f8])).
% 2.95/1.82 thf(f8,axiom,(
% 2.95/1.82 ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (dual @ alpha))) != none_game)),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',fact_7_def)).
% 2.95/1.82 thf(f2865,plain,(
% 2.95/1.82 spl93_23 | ~spl93_4),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f2752,f1983,f2755])).
% 2.95/1.82 thf(f1983,definition,(
% 2.95/1.82 spl93_4 <=> ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $false)),
% 2.95/1.82 introduced(definition,[new_symbols(naming,[spl93_4])],[avatar_definition])).
% 2.95/1.82 thf(f2752,plain,(
% 2.95/1.82 ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | ~spl93_4),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f2731])).
% 2.95/1.82 thf(f2731,plain,(
% 2.95/1.82 ($true = $false) | ($true = (member_variable_real @ nu2 @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) | ~spl93_4),
% 2.95/1.82 inference(superposition,[status(thm)],[f1985,f1563])).
% 2.95/1.82 thf(f1985,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $false) | ~spl93_4),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f1983])).
% 2.95/1.82 thf(f2788,plain,(
% 2.95/1.82 spl93_7 | ~spl93_1 | ~spl93_8),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f2772,f2031,f1970,f2027])).
% 2.95/1.82 thf(f2772,plain,(
% 2.95/1.82 ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) = none_game) | (~spl93_1 | ~spl93_8)),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f2768])).
% 2.95/1.82 thf(f2768,plain,(
% 2.95/1.82 ($true = $false) | ((produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) = none_game) | (~spl93_1 | ~spl93_8)),
% 2.95/1.82 inference(superposition,[status(thm)],[f1972,f2032])).
% 2.95/1.82 thf(f2032,plain,(
% 2.95/1.82 ( ! [X0 : set_variable] : (($false = (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha))) @ (uminus430703407e_real @ xa))))) | (none_game = (produc293487213n_game @ (uSubst516392814stappp @ sigma @ X0 @ alpha)))) ) | ~spl93_8),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f2031])).
% 2.95/1.82 thf(f1972,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $true) | ~spl93_1),
% 2.95/1.82 inference(avatar_component_clause,[status(thm)],[f1970])).
% 2.95/1.82 thf(f2777,plain,(
% 2.95/1.82 ~spl93_5 | ~spl93_1),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f2774,f1970,f2018])).
% 2.95/1.82 thf(f2774,plain,(
% 2.95/1.82 ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | ~spl93_1),
% 2.95/1.82 inference(trivial_inequality_removal,[status(thm)],[f2770])).
% 2.95/1.82 thf(f2770,plain,(
% 2.95/1.82 ($true != (member_variable_real @ nu2 @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) | ($true != $true) | ~spl93_1),
% 2.95/1.82 inference(superposition,[status(thm)],[f1562,f1972])).
% 2.95/1.82 thf(f1562,plain,(
% 2.95/1.82 ( ! [X0 : variable > real,X1 : set_variable_real] : (($true != (member_variable_real @ X0 @ (uminus430703407e_real @ X1))) | ($true != (member_variable_real @ X0 @ X1))) )),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f1296])).
% 2.95/1.82 thf(f1986,plain,(
% 2.95/1.82 spl93_3 | spl93_4),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f1968,f1983,f1979])).
% 2.95/1.82 thf(f1968,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $false) | ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $false)),
% 2.95/1.82 inference(binary_proxy_clausification,[status(thm)],[f1444])).
% 2.95/1.82 thf(f1444,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) != (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))))),
% 2.95/1.82 inference(cnf_transformation,[status(thm)],[f985])).
% 2.95/1.82 thf(f985,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) != (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))))),
% 2.95/1.82 inference(flattening,[status(thm)],[f356])).
% 2.95/1.82 thf(f356,negated_conjecture,(
% 2.95/1.82 ~((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))))),
% 2.95/1.82 inference(negated_conjecture,[status(cth)],[f355])).
% 2.95/1.82 thf(f355,conjecture,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = (member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))))),
% 2.95/1.82 file('/export/starexec/sandbox/tmp/tmp.16sPC1GfKW/DTF2THF_28368.p',conj_0)).
% 2.95/1.82 thf(f1977,plain,(
% 2.95/1.82 spl93_1 | spl93_2),
% 2.95/1.82 inference(avatar_split_clause,[status(thm)],[f1967,f1974,f1970])).
% 2.95/1.82 thf(f1967,plain,(
% 2.95/1.82 ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ (uSubst1599435252djoint @ sigma @ i @ omega2) @ alpha @ (uminus430703407e_real @ xa)))) = $true) | ((member_variable_real @ nu2 @ (uminus430703407e_real @ (denota1245701238me_sem @ i @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))) @ (uminus430703407e_real @ xa)))) = $true)),
% 2.95/1.82 inference(binary_proxy_clausification,[status(thm)],[f1444])).
% 2.95/1.82 % SZS output end Proof for DTF2THF_28368
% 2.95/1.82 % (28489)------------------------------
% 2.95/1.82 % (28489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.82 % (28489)Termination reason: Refutation
% 2.95/1.82
% 2.95/1.82 % (28489)Memory used [KB]: 7803
% 2.95/1.82 % (28489)Time elapsed: 0.175 s
% 2.95/1.82 % (28489)Instructions burned: 614 (million)
% 2.95/1.82 % (28489)------------------------------
% 2.95/1.82 % (28489)------------------------------
% 2.95/1.82 % (28466)Success in time 0.254 s
%------------------------------------------------------------------------------