%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP205^1 : 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 : n020.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 08:56:24 AM UTC 2026
% Result : Theorem 29.33s 5.47s
% Output : Refutation 29.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 24 unt; 0 typ; 2 def)
% Number of atoms : 302 ( 84 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1057 ( 55 ~; 49 |; 0 &; 930 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 104 usr; 9 con; 0-4 aty)
% Number of variables : 90 ( 0 ^; 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1625152599n_game: $tType ).
thf(type_def_6,type,
option_game: $tType ).
thf(type_def_7,type,
set_variable: $tType ).
thf(type_def_9,type,
produc1078154247n_game: $tType ).
thf(type_def_10,type,
produc1016592119n_game: $tType ).
thf(type_def_11,type,
variable: $tType ).
thf(type_def_12,type,
set_Pr166476775n_game: $tType ).
thf(type_def_13,type,
game: $tType ).
thf(type_def_14,type,
produc735959047riable: $tType ).
thf(type_def_15,type,
produc1418842292n_game: $tType ).
thf(func_def_0,type,
produc1418842292n_game: $tType ).
thf(func_def_1,type,
set_Pr1625152599n_game: $tType ).
thf(func_def_2,type,
set_Pr166476775n_game: $tType ).
thf(func_def_3,type,
produc1016592119n_game: $tType ).
thf(func_def_4,type,
produc1078154247n_game: $tType ).
thf(func_def_5,type,
produc735959047riable: $tType ).
thf(func_def_6,type,
option_game: $tType ).
thf(func_def_7,type,
set_variable: $tType ).
thf(func_def_8,type,
variable: $tType ).
thf(func_def_9,type,
game: $tType ).
thf(func_def_10,type,
bNF_Ca1986151756riable: set_Pr1625152599n_game > ( option_game > set_variable ) > $o ).
thf(func_def_11,type,
bNF_fs984229733n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
thf(func_def_12,type,
bNF_pi856525207n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > set_variable > option_game > option_game ).
thf(func_def_13,type,
bNF_pi1813424679n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > set_variable > option_game > set_variable ).
thf(func_def_14,type,
bNF_sn1374695591n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1016592119n_game ).
thf(func_def_15,type,
bNF_sn582998327n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
thf(func_def_16,type,
sup_su169929796game_o: ( option_game > option_game > $o ) > ( option_game > option_game > $o ) > option_game > option_game > $o ).
thf(func_def_17,type,
sup_su1229228248game_o: ( option_game > $o ) > ( option_game > $o ) > option_game > $o ).
thf(func_def_18,type,
sup_su1227468340game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > set_variable > option_game > $o ).
thf(func_def_19,type,
sup_sup_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
thf(func_def_20,type,
sup_sup_o: $o > $o > $o ).
thf(func_def_21,type,
sup_su423136299n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > set_Pr1625152599n_game ).
thf(func_def_22,type,
sup_su796825019n_game: set_Pr166476775n_game > set_Pr166476775n_game > set_Pr166476775n_game ).
thf(func_def_23,type,
sup_sup_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_24,type,
none_game: option_game ).
thf(func_def_25,type,
some_game: game > option_game ).
thf(func_def_26,type,
the_game: option_game > game ).
thf(func_def_27,type,
ord_le707292176game_o: ( option_game > option_game > $o ) > ( option_game > option_game > $o ) > $o ).
thf(func_def_28,type,
ord_le2134856704game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > $o ).
thf(func_def_29,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_30,type,
ord_le1780499447n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > $o ).
thf(func_def_31,type,
ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o ).
thf(func_def_32,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_33,type,
order_272405634riable: ( set_variable > $o ) > set_variable ).
thf(func_def_34,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_35,type,
produc1140431679riable: option_game > set_variable > produc735959047riable ).
thf(func_def_36,type,
produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
thf(func_def_37,type,
produc1942569115n_game: produc1016592119n_game > option_game ).
thf(func_def_38,type,
produc884810027riable: produc735959047riable > option_game ).
thf(func_def_39,type,
produc893821739n_game: produc1078154247n_game > set_variable ).
thf(func_def_40,type,
produc279011037n_game: produc1016592119n_game > option_game ).
thf(func_def_41,type,
produc284475501riable: produc735959047riable > set_variable ).
thf(func_def_42,type,
produc293487213n_game: produc1078154247n_game > option_game ).
thf(func_def_43,type,
produc1696194127n_game: produc1016592119n_game > produc1016592119n_game ).
thf(func_def_44,type,
produc345397471riable: produc735959047riable > produc1078154247n_game ).
thf(func_def_45,type,
produc354409183n_game: produc1078154247n_game > produc735959047riable ).
thf(func_def_46,type,
collec884051426n_game: ( produc1016592119n_game > $o ) > set_Pr1625152599n_game ).
thf(func_def_47,type,
collec1702522994n_game: ( produc1078154247n_game > $o ) > set_Pr166476775n_game ).
thf(func_def_48,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_49,type,
static_BVG: game > set_variable ).
thf(func_def_50,type,
choice: game > game > game ).
thf(func_def_51,type,
compose: game > game > game ).
thf(func_def_52,type,
loop: game > game ).
thf(func_def_53,type,
uSubst1484167963hoiceo: option_game > option_game > option_game ).
thf(func_def_54,type,
uSubst532817840mposeo: option_game > option_game > option_game ).
thf(func_def_55,type,
uSubst23177304_Loopo: option_game > option_game ).
thf(func_def_56,type,
uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
thf(func_def_57,type,
member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
thf(func_def_58,type,
member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o ).
thf(func_def_59,type,
member_variable: variable > set_variable > $o ).
thf(func_def_60,type,
ua: set_variable ).
thf(func_def_61,type,
alpha: game ).
thf(func_def_62,type,
beta: game ).
thf(func_def_63,type,
sigma: produc1418842292n_game ).
thf(func_def_78,type,
sP0: ( option_game > option_game > $o ) > option_game > option_game > $o ).
thf(func_def_79,type,
sK1: ( set_variable > set_variable ) > set_variable ).
thf(func_def_80,type,
sK2: ( set_variable > set_variable ) > set_variable ).
thf(func_def_81,type,
sK3: ( set_variable > set_variable ) > set_variable ).
thf(func_def_82,type,
sK4: ( set_variable > set_variable ) > set_variable ).
thf(func_def_83,type,
sK5: option_game > game ).
thf(func_def_84,type,
sK6: ( option_game > $o ) > game ).
thf(func_def_85,type,
sK7: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_86,type,
sK8: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_87,type,
sK9: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_88,type,
sK10: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_89,type,
sK11: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_90,type,
sK12: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_91,type,
sK13: ( set_variable > set_variable > set_variable ) > set_variable ).
thf(func_def_92,type,
sK14: set_variable > set_variable > set_variable > set_variable ).
thf(func_def_93,type,
sK15: set_variable > set_variable > set_variable > set_variable ).
thf(func_def_94,type,
sK16: option_game > game ).
thf(func_def_95,type,
sK17: ( produc1078154247n_game > $o ) > option_game ).
thf(func_def_96,type,
sK18: ( produc1078154247n_game > $o ) > set_variable ).
thf(func_def_97,type,
sK19: option_game > game ).
thf(func_def_98,type,
sK20: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_99,type,
sK21: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_100,type,
sK22: option_game > game ).
thf(func_def_101,type,
sK23: produc1078154247n_game > option_game ).
thf(func_def_102,type,
sK24: produc1078154247n_game > set_variable ).
thf(func_def_103,type,
sK25: produc1078154247n_game > set_variable > option_game ).
thf(func_def_104,type,
sK26: ( produc1078154247n_game > $o ) > set_variable ).
thf(func_def_105,type,
sK27: ( produc1078154247n_game > $o ) > option_game ).
thf(func_def_106,type,
sK28: option_game > game ).
thf(func_def_107,type,
sK29: produc1016592119n_game > option_game ).
thf(func_def_108,type,
sK30: produc1016592119n_game > game ).
thf(func_def_109,type,
sK31: produc1016592119n_game > game ).
thf(func_def_110,type,
sK32: produc1016592119n_game > game ).
thf(func_def_111,type,
sK33: produc1078154247n_game > option_game > set_variable ).
thf(func_def_112,type,
sK34: ( option_game > option_game > $o ) > option_game ).
thf(func_def_113,type,
sK35: ( option_game > option_game > $o ) > game ).
thf(func_def_114,type,
sK36: ( option_game > option_game > $o ) > game ).
thf(func_def_115,type,
sK37: ( option_game > option_game > $o ) > game ).
thf(func_def_116,type,
sK38: ( set_variable > set_variable ) > set_variable ).
thf(func_def_117,type,
sK39: ( set_variable > set_variable ) > set_variable ).
thf(func_def_118,type,
sK40: ( set_variable > set_variable ) > set_variable ).
thf(func_def_119,type,
sK41: ( set_variable > set_variable ) > set_variable ).
thf(func_def_120,type,
sK42: produc1078154247n_game > option_game ).
thf(func_def_121,type,
sK43: produc1078154247n_game > set_variable ).
thf(func_def_122,type,
sK44: ( option_game > $o ) > game ).
thf(func_def_123,type,
sK45: ( option_game > set_variable > $o ) > set_variable ).
thf(func_def_124,type,
sK46: ( option_game > set_variable > $o ) > option_game ).
thf(func_def_126,type,
ph48:
!>[X0: $tType] : X0 ).
thf(f10714,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1328,f1397,f10713]) ).
thf(f10713,plain,
spl47_1,
inference(avatar_contradiction_clause,[status(thm)],[f10712]) ).
thf(f10712,plain,
( $false
| spl47_1 ),
inference(subsumption_resolution,[status(thm)],[f10643,f1206]) ).
thf(f1206,plain,
( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f543]) ).
thf(f543,plain,
( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f542]) ).
thf(f542,plain,
ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_1_fact) ).
thf(f10643,plain,
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_1 ),
inference(trivial_inequality_removal,[status(thm)],[f10634]) ).
thf(f10634,plain,
( ( $true != $true )
| ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_1 ),
inference(superposition,[status(thm)],[f2521,f1176]) ).
thf(f1176,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X1 @ X0 ) )
= $true )
| ( $true
!= ( ord_le282106107riable @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f915]) ).
thf(f915,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X1 @ X0 ) )
= $true )
| ( $true
!= ( ord_le282106107riable @ X2 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f687]) ).
thf(f687,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( $true
= ( ord_le282106107riable @ X2 @ X0 ) )
=> ( ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f686]) ).
thf(f686,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ord_le282106107riable @ X2 @ X0 )
=> ( ord_le282106107riable @ X2 @ ( sup_sup_set_variable @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f164]) ).
thf(f164,axiom,
! [X10: set_variable,X12: set_variable,X11: set_variable] :
( ( ord_le282106107riable @ X11 @ X10 )
=> ( ord_le282106107riable @ X11 @ ( sup_sup_set_variable @ X12 @ X10 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_163_sup_OcoboundedI2) ).
thf(f2521,plain,
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ua @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ) )
!= $true )
| spl47_1 ),
inference(forward_demodulation,[status(thm)],[f2513,f1062]) ).
thf(f1062,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( sup_sup_set_variable @ X0 @ ( sup_sup_set_variable @ X1 @ X2 ) )
= ( sup_sup_set_variable @ ( sup_sup_set_variable @ X0 @ X1 ) @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f807]) ).
thf(f807,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( sup_sup_set_variable @ X0 @ ( sup_sup_set_variable @ X1 @ X2 ) )
= ( sup_sup_set_variable @ ( sup_sup_set_variable @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[status(thm)],[f149]) ).
thf(f149,axiom,
! [X7: set_variable,X8: set_variable,X9: set_variable] :
( ( sup_sup_set_variable @ X7 @ ( sup_sup_set_variable @ X8 @ X9 ) )
= ( sup_sup_set_variable @ ( sup_sup_set_variable @ X7 @ X8 ) @ X9 ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_148_inf__sup__aci_I6_J) ).
thf(f2513,plain,
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_1 ),
inference(trivial_inequality_removal,[status(thm)],[f2466]) ).
thf(f2466,plain,
( ( $true != $true )
| ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_1 ),
inference(superposition,[status(thm)],[f1490,f1175]) ).
thf(f1175,plain,
( ( ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f573]) ).
thf(f573,plain,
( ( ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f572]) ).
thf(f572,plain,
ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062) ).
thf(f1490,plain,
( ! [X0: set_variable] :
( ( ( ord_le282106107riable @ X0 @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true )
| ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ X0 )
!= $true ) )
| spl47_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1482]) ).
thf(f1482,plain,
( ! [X0: set_variable] :
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( ord_le282106107riable @ X0 @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true ) )
| spl47_1 ),
inference(superposition,[status(thm)],[f1300,f1078]) ).
thf(f1078,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X1 )
= $true )
| ( ( ord_le282106107riable @ X2 @ X1 )
!= $true )
| ( ( ord_le282106107riable @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f956]) ).
thf(f956,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X1 )
= $true )
| ( ( ord_le282106107riable @ X0 @ X2 )
!= $true )
| ( ( ord_le282106107riable @ X2 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f955]) ).
thf(f955,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X1 )
= $true )
| ( ( ord_le282106107riable @ X0 @ X2 )
!= $true )
| ( ( ord_le282106107riable @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f657]) ).
thf(f657,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X2 @ X1 )
= $true )
=> ( ( ( ord_le282106107riable @ X0 @ X2 )
= $true )
=> ( ( ord_le282106107riable @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f656]) ).
thf(f656,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ord_le282106107riable @ X2 @ X1 )
=> ( ( ord_le282106107riable @ X0 @ X2 )
=> ( ord_le282106107riable @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f230]) ).
thf(f230,axiom,
! [X11: set_variable,X12: set_variable,X10: set_variable] :
( ( ord_le282106107riable @ X10 @ X12 )
=> ( ( ord_le282106107riable @ X11 @ X10 )
=> ( ord_le282106107riable @ X11 @ X12 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_229_dual__order_Otrans) ).
thf(f1300,plain,
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true )
| spl47_1 ),
inference(avatar_component_clause,[status(thm)],[f1298]) ).
thf(f1298,definition,
( spl47_1
<=> ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl47_1])],[avatar_definition]) ).
thf(f1397,plain,
spl47_2,
inference(avatar_contradiction_clause,[status(thm)],[f1396]) ).
thf(f1396,plain,
( $false
| spl47_2 ),
inference(subsumption_resolution,[status(thm)],[f1395,f1099]) ).
thf(f1099,plain,
! [X0: set_variable,X1: set_variable] :
( ( ord_le282106107riable @ X0 @ ( sup_sup_set_variable @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f735]) ).
thf(f735,plain,
! [X0: set_variable,X1: set_variable] :
( ( ord_le282106107riable @ X0 @ ( sup_sup_set_variable @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f734]) ).
thf(f734,plain,
! [X0: set_variable,X1: set_variable] : ( ord_le282106107riable @ X0 @ ( sup_sup_set_variable @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f197]) ).
thf(f197,axiom,
! [X4: set_variable,X5: set_variable] : ( ord_le282106107riable @ X4 @ ( sup_sup_set_variable @ X4 @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_196_Un__upper1) ).
thf(f1395,plain,
( ( ( ord_le282106107riable @ ua @ ( sup_sup_set_variable @ ua @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ) )
!= $true )
| spl47_2 ),
inference(forward_demodulation,[status(thm)],[f1375,f1062]) ).
thf(f1375,plain,
( ( ( ord_le282106107riable @ ua @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1340]) ).
thf(f1340,plain,
( ( $true != $true )
| ( ( ord_le282106107riable @ ua @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) )
!= $true )
| spl47_2 ),
inference(superposition,[status(thm)],[f1338,f1175]) ).
thf(f1338,plain,
( ! [X0: set_variable] :
( ( ( ord_le282106107riable @ X0 @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true )
| ( ( ord_le282106107riable @ ua @ X0 )
!= $true ) )
| spl47_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1329]) ).
thf(f1329,plain,
( ! [X0: set_variable] :
( ( ( ord_le282106107riable @ ua @ X0 )
!= $true )
| ( $true != $true )
| ( ( ord_le282106107riable @ X0 @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true ) )
| spl47_2 ),
inference(superposition,[status(thm)],[f1304,f1053]) ).
thf(f1053,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X2 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X2 ) )
| ( ( ord_le282106107riable @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f856]) ).
thf(f856,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X1 )
!= $true )
| ( ( ord_le282106107riable @ X0 @ X2 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X2 ) ) ),
inference(flattening,[status(thm)],[f855]) ).
thf(f855,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X2 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X2 ) )
| ( ( ord_le282106107riable @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f369]) ).
thf(f369,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ X0 @ X1 )
= $true )
=> ( ( $true
= ( ord_le282106107riable @ X1 @ X2 ) )
=> ( ( ord_le282106107riable @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f368]) ).
thf(f368,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ord_le282106107riable @ X0 @ X1 )
=> ( ( ord_le282106107riable @ X1 @ X2 )
=> ( ord_le282106107riable @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f81]) ).
thf(f81,axiom,
! [X4: set_variable,X5: set_variable,X6: set_variable] :
( ( ord_le282106107riable @ X4 @ X5 )
=> ( ( ord_le282106107riable @ X5 @ X6 )
=> ( ord_le282106107riable @ X4 @ X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_80_subset__trans) ).
thf(f1304,plain,
( ( $true
!= ( ord_le282106107riable @ ua @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) )
| spl47_2 ),
inference(avatar_component_clause,[status(thm)],[f1302]) ).
thf(f1302,definition,
( spl47_2
<=> ( $true
= ( ord_le282106107riable @ ua @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl47_2])],[avatar_definition]) ).
thf(f1328,plain,
( ~ spl47_2
| ~ spl47_1 ),
inference(avatar_split_clause,[status(thm)],[f1285,f1298,f1302]) ).
thf(f1285,plain,
( ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true )
| ( $true
!= ( ord_le282106107riable @ ua @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1280]) ).
thf(f1280,plain,
( ( $true
!= ( ord_le282106107riable @ ua @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) )
| ( ( ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1073,f1098]) ).
thf(f1098,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ X1 ) @ X0 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X0 ) )
| ( $true
!= ( ord_le282106107riable @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f923]) ).
thf(f923,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ X1 ) @ X0 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X0 ) )
| ( $true
!= ( ord_le282106107riable @ X2 @ X0 ) ) ),
inference(flattening,[status(thm)],[f922]) ).
thf(f922,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ X1 ) @ X0 )
= $true )
| ( $true
!= ( ord_le282106107riable @ X1 @ X0 ) )
| ( $true
!= ( ord_le282106107riable @ X2 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f467]) ).
thf(f467,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( $true
= ( ord_le282106107riable @ X2 @ X0 ) )
=> ( ( $true
= ( ord_le282106107riable @ X1 @ X0 ) )
=> ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ X1 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f466]) ).
thf(f466,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( ord_le282106107riable @ X2 @ X0 )
=> ( ( ord_le282106107riable @ X1 @ X0 )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ X2 @ X1 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f181]) ).
thf(f181,axiom,
! [X7: set_variable,X9: set_variable,X8: set_variable] :
( ( ord_le282106107riable @ X8 @ X7 )
=> ( ( ord_le282106107riable @ X9 @ X7 )
=> ( ord_le282106107riable @ ( sup_sup_set_variable @ X8 @ X9 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_180_sup__least) ).
thf(f1073,plain,
( ( ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f802]) ).
thf(f802,plain,
( ( ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true ),
inference(flattening,[status(thm)],[f707]) ).
thf(f707,plain,
( ( ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f706]) ).
thf(f706,plain,
~ ( ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
~ ( ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ),
file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP205^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:29:57 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP205^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer USubst problem prob_966__6345404_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : USubst/prob_966__6345404_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 419 ( 232 unt; 64 typ; 0 def)
% 0.28/0.47 % Number of atoms : 868 ( 399 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 9 ( 2 avg)
% 0.28/0.47 % Number of connectives : 2595 ( 72 ~; 9 |; 47 &;2211 @)
% 0.28/0.47 % ( 0 <=>; 256 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 16 ( 5 avg)
% 0.28/0.47 % Number of types : 11 ( 10 usr)
% 0.28/0.47 % Number of type conns : 375 ( 375 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 55 ( 54 usr; 5 con; 0-4 aty)
% 0.28/0.47 % Number of variables : 982 ( 157 ^; 808 !; 17 ?; 982 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:23.013
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (10)
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% 0.28/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
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% 0.28/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
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% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.28/0.47 thf(ty_n_t__Syntax__Ovariable,type,
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% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Syntax__Ogame,type,
% 0.28/0.47 game: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (54)
% 0.28/0.47 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_BNF__Def_OfstOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 bNF_fs984229733n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 bNF_pi856525207n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > set_variable > option_game > option_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 bNF_pi1813424679n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > set_variable > option_game > set_variable ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 bNF_sn1374695591n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1016592119n_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 bNF_sn582998327n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J,type,
% 0.28/0.47 sup_su1229228248game_o: ( option_game > $o ) > ( option_game > $o ) > option_game > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
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% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.28/0.47 sup_sup_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_Eo,type,
% 0.28/0.47 sup_sup_o: $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
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% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 0.28/0.47 some_game: game > option_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
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% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
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% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
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% 0.28/0.47 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,
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% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.28/0.47 ord_le282106107riable: set_variable > set_variable > $o ).
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% 0.28/0.47 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.28/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
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% 0.28/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.28/0.47 produc1140431679riable: option_game > set_variable > produc735959047riable ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.28/0.47 produc884810027riable: produc735959047riable > option_game ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 produc279011037n_game: produc1016592119n_game > option_game ).
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.28/0.47 produc284475501riable: produc735959047riable > set_variable ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.28/0.47 produc1696194127n_game: produc1016592119n_game > produc1016592119n_game ).
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.28/0.47 thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
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% 0.28/0.47 thf(sy_c_Syntax_Ogame_OChoice,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Syntax_Ogame_OCompose,type,
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% 0.28/0.47
% 0.28/0.47 thf(sy_c_Syntax_Ogame_OLoop,type,
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% 0.28/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OComposeo,type,
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% 0.28/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OLoopo,type,
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% 0.28/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappp,type,
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% 0.28/0.47 thf(sy_v__092_060alpha_062_H____,type,
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% 0.28/0.47 thf(sy_v__092_060beta_062____,type,
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% 0.28/0.47 thf(sy_v__092_060sigma_062,type,
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% 0.28/0.47
% 0.28/0.47 % Relevant facts (354)
% 0.28/0.47 thf(fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062,axiom,
% 0.28/0.47 ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>U \<union> BVG (the (snd (usubstappp \<sigma> U \<alpha>))) \<union> BVG (the (snd (usubstappp \<sigma> (fst (usubstappp \<sigma> U \<alpha>)) \<beta>))) \<subseteq> fst (usubstappp \<sigma> (fst (usubstappp \<sigma> U \<alpha>)) \<beta>)\<close>
% 0.28/0.47 thf(fact_1_fact,axiom,
% 0.28/0.47 ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fact
% 0.28/0.47 thf(fact_2_IHa,axiom,
% 0.28/0.47 ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ).
% 0.28/0.47
% 0.28/0.47 % IHa
% 0.28/0.47 thf(fact_3_IHb,axiom,
% 0.28/0.47 ord_le282106107riable @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.28/0.47
% 0.28/0.47 % IHb
% 0.28/0.47 thf(fact_4_Compose_Oprems,axiom,
% 0.28/0.47 ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) )
% 0.28/0.47 != none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Compose.prems
% 0.28/0.47 thf(fact_5_usubst__taboos__mon,axiom,
% 0.28/0.47 ! [U: set_variable,Sigma: produc1418842292n_game,Alpha: game] : ( ord_le282106107riable @ U @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubst_taboos_mon
% 0.28/0.47 thf(fact_6_usubstappp__fst__mon,axiom,
% 0.28/0.47 ! [U: set_variable,V: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.28/0.47 ( ( ord_le282106107riable @ U @ V )
% 0.28/0.47 => ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_fst_mon
% 0.28/0.47 thf(fact_7_Compose_OIH_I2_J,axiom,
% 0.28/0.47 ! [U: set_variable] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ U @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compose.IH(2)
% 0.28/0.47 thf(fact_8_Compose_OIH_I1_J,axiom,
% 0.28/0.47 ! [U: set_variable] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ U @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compose.IH(1)
% 0.28/0.47 thf(fact_9_Un__subset__iff,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ A @ B ) @ C )
% 0.28/0.47 = ( ( ord_le1780499447n_game @ A @ C )
% 0.28/0.47 & ( ord_le1780499447n_game @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_subset_iff
% 0.28/0.47 thf(fact_10_Un__subset__iff,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ A @ B ) @ C )
% 0.28/0.47 = ( ( ord_le17855367n_game @ A @ C )
% 0.28/0.47 & ( ord_le17855367n_game @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_subset_iff
% 0.28/0.47 thf(fact_11_Un__subset__iff,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
% 0.28/0.47 = ( ( ord_le282106107riable @ A @ C )
% 0.28/0.47 & ( ord_le282106107riable @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_subset_iff
% 0.28/0.47 thf(fact_12_le__sup__iff,axiom,
% 0.28/0.47 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 0.28/0.47 ( ( ord_le1407353162able_o @ ( sup_sup_variable_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le1407353162able_o @ X @ Z )
% 0.28/0.47 & ( ord_le1407353162able_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_13_le__sup__iff,axiom,
% 0.28/0.47 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le1780499447n_game @ X @ Z )
% 0.28/0.47 & ( ord_le1780499447n_game @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_14_le__sup__iff,axiom,
% 0.28/0.47 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le17855367n_game @ X @ Z )
% 0.28/0.47 & ( ord_le17855367n_game @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_15_le__sup__iff,axiom,
% 0.28/0.47 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 0.28/0.47 ( ( ord_le707292176game_o @ ( sup_su169929796game_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le707292176game_o @ X @ Z )
% 0.28/0.47 & ( ord_le707292176game_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_16_le__sup__iff,axiom,
% 0.28/0.47 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 0.28/0.47 ( ( ord_le2134856704game_o @ ( sup_su1227468340game_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le2134856704game_o @ X @ Z )
% 0.28/0.47 & ( ord_le2134856704game_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_17_le__sup__iff,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.28/0.47 = ( ( ord_le282106107riable @ X @ Z )
% 0.28/0.47 & ( ord_le282106107riable @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_18_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: variable > $o,C2: variable > $o,A2: variable > $o] :
% 0.28/0.47 ( ( ord_le1407353162able_o @ ( sup_sup_variable_o @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le1407353162able_o @ B2 @ A2 )
% 0.28/0.47 & ( ord_le1407353162able_o @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_19_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game,A2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le1780499447n_game @ B2 @ A2 )
% 0.28/0.47 & ( ord_le1780499447n_game @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_20_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: set_Pr166476775n_game,C2: set_Pr166476775n_game,A2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le17855367n_game @ B2 @ A2 )
% 0.28/0.47 & ( ord_le17855367n_game @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_21_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: option_game > option_game > $o,C2: option_game > option_game > $o,A2: option_game > option_game > $o] :
% 0.28/0.47 ( ( ord_le707292176game_o @ ( sup_su169929796game_o @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le707292176game_o @ B2 @ A2 )
% 0.28/0.47 & ( ord_le707292176game_o @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_22_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: set_variable > option_game > $o,C2: set_variable > option_game > $o,A2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( ord_le2134856704game_o @ ( sup_su1227468340game_o @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le2134856704game_o @ B2 @ A2 )
% 0.28/0.47 & ( ord_le2134856704game_o @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_23_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [B2: set_variable,C2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 & ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_24_BVG__compose,axiom,
% 0.28/0.47 ! [Alpha: game,Beta: game] : ( ord_le282106107riable @ ( static_BVG @ ( compose @ Alpha @ Beta ) ) @ ( sup_sup_set_variable @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % BVG_compose
% 0.28/0.47 thf(fact_25_game_Oinject_I5_J,axiom,
% 0.28/0.47 ! [X51: game,X52: game,Y51: game,Y52: game] :
% 0.28/0.47 ( ( ( compose @ X51 @ X52 )
% 0.28/0.47 = ( compose @ Y51 @ Y52 ) )
% 0.28/0.47 = ( ( X51 = Y51 )
% 0.28/0.47 & ( X52 = Y52 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.inject(5)
% 0.28/0.47 thf(fact_26_UnCI,axiom,
% 0.28/0.47 ! [C2: produc1016592119n_game,B: set_Pr1625152599n_game,A: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ~ ( member191809696n_game @ C2 @ B )
% 0.28/0.47 => ( member191809696n_game @ C2 @ A ) )
% 0.28/0.47 => ( member191809696n_game @ C2 @ ( sup_su423136299n_game @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnCI
% 0.28/0.47 thf(fact_27_UnCI,axiom,
% 0.28/0.47 ! [C2: produc1078154247n_game,B: set_Pr166476775n_game,A: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ~ ( member171223600n_game @ C2 @ B )
% 0.28/0.47 => ( member171223600n_game @ C2 @ A ) )
% 0.28/0.47 => ( member171223600n_game @ C2 @ ( sup_su796825019n_game @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnCI
% 0.28/0.47 thf(fact_28_UnCI,axiom,
% 0.28/0.47 ! [C2: variable,B: set_variable,A: set_variable] :
% 0.28/0.47 ( ( ~ ( member_variable @ C2 @ B )
% 0.28/0.47 => ( member_variable @ C2 @ A ) )
% 0.28/0.47 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnCI
% 0.28/0.47 thf(fact_29_union__or,axiom,
% 0.28/0.47 ! [C2: produc1016592119n_game,A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( member191809696n_game @ C2 @ ( sup_su423136299n_game @ A @ B ) )
% 0.28/0.47 = ( ( member191809696n_game @ C2 @ A )
% 0.28/0.47 | ( member191809696n_game @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % union_or
% 0.28/0.47 thf(fact_30_union__or,axiom,
% 0.28/0.47 ! [C2: produc1078154247n_game,A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ( member171223600n_game @ C2 @ ( sup_su796825019n_game @ A @ B ) )
% 0.28/0.47 = ( ( member171223600n_game @ C2 @ A )
% 0.28/0.47 | ( member171223600n_game @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % union_or
% 0.28/0.47 thf(fact_31_union__or,axiom,
% 0.28/0.47 ! [C2: variable,A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 = ( ( member_variable @ C2 @ A )
% 0.28/0.47 | ( member_variable @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % union_or
% 0.28/0.47 thf(fact_32_sup__apply,axiom,
% 0.28/0.47 ( sup_sup_variable_o
% 0.28/0.47 = ( ^ [F: variable > $o,G: variable > $o,X2: variable] : ( sup_sup_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_apply
% 0.28/0.47 thf(fact_33_sup__apply,axiom,
% 0.28/0.47 ( sup_su169929796game_o
% 0.28/0.47 = ( ^ [F: option_game > option_game > $o,G: option_game > option_game > $o,X2: option_game] : ( sup_su1229228248game_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_apply
% 0.28/0.47 thf(fact_34_sup__apply,axiom,
% 0.28/0.47 ( sup_su1227468340game_o
% 0.28/0.47 = ( ^ [F: set_variable > option_game > $o,G: set_variable > option_game > $o,X2: set_variable] : ( sup_su1229228248game_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_apply
% 0.28/0.47 thf(fact_35_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_36_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_37_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_38_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_39_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_40_sup_Oidem,axiom,
% 0.28/0.47 ! [A2: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A2 @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_41_sup__idem,axiom,
% 0.28/0.47 ! [X: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_42_sup__idem,axiom,
% 0.28/0.47 ! [X: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_43_sup__idem,axiom,
% 0.28/0.47 ! [X: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_44_sup__idem,axiom,
% 0.28/0.47 ! [X: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_45_sup__idem,axiom,
% 0.28/0.47 ! [X: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_46_sup__idem,axiom,
% 0.28/0.47 ! [X: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X @ X )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_47_subset__antisym,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ A @ B )
% 0.28/0.47 => ( ( ord_le1780499447n_game @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_48_subset__antisym,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ A @ B )
% 0.28/0.47 => ( ( ord_le17855367n_game @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_49_subset__antisym,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ( ( ord_le282106107riable @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_50_subsetI,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ! [X3: produc1016592119n_game] :
% 0.28/0.47 ( ( member191809696n_game @ X3 @ A )
% 0.28/0.47 => ( member191809696n_game @ X3 @ B ) )
% 0.28/0.47 => ( ord_le1780499447n_game @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_51_subsetI,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ! [X3: produc1078154247n_game] :
% 0.28/0.47 ( ( member171223600n_game @ X3 @ A )
% 0.28/0.47 => ( member171223600n_game @ X3 @ B ) )
% 0.28/0.47 => ( ord_le17855367n_game @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_52_subsetI,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ! [X3: variable] :
% 0.28/0.47 ( ( member_variable @ X3 @ A )
% 0.28/0.47 => ( member_variable @ X3 @ B ) )
% 0.28/0.47 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_53_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: variable > $o,B2: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_sup_variable_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_54_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_su169929796game_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_55_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_su423136299n_game @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_56_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_su1227468340game_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_57_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_su796825019n_game @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_58_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_59_sup__left__idem,axiom,
% 0.28/0.47 ! [X: variable > $o,Y: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ X @ Y ) )
% 0.28/0.47 = ( sup_sup_variable_o @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_60_sup__left__idem,axiom,
% 0.28/0.47 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ X @ Y ) )
% 0.28/0.47 = ( sup_su169929796game_o @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_61_sup__left__idem,axiom,
% 0.28/0.47 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ X @ Y ) )
% 0.28/0.47 = ( sup_su423136299n_game @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_62_sup__left__idem,axiom,
% 0.28/0.47 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ X @ Y ) )
% 0.28/0.47 = ( sup_su1227468340game_o @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_63_sup__left__idem,axiom,
% 0.28/0.47 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ X @ Y ) )
% 0.28/0.47 = ( sup_su796825019n_game @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_64_sup__left__idem,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 0.28/0.47 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_65_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: variable > $o,B2: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_sup_variable_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_66_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_su169929796game_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_67_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_su423136299n_game @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_68_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_su1227468340game_o @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_69_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_su796825019n_game @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_70_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_71_usubstappp__det,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,V: set_variable] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_det
% 0.28/0.47 thf(fact_72_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P: produc1016592119n_game > $o,Q: produc1016592119n_game > $o] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ ( collec884051426n_game @ P ) @ ( collec884051426n_game @ Q ) )
% 0.28/0.47 = ( ! [X2: produc1016592119n_game] :
% 0.28/0.47 ( ( P @ X2 )
% 0.28/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_73_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P: produc1078154247n_game > $o,Q: produc1078154247n_game > $o] :
% 0.28/0.47 ( ( ord_le17855367n_game @ ( collec1702522994n_game @ P ) @ ( collec1702522994n_game @ Q ) )
% 0.28/0.47 = ( ! [X2: produc1078154247n_game] :
% 0.28/0.47 ( ( P @ X2 )
% 0.28/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_74_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P: variable > $o,Q: variable > $o] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 0.28/0.47 = ( ! [X2: variable] :
% 0.28/0.47 ( ( P @ X2 )
% 0.28/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_75_set__eq__subset,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pr1625152599n_game,Z2: set_Pr1625152599n_game] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ A3 @ B3 )
% 0.28/0.47 & ( ord_le1780499447n_game @ B3 @ A3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_76_set__eq__subset,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pr166476775n_game,Z2: set_Pr166476775n_game] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ A3 @ B3 )
% 0.28/0.47 & ( ord_le17855367n_game @ B3 @ A3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_77_set__eq__subset,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.28/0.47 & ( ord_le282106107riable @ B3 @ A3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_78_subset__trans,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ A @ B )
% 0.28/0.47 => ( ( ord_le1780499447n_game @ B @ C )
% 0.28/0.47 => ( ord_le1780499447n_game @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_79_subset__trans,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ A @ B )
% 0.28/0.47 => ( ( ord_le17855367n_game @ B @ C )
% 0.28/0.47 => ( ord_le17855367n_game @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_80_subset__trans,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ( ( ord_le282106107riable @ B @ C )
% 0.28/0.47 => ( ord_le282106107riable @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_81_Collect__mono,axiom,
% 0.28/0.47 ! [P: produc1016592119n_game > $o,Q: produc1016592119n_game > $o] :
% 0.28/0.47 ( ! [X3: produc1016592119n_game] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_le1780499447n_game @ ( collec884051426n_game @ P ) @ ( collec884051426n_game @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_82_Collect__mono,axiom,
% 0.28/0.47 ! [P: produc1078154247n_game > $o,Q: produc1078154247n_game > $o] :
% 0.28/0.47 ( ! [X3: produc1078154247n_game] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_le17855367n_game @ ( collec1702522994n_game @ P ) @ ( collec1702522994n_game @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_83_Collect__mono,axiom,
% 0.28/0.47 ! [P: variable > $o,Q: variable > $o] :
% 0.28/0.47 ( ! [X3: variable] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_84_subset__refl,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game] : ( ord_le1780499447n_game @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_85_subset__refl,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game] : ( ord_le17855367n_game @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_86_subset__refl,axiom,
% 0.28/0.47 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_87_subset__iff,axiom,
% 0.28/0.47 ( ord_le1780499447n_game
% 0.28/0.47 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 0.28/0.47 ! [T: produc1016592119n_game] :
% 0.28/0.47 ( ( member191809696n_game @ T @ A3 )
% 0.28/0.47 => ( member191809696n_game @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_88_subset__iff,axiom,
% 0.28/0.47 ( ord_le17855367n_game
% 0.28/0.47 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 0.28/0.47 ! [T: produc1078154247n_game] :
% 0.28/0.47 ( ( member171223600n_game @ T @ A3 )
% 0.28/0.47 => ( member171223600n_game @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_89_subset__iff,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ! [T: variable] :
% 0.28/0.47 ( ( member_variable @ T @ A3 )
% 0.28/0.47 => ( member_variable @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_90_equalityD2,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le1780499447n_game @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_91_equalityD2,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le17855367n_game @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_92_equalityD2,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le282106107riable @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_93_equalityD1,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le1780499447n_game @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_94_equalityD1,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le17855367n_game @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_95_equalityD1,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_96_subset__eq,axiom,
% 0.28/0.47 ( ord_le1780499447n_game
% 0.28/0.47 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 0.28/0.47 ! [X2: produc1016592119n_game] :
% 0.28/0.47 ( ( member191809696n_game @ X2 @ A3 )
% 0.28/0.47 => ( member191809696n_game @ X2 @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_97_subset__eq,axiom,
% 0.28/0.47 ( ord_le17855367n_game
% 0.28/0.47 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 0.28/0.47 ! [X2: produc1078154247n_game] :
% 0.28/0.47 ( ( member171223600n_game @ X2 @ A3 )
% 0.28/0.47 => ( member171223600n_game @ X2 @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_98_subset__eq,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ! [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A3 )
% 0.28/0.47 => ( member_variable @ X2 @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_99_equalityE,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ~ ( ( ord_le1780499447n_game @ A @ B )
% 0.28/0.47 => ~ ( ord_le1780499447n_game @ B @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_100_equalityE,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ~ ( ( ord_le17855367n_game @ A @ B )
% 0.28/0.47 => ~ ( ord_le17855367n_game @ B @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_101_equalityE,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ~ ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_102_subsetD,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C2: produc1016592119n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ A @ B )
% 0.28/0.47 => ( ( member191809696n_game @ C2 @ A )
% 0.28/0.47 => ( member191809696n_game @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_103_subsetD,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C2: produc1078154247n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ A @ B )
% 0.28/0.47 => ( ( member171223600n_game @ C2 @ A )
% 0.28/0.47 => ( member171223600n_game @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_104_subsetD,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,C2: variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ( ( member_variable @ C2 @ A )
% 0.28/0.47 => ( member_variable @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_105_in__mono,axiom,
% 0.28/0.47 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,X: produc1016592119n_game] :
% 0.28/0.47 ( ( ord_le1780499447n_game @ A @ B )
% 0.28/0.47 => ( ( member191809696n_game @ X @ A )
% 0.28/0.47 => ( member191809696n_game @ X @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_106_in__mono,axiom,
% 0.28/0.47 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,X: produc1078154247n_game] :
% 0.28/0.47 ( ( ord_le17855367n_game @ A @ B )
% 0.28/0.47 => ( ( member171223600n_game @ X @ A )
% 0.28/0.47 => ( member171223600n_game @ X @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_107_in__mono,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,X: variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ( ( member_variable @ X @ A )
% 0.28/0.47 => ( member_variable @ X @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_108_sup__left__commute,axiom,
% 0.28/0.47 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ Y @ Z ) )
% 0.28/0.47 = ( sup_sup_variable_o @ Y @ ( sup_sup_variable_o @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_109_sup__left__commute,axiom,
% 0.28/0.47 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ Y @ Z ) )
% 0.28/0.47 = ( sup_su169929796game_o @ Y @ ( sup_su169929796game_o @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_110_sup__left__commute,axiom,
% 0.28/0.47 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ Y @ Z ) )
% 0.28/0.47 = ( sup_su423136299n_game @ Y @ ( sup_su423136299n_game @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_111_sup__left__commute,axiom,
% 0.28/0.47 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ Y @ Z ) )
% 0.28/0.47 = ( sup_su1227468340game_o @ Y @ ( sup_su1227468340game_o @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_112_sup__left__commute,axiom,
% 0.28/0.47 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ Y @ Z ) )
% 0.28/0.47 = ( sup_su796825019n_game @ Y @ ( sup_su796825019n_game @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_113_sup__left__commute,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 0.28/0.47 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_114_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: variable > $o,A2: variable > $o,C2: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ B2 @ ( sup_sup_variable_o @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_115_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: option_game > option_game > $o,A2: option_game > option_game > $o,C2: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ B2 @ ( sup_su169929796game_o @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_116_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: set_Pr1625152599n_game,A2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ B2 @ ( sup_su423136299n_game @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_117_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: set_variable > option_game > $o,A2: set_variable > option_game > $o,C2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ B2 @ ( sup_su1227468340game_o @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_118_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: set_Pr166476775n_game,A2: set_Pr166476775n_game,C2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ B2 @ ( sup_su796825019n_game @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_119_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_120_sup__commute,axiom,
% 0.28/0.47 ( sup_sup_variable_o
% 0.28/0.47 = ( ^ [X2: variable > $o,Y3: variable > $o] : ( sup_sup_variable_o @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_121_sup__commute,axiom,
% 0.28/0.47 ( sup_su169929796game_o
% 0.28/0.47 = ( ^ [X2: option_game > option_game > $o,Y3: option_game > option_game > $o] : ( sup_su169929796game_o @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_122_sup__commute,axiom,
% 0.28/0.47 ( sup_su423136299n_game
% 0.28/0.47 = ( ^ [X2: set_Pr1625152599n_game,Y3: set_Pr1625152599n_game] : ( sup_su423136299n_game @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_123_sup__commute,axiom,
% 0.28/0.47 ( sup_su1227468340game_o
% 0.28/0.47 = ( ^ [X2: set_variable > option_game > $o,Y3: set_variable > option_game > $o] : ( sup_su1227468340game_o @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_124_sup__commute,axiom,
% 0.28/0.47 ( sup_su796825019n_game
% 0.28/0.47 = ( ^ [X2: set_Pr166476775n_game,Y3: set_Pr166476775n_game] : ( sup_su796825019n_game @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_125_sup__commute,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_126_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_sup_variable_o
% 0.28/0.47 = ( ^ [A4: variable > $o,B4: variable > $o] : ( sup_sup_variable_o @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_127_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_su169929796game_o
% 0.28/0.47 = ( ^ [A4: option_game > option_game > $o,B4: option_game > option_game > $o] : ( sup_su169929796game_o @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_128_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_su423136299n_game
% 0.28/0.47 = ( ^ [A4: set_Pr1625152599n_game,B4: set_Pr1625152599n_game] : ( sup_su423136299n_game @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_129_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_su1227468340game_o
% 0.28/0.47 = ( ^ [A4: set_variable > option_game > $o,B4: set_variable > option_game > $o] : ( sup_su1227468340game_o @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_130_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_su796825019n_game
% 0.28/0.47 = ( ^ [A4: set_Pr166476775n_game,B4: set_Pr166476775n_game] : ( sup_su796825019n_game @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_131_sup_Ocommute,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [A4: set_variable,B4: set_variable] : ( sup_sup_set_variable @ B4 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_132_sup__assoc,axiom,
% 0.28/0.47 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_133_sup__assoc,axiom,
% 0.28/0.47 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_134_sup__assoc,axiom,
% 0.28/0.47 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_135_sup__assoc,axiom,
% 0.28/0.47 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_136_sup__assoc,axiom,
% 0.28/0.47 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_137_sup__assoc,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_138_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: variable > $o,B2: variable > $o,C2: variable > $o] :
% 0.28/0.47 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_139_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o,C2: option_game > option_game > $o] :
% 0.28/0.47 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_140_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_141_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o,C2: set_variable > option_game > $o] :
% 0.28/0.47 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_142_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game,C2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_143_sup_Oassoc,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_144_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.47 ! [B: set_Pr166476775n_game,K: set_Pr166476775n_game,B2: set_Pr166476775n_game,A2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( B
% 0.28/0.47 = ( sup_su796825019n_game @ K @ B2 ) )
% 0.28/0.47 => ( ( sup_su796825019n_game @ A2 @ B )
% 0.28/0.47 = ( sup_su796825019n_game @ K @ ( sup_su796825019n_game @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % boolean_algebra_cancel.sup2
% 0.28/0.47 thf(fact_145_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.47 ! [B: set_variable,K: set_variable,B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( B
% 0.28/0.47 = ( sup_sup_set_variable @ K @ B2 ) )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A2 @ B )
% 0.28/0.47 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % boolean_algebra_cancel.sup2
% 0.28/0.47 thf(fact_146_boolean__algebra__cancel_Osup1,axiom,
% 0.28/0.47 ! [A: set_variable,K: set_variable,A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( A
% 0.28/0.47 = ( sup_sup_set_variable @ K @ A2 ) )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A @ B2 )
% 0.28/0.47 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % boolean_algebra_cancel.sup1
% 0.28/0.47 thf(fact_147_inf__sup__aci_I5_J,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(5)
% 0.28/0.47 thf(fact_148_inf__sup__aci_I6_J,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.28/0.47 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(6)
% 0.28/0.47 thf(fact_149_inf__sup__aci_I7_J,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 0.28/0.47 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(7)
% 0.28/0.47 thf(fact_150_inf__sup__aci_I8_J,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 0.28/0.47 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(8)
% 0.28/0.47 thf(fact_151_not__union__or,axiom,
% 0.28/0.47 ! [X: variable,A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( ~ ( member_variable @ X @ ( sup_sup_set_variable @ A @ B ) ) )
% 0.28/0.47 = ( ~ ( member_variable @ X @ A )
% 0.28/0.47 & ~ ( member_variable @ X @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_union_or
% 0.28/0.47 thf(fact_152_Un__left__commute,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
% 0.28/0.47 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_left_commute
% 0.28/0.47 thf(fact_153_Un__left__absorb,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 = ( sup_sup_set_variable @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_left_absorb
% 0.28/0.47 thf(fact_154_Un__commute,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] : ( sup_sup_set_variable @ B3 @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_commute
% 0.28/0.47 thf(fact_155_Un__absorb,axiom,
% 0.28/0.47 ! [A: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A @ A )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb
% 0.28/0.47 thf(fact_156_Un__assoc,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
% 0.28/0.47 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_assoc
% 0.28/0.47 thf(fact_157_ball__Un,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.28/0.47 ( ( ! [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 => ( P @ X2 ) ) )
% 0.28/0.47 = ( ! [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A )
% 0.28/0.47 => ( P @ X2 ) )
% 0.28/0.47 & ! [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ B )
% 0.28/0.47 => ( P @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ball_Un
% 0.28/0.47 thf(fact_158_bex__Un,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 0.28/0.47 ( ( ? [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 & ( P @ X2 ) ) )
% 0.28/0.47 = ( ? [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A )
% 0.28/0.47 & ( P @ X2 ) )
% 0.28/0.47 | ? [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ B )
% 0.28/0.47 & ( P @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bex_Un
% 0.28/0.47 thf(fact_159_UnI2,axiom,
% 0.28/0.47 ! [C2: variable,B: set_variable,A: set_variable] :
% 0.28/0.47 ( ( member_variable @ C2 @ B )
% 0.28/0.47 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnI2
% 0.28/0.47 thf(fact_160_UnI1,axiom,
% 0.28/0.47 ! [C2: variable,A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( member_variable @ C2 @ A )
% 0.28/0.47 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnI1
% 0.28/0.47 thf(fact_161_UnE,axiom,
% 0.28/0.47 ! [C2: variable,A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 => ( ~ ( member_variable @ C2 @ A )
% 0.28/0.47 => ( member_variable @ C2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnE
% 0.28/0.47 thf(fact_162_usubstappp__antimon,axiom,
% 0.28/0.47 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 0.28/0.47 ( ( ord_le282106107riable @ V @ U )
% 0.28/0.47 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_antimon
% 0.28/0.47 thf(fact_163_sup_OcoboundedI2,axiom,
% 0.28/0.47 ! [C2: set_variable,B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ C2 @ B2 )
% 0.28/0.47 => ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.coboundedI2
% 0.28/0.47 thf(fact_164_sup_OcoboundedI1,axiom,
% 0.28/0.47 ! [C2: set_variable,A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ C2 @ A2 )
% 0.28/0.47 => ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.coboundedI1
% 0.28/0.47 thf(fact_165_sup_Oabsorb__iff2,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A4 @ B4 )
% 0.28/0.47 = B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb_iff2
% 0.28/0.47 thf(fact_166_sup_Oabsorb__iff1,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [B4: set_variable,A4: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A4 @ B4 )
% 0.28/0.47 = A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb_iff1
% 0.28/0.47 thf(fact_167_sup_Ocobounded2,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable] : ( ord_le282106107riable @ B2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.cobounded2
% 0.28/0.47 thf(fact_168_sup_Ocobounded1,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] : ( ord_le282106107riable @ A2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.cobounded1
% 0.28/0.47 thf(fact_169_sup_Oorder__iff,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [B4: set_variable,A4: set_variable] :
% 0.28/0.47 ( A4
% 0.28/0.47 = ( sup_sup_set_variable @ A4 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.order_iff
% 0.28/0.47 thf(fact_170_sup_OboundedI,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ C2 @ A2 )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.boundedI
% 0.28/0.47 thf(fact_171_sup_OboundedE,axiom,
% 0.28/0.47 ! [B2: set_variable,C2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 )
% 0.28/0.47 => ~ ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ~ ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.boundedE
% 0.28/0.47 thf(fact_172_sup__absorb2,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X @ Y )
% 0.28/0.47 => ( ( sup_sup_set_variable @ X @ Y )
% 0.28/0.47 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_absorb2
% 0.28/0.47 thf(fact_173_sup__absorb1,axiom,
% 0.28/0.47 ! [Y: set_variable,X: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ Y @ X )
% 0.28/0.47 => ( ( sup_sup_set_variable @ X @ Y )
% 0.28/0.47 = X ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_absorb1
% 0.28/0.47 thf(fact_174_sup_Oabsorb2,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 0.28/0.47 = B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb2
% 0.28/0.47 thf(fact_175_sup_Oabsorb1,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb1
% 0.28/0.47 thf(fact_176_sup__unique,axiom,
% 0.28/0.47 ! [F2: set_variable > set_variable > set_variable,X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ! [X3: set_variable,Y4: set_variable] : ( ord_le282106107riable @ X3 @ ( F2 @ X3 @ Y4 ) )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable] : ( ord_le282106107riable @ Y4 @ ( F2 @ X3 @ Y4 ) )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable,Z3: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ Y4 @ X3 )
% 0.28/0.47 => ( ( ord_le282106107riable @ Z3 @ X3 )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ Y4 @ Z3 ) @ X3 ) ) )
% 0.28/0.47 => ( ( sup_sup_set_variable @ X @ Y )
% 0.28/0.47 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_unique
% 0.28/0.47 thf(fact_177_sup_OorderI,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ B2 ) )
% 0.28/0.47 => ( ord_le282106107riable @ B2 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.orderI
% 0.28/0.47 thf(fact_178_sup_OorderE,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( A2
% 0.28/0.47 = ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.orderE
% 0.28/0.47 thf(fact_179_le__iff__sup,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ X2 @ Y3 )
% 0.28/0.47 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_iff_sup
% 0.28/0.47 thf(fact_180_sup__least,axiom,
% 0.28/0.47 ! [Y: set_variable,X: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ Y @ X )
% 0.28/0.47 => ( ( ord_le282106107riable @ Z @ X )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ Y @ Z ) @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_least
% 0.28/0.47 thf(fact_181_sup__mono,axiom,
% 0.28/0.47 ! [A2: set_variable,C2: set_variable,B2: set_variable,D: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ C2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ D )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ ( sup_sup_set_variable @ C2 @ D ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_mono
% 0.28/0.47 thf(fact_182_sup_Omono,axiom,
% 0.28/0.47 ! [C2: set_variable,A2: set_variable,D: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ C2 @ A2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ D @ B2 )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ C2 @ D ) @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.mono
% 0.28/0.47 thf(fact_183_le__supI2,axiom,
% 0.28/0.47 ! [X: set_variable,B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X @ B2 )
% 0.28/0.47 => ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI2
% 0.28/0.47 thf(fact_184_le__supI1,axiom,
% 0.28/0.47 ! [X: set_variable,A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X @ A2 )
% 0.28/0.47 => ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI1
% 0.28/0.47 thf(fact_185_sup__ge2,axiom,
% 0.28/0.47 ! [Y: set_variable,X: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_ge2
% 0.28/0.47 thf(fact_186_sup__ge1,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] : ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_ge1
% 0.28/0.47 thf(fact_187_le__supI,axiom,
% 0.28/0.47 ! [A2: set_variable,X: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ X )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ X )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI
% 0.28/0.47 thf(fact_188_le__supE,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,X: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ X )
% 0.28/0.47 => ~ ( ( ord_le282106107riable @ A2 @ X )
% 0.28/0.47 => ~ ( ord_le282106107riable @ B2 @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supE
% 0.28/0.47 thf(fact_189_inf__sup__ord_I3_J,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] : ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_ord(3)
% 0.28/0.47 thf(fact_190_inf__sup__ord_I4_J,axiom,
% 0.28/0.47 ! [Y: set_variable,X: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_ord(4)
% 0.28/0.47 thf(fact_191_subset__Un__eq,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ( ( sup_sup_set_variable @ A3 @ B3 )
% 0.28/0.47 = B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Un_eq
% 0.28/0.47 thf(fact_192_subset__UnE,axiom,
% 0.28/0.47 ! [C: set_variable,A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A @ B ) )
% 0.28/0.47 => ~ ! [A5: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A5 @ A )
% 0.28/0.47 => ! [B5: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B5 @ B )
% 0.28/0.47 => ( C
% 0.28/0.47 != ( sup_sup_set_variable @ A5 @ B5 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_UnE
% 0.28/0.47 thf(fact_193_Un__absorb2,axiom,
% 0.28/0.47 ! [B: set_variable,A: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B @ A )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A @ B )
% 0.28/0.47 = A ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb2
% 0.28/0.47 thf(fact_194_Un__absorb1,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ B )
% 0.28/0.47 => ( ( sup_sup_set_variable @ A @ B )
% 0.28/0.47 = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb1
% 0.28/0.47 thf(fact_195_Un__upper2,axiom,
% 0.28/0.47 ! [B: set_variable,A: set_variable] : ( ord_le282106107riable @ B @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_upper2
% 0.28/0.47 thf(fact_196_Un__upper1,axiom,
% 0.28/0.47 ! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_upper1
% 0.28/0.47 thf(fact_197_Un__least,axiom,
% 0.28/0.47 ! [A: set_variable,C: set_variable,B: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ C )
% 0.28/0.47 => ( ( ord_le282106107riable @ B @ C )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_least
% 0.28/0.47 thf(fact_198_Un__mono,axiom,
% 0.28/0.47 ! [A: set_variable,C: set_variable,B: set_variable,D2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A @ C )
% 0.28/0.47 => ( ( ord_le282106107riable @ B @ D2 )
% 0.28/0.47 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ ( sup_sup_set_variable @ C @ D2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_mono
% 0.28/0.47 thf(fact_199_order__refl,axiom,
% 0.28/0.47 ! [X: set_variable] : ( ord_le282106107riable @ X @ X ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_200_option_Oexpand,axiom,
% 0.28/0.47 ! [Option: option_game,Option2: option_game] :
% 0.28/0.47 ( ( ( Option = none_game )
% 0.28/0.47 = ( Option2 = none_game ) )
% 0.28/0.47 => ( ( ( Option != none_game )
% 0.28/0.47 => ( ( Option2 != none_game )
% 0.28/0.47 => ( ( the_game @ Option )
% 0.28/0.47 = ( the_game @ Option2 ) ) ) )
% 0.28/0.47 => ( Option = Option2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.expand
% 0.28/0.47 thf(fact_201_prod__eq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: produc1078154247n_game,Z2: produc1078154247n_game] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [S: produc1078154247n_game,T: produc1078154247n_game] :
% 0.28/0.47 ( ( ( produc893821739n_game @ S )
% 0.28/0.47 = ( produc893821739n_game @ T ) )
% 0.28/0.47 & ( ( produc293487213n_game @ S )
% 0.28/0.47 = ( produc293487213n_game @ T ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_eq_iff
% 0.28/0.47 thf(fact_202_prod_Oexpand,axiom,
% 0.28/0.47 ! [Prod: produc1078154247n_game,Prod2: produc1078154247n_game] :
% 0.28/0.47 ( ( ( ( produc893821739n_game @ Prod )
% 0.28/0.47 = ( produc893821739n_game @ Prod2 ) )
% 0.28/0.47 & ( ( produc293487213n_game @ Prod )
% 0.28/0.47 = ( produc293487213n_game @ Prod2 ) ) )
% 0.28/0.47 => ( Prod = Prod2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.expand
% 0.28/0.47 thf(fact_203_exE__realizer_H,axiom,
% 0.28/0.47 ! [P: option_game > set_variable > $o,P2: produc1078154247n_game] :
% 0.28/0.47 ( ( P @ ( produc293487213n_game @ P2 ) @ ( produc893821739n_game @ P2 ) )
% 0.28/0.47 => ~ ! [X3: set_variable,Y4: option_game] :
% 0.28/0.47 ~ ( P @ Y4 @ X3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % exE_realizer'
% 0.28/0.47 thf(fact_204_prod__eqI,axiom,
% 0.28/0.47 ! [P2: produc1078154247n_game,Q2: produc1078154247n_game] :
% 0.28/0.47 ( ( ( produc893821739n_game @ P2 )
% 0.28/0.47 = ( produc893821739n_game @ Q2 ) )
% 0.28/0.47 => ( ( ( produc293487213n_game @ P2 )
% 0.28/0.47 = ( produc293487213n_game @ Q2 ) )
% 0.28/0.47 => ( P2 = Q2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_eqI
% 0.28/0.47 thf(fact_205_usubstappp__loop__conv,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 0.28/0.47 != none_game ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_loop_conv
% 0.28/0.47 thf(fact_206_BVG__choice,axiom,
% 0.28/0.47 ! [Alpha: game,Beta: game] : ( ord_le282106107riable @ ( static_BVG @ ( choice @ Alpha @ Beta ) ) @ ( sup_sup_set_variable @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % BVG_choice
% 0.28/0.47 thf(fact_207_usubstappp__choice__conv,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 0.28/0.47 != none_game )
% 0.28/0.47 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) )
% 0.28/0.47 != none_game ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_choice_conv
% 0.28/0.47 thf(fact_208_game_Oinject_I6_J,axiom,
% 0.28/0.47 ! [X6: game,Y6: game] :
% 0.28/0.47 ( ( ( loop @ X6 )
% 0.28/0.47 = ( loop @ Y6 ) )
% 0.28/0.47 = ( X6 = Y6 ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.inject(6)
% 0.28/0.47 thf(fact_209_game_Oinject_I4_J,axiom,
% 0.28/0.47 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 0.28/0.47 ( ( ( choice @ X41 @ X42 )
% 0.28/0.47 = ( choice @ Y41 @ Y42 ) )
% 0.28/0.47 = ( ( X41 = Y41 )
% 0.28/0.47 & ( X42 = Y42 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.inject(4)
% 0.28/0.47 thf(fact_210_game_Odistinct_I39_J,axiom,
% 0.28/0.47 ! [X41: game,X42: game,X6: game] :
% 0.28/0.47 ( ( choice @ X41 @ X42 )
% 0.28/0.47 != ( loop @ X6 ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.distinct(39)
% 0.28/0.47 thf(fact_211_game_Odistinct_I45_J,axiom,
% 0.28/0.47 ! [X51: game,X52: game,X6: game] :
% 0.28/0.47 ( ( compose @ X51 @ X52 )
% 0.28/0.47 != ( loop @ X6 ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.distinct(45)
% 0.28/0.47 thf(fact_212_game_Odistinct_I37_J,axiom,
% 0.28/0.47 ! [X41: game,X42: game,X51: game,X52: game] :
% 0.28/0.47 ( ( choice @ X41 @ X42 )
% 0.28/0.47 != ( compose @ X51 @ X52 ) ) ).
% 0.28/0.47
% 0.28/0.47 % game.distinct(37)
% 0.28/0.47 thf(fact_213_BVG__loop,axiom,
% 0.28/0.47 ! [Alpha: game] : ( ord_le282106107riable @ ( static_BVG @ ( loop @ Alpha ) ) @ ( static_BVG @ Alpha ) ) ).
% 0.28/0.47
% 0.28/0.47 % BVG_loop
% 0.28/0.47 thf(fact_214_order__subst1,axiom,
% 0.28/0.47 ! [A2: set_variable,F2: set_variable > set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ ( F2 @ B2 ) )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ C2 )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X3 @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.28/0.47 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_215_order__subst2,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ ( F2 @ B2 ) @ C2 )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X3 @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_216_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A2: set_variable,F2: set_variable > set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( F2 @ B2 ) )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ C2 )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X3 @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.28/0.47 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_217_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( ( F2 @ B2 )
% 0.28/0.47 = C2 )
% 0.28/0.47 => ( ! [X3: set_variable,Y4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X3 @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 0.28/0.47 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_218_eq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X2 @ Y3 )
% 0.28/0.47 & ( ord_le282106107riable @ Y3 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_219_antisym,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X @ Y )
% 0.28/0.47 => ( ( ord_le282106107riable @ Y @ X )
% 0.28/0.47 => ( X = Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_220_eq__refl,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable] :
% 0.28/0.47 ( ( X = Y )
% 0.28/0.47 => ( ord_le282106107riable @ X @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_221_order_Otrans,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ C2 )
% 0.28/0.47 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_222_antisym__conv,axiom,
% 0.28/0.47 ! [Y: set_variable,X: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ Y @ X )
% 0.28/0.47 => ( ( ord_le282106107riable @ X @ Y )
% 0.28/0.47 = ( X = Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_223_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A4 @ B4 )
% 0.28/0.47 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47 thf(fact_224_ord__eq__le__trans,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( A2 = B2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ C2 )
% 0.28/0.47 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_trans
% 0.28/0.47 thf(fact_225_ord__le__eq__trans,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( B2 = C2 )
% 0.28/0.47 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_trans
% 0.28/0.47 thf(fact_226_order__class_Oorder_Oantisym,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( A2 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.antisym
% 0.28/0.47 thf(fact_227_order__trans,axiom,
% 0.28/0.47 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ X @ Y )
% 0.28/0.47 => ( ( ord_le282106107riable @ Y @ Z )
% 0.28/0.47 => ( ord_le282106107riable @ X @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_trans
% 0.28/0.47 thf(fact_228_dual__order_Orefl,axiom,
% 0.28/0.47 ! [A2: set_variable] : ( ord_le282106107riable @ A2 @ A2 ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.refl
% 0.28/0.47 thf(fact_229_dual__order_Otrans,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ C2 @ B2 )
% 0.28/0.47 => ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.trans
% 0.28/0.47 thf(fact_230_dual__order_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 0.28/0.47 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B4 @ A4 )
% 0.28/0.47 & ( ord_le282106107riable @ A4 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.eq_iff
% 0.28/0.47 thf(fact_231_dual__order_Oantisym,axiom,
% 0.28/0.47 ! [B2: set_variable,A2: set_variable] :
% 0.28/0.47 ( ( ord_le282106107riable @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_le282106107riable @ A2 @ B2 )
% 0.28/0.47 => ( A2 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.antisym
% 0.28/0.47 thf(fact_232_fst__swap,axiom,
% 0.28/0.47 ! [X: produc735959047riable] :
% 0.28/0.47 ( ( produc893821739n_game @ ( produc345397471riable @ X ) )
% 0.28/0.47 = ( produc284475501riable @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % fst_swap
% 0.28/0.47 thf(fact_233_fst__swap,axiom,
% 0.28/0.47 ! [X: produc1078154247n_game] :
% 0.28/0.47 ( ( produc884810027riable @ ( produc354409183n_game @ X ) )
% 0.28/0.47 = ( produc293487213n_game @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % fst_swap
% 0.28/0.47 thf(fact_234_snd__swap,axiom,
% 0.28/0.47 ! [X: produc1078154247n_game] :
% 0.28/0.47 ( ( produc284475501riable @ ( produc354409183n_game @ X ) )
% 0.28/0.47 = ( produc893821739n_game @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % snd_swap
% 0.28/0.47 thf(fact_235_snd__swap,axiom,
% 0.28/0.47 ! [X: produc735959047riable] :
% 0.28/0.47 ( ( produc293487213n_game @ ( produc345397471riable @ X ) )
% 0.28/0.47 = ( produc884810027riable @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % snd_swap
% 0.28/0.47 thf(fact_236_usubstappp__choice,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.28/0.47 = ( 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 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_choice
% 0.28/0.47 thf(fact_237_GreatestI2__order,axiom,
% 0.28/0.47 ! [P: set_variable > $o,X: set_variable,Q: set_variable > $o] :
% 0.28/0.47 ( ( P @ X )
% 0.28/0.47 => ( ! [Y4: set_variable] :
% 0.28/0.47 ( ( P @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ Y4 @ X ) )
% 0.28/0.47 => ( ! [X3: set_variable] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( ! [Y5: set_variable] :
% 0.28/0.47 ( ( P @ Y5 )
% 0.28/0.47 => ( ord_le282106107riable @ Y5 @ X3 ) )
% 0.28/0.47 => ( Q @ X3 ) ) )
% 0.28/0.47 => ( Q @ ( order_272405634riable @ P ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % GreatestI2_order
% 0.28/0.47 thf(fact_238_Greatest__equality,axiom,
% 0.28/0.47 ! [P: set_variable > $o,X: set_variable] :
% 0.28/0.47 ( ( P @ X )
% 0.28/0.47 => ( ! [Y4: set_variable] :
% 0.28/0.47 ( ( P @ Y4 )
% 0.28/0.47 => ( ord_le282106107riable @ Y4 @ X ) )
% 0.28/0.47 => ( ( order_272405634riable @ P )
% 0.28/0.47 = X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Greatest_equality
% 0.28/0.47 thf(fact_239_old_Oprod_Oinject,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: option_game,A6: set_variable,B6: option_game] :
% 0.28/0.47 ( ( ( produc1149443391n_game @ A2 @ B2 )
% 0.28/0.47 = ( produc1149443391n_game @ A6 @ B6 ) )
% 0.28/0.47 = ( ( A2 = A6 )
% 0.28/0.47 & ( B2 = B6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inject
% 0.28/0.47 thf(fact_240_old_Oprod_Oinject,axiom,
% 0.28/0.47 ! [A2: option_game,B2: option_game,A6: option_game,B6: option_game] :
% 0.28/0.47 ( ( ( produc1111617711n_game @ A2 @ B2 )
% 0.28/0.47 = ( produc1111617711n_game @ A6 @ B6 ) )
% 0.28/0.47 = ( ( A2 = A6 )
% 0.28/0.47 & ( B2 = B6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inject
% 0.28/0.47 thf(fact_241_prod_Oinject,axiom,
% 0.28/0.47 ! [X1: set_variable,X22: option_game,Y1: set_variable,Y22: option_game] :
% 0.28/0.47 ( ( ( produc1149443391n_game @ X1 @ X22 )
% 0.28/0.47 = ( produc1149443391n_game @ Y1 @ Y22 ) )
% 0.28/0.47 = ( ( X1 = Y1 )
% 0.28/0.47 & ( X22 = Y22 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.inject
% 0.28/0.47 thf(fact_242_prod_Oinject,axiom,
% 0.28/0.47 ! [X1: option_game,X22: option_game,Y1: option_game,Y22: option_game] :
% 0.28/0.47 ( ( ( produc1111617711n_game @ X1 @ X22 )
% 0.28/0.47 = ( produc1111617711n_game @ Y1 @ Y22 ) )
% 0.28/0.47 = ( ( X1 = Y1 )
% 0.28/0.47 & ( X22 = Y22 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.inject
% 0.28/0.47 thf(fact_243_swap__simp,axiom,
% 0.28/0.47 ! [X: option_game,Y: set_variable] :
% 0.28/0.47 ( ( produc345397471riable @ ( produc1140431679riable @ X @ Y ) )
% 0.28/0.47 = ( produc1149443391n_game @ Y @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % swap_simp
% 0.28/0.47 thf(fact_244_swap__simp,axiom,
% 0.28/0.47 ! [X: set_variable,Y: option_game] :
% 0.28/0.47 ( ( produc354409183n_game @ ( produc1149443391n_game @ X @ Y ) )
% 0.28/0.47 = ( produc1140431679riable @ Y @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % swap_simp
% 0.28/0.47 thf(fact_245_swap__simp,axiom,
% 0.28/0.47 ! [X: option_game,Y: option_game] :
% 0.28/0.47 ( ( produc1696194127n_game @ ( produc1111617711n_game @ X @ Y ) )
% 0.28/0.47 = ( produc1111617711n_game @ Y @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % swap_simp
% 0.28/0.47 thf(fact_246_prod_Ocollapse,axiom,
% 0.28/0.47 ! [Prod: produc1016592119n_game] :
% 0.28/0.47 ( ( produc1111617711n_game @ ( produc1942569115n_game @ Prod ) @ ( produc279011037n_game @ Prod ) )
% 0.28/0.47 = Prod ) ).
% 0.28/0.47
% 0.28/0.47 % prod.collapse
% 0.28/0.47 thf(fact_247_prod_Ocollapse,axiom,
% 0.28/0.47 ! [Prod: produc1078154247n_game] :
% 0.28/0.47 ( ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) )
% 0.28/0.47 = Prod ) ).
% 0.28/0.47
% 0.28/0.47 % prod.collapse
% 0.28/0.47 thf(fact_248_old_Oprod_Oinducts,axiom,
% 0.28/0.47 ! [P: produc1078154247n_game > $o,Prod: produc1078154247n_game] :
% 0.28/0.47 ( ! [A7: set_variable,B7: option_game] : ( P @ ( produc1149443391n_game @ A7 @ B7 ) )
% 0.28/0.47 => ( P @ Prod ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inducts
% 0.28/0.47 thf(fact_249_old_Oprod_Oinducts,axiom,
% 0.28/0.47 ! [P: produc1016592119n_game > $o,Prod: produc1016592119n_game] :
% 0.28/0.47 ( ! [A7: option_game,B7: option_game] : ( P @ ( produc1111617711n_game @ A7 @ B7 ) )
% 0.28/0.47 => ( P @ Prod ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inducts
% 0.28/0.47 thf(fact_250_old_Oprod_Oexhaust,axiom,
% 0.28/0.47 ! [Y: produc1078154247n_game] :
% 0.28/0.47 ~ ! [A7: set_variable,B7: option_game] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( produc1149443391n_game @ A7 @ B7 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.exhaust
% 0.28/0.47 thf(fact_251_old_Oprod_Oexhaust,axiom,
% 0.28/0.47 ! [Y: produc1016592119n_game] :
% 0.28/0.47 ~ ! [A7: option_game,B7: option_game] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( produc1111617711n_game @ A7 @ B7 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.exhaust
% 0.28/0.47 thf(fact_252_Pair__inject,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: option_game,A6: set_variable,B6: option_game] :
% 0.28/0.47 ( ( ( produc1149443391n_game @ A2 @ B2 )
% 0.28/0.47 = ( produc1149443391n_game @ A6 @ B6 ) )
% 0.28/0.47 => ~ ( ( A2 = A6 )
% 0.28/0.47 => ( B2 != B6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_inject
% 0.28/0.47 thf(fact_253_Pair__inject,axiom,
% 0.28/0.47 ! [A2: option_game,B2: option_game,A6: option_game,B6: option_game] :
% 0.28/0.47 ( ( ( produc1111617711n_game @ A2 @ B2 )
% 0.28/0.47 = ( produc1111617711n_game @ A6 @ B6 ) )
% 0.28/0.47 => ~ ( ( A2 = A6 )
% 0.28/0.47 => ( B2 != B6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_inject
% 0.28/0.47 thf(fact_254_prod__cases,axiom,
% 0.28/0.47 ! [P: produc1078154247n_game > $o,P2: produc1078154247n_game] :
% 0.28/0.47 ( ! [A7: set_variable,B7: option_game] : ( P @ ( produc1149443391n_game @ A7 @ B7 ) )
% 0.28/0.47 => ( P @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases
% 0.28/0.47 thf(fact_255_prod__cases,axiom,
% 0.28/0.47 ! [P: produc1016592119n_game > $o,P2: produc1016592119n_game] :
% 0.28/0.47 ( ! [A7: option_game,B7: option_game] : ( P @ ( produc1111617711n_game @ A7 @ B7 ) )
% 0.28/0.47 => ( P @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases
% 0.28/0.47 thf(fact_256_surj__pair,axiom,
% 0.28/0.47 ! [P2: produc1078154247n_game] :
% 0.28/0.47 ? [X3: set_variable,Y4: option_game] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1149443391n_game @ X3 @ Y4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_pair
% 0.28/0.47 thf(fact_257_surj__pair,axiom,
% 0.28/0.47 ! [P2: produc1016592119n_game] :
% 0.28/0.47 ? [X3: option_game,Y4: option_game] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1111617711n_game @ X3 @ Y4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_pair
% 0.28/0.47 thf(fact_258_fst__eqD,axiom,
% 0.28/0.47 ! [X: option_game,Y: option_game,A2: option_game] :
% 0.28/0.47 ( ( ( produc1942569115n_game @ ( produc1111617711n_game @ X @ Y ) )
% 0.28/0.47 = A2 )
% 0.28/0.47 => ( X = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fst_eqD
% 0.28/0.47 thf(fact_259_fst__eqD,axiom,
% 0.28/0.47 ! [X: set_variable,Y: option_game,A2: set_variable] :
% 0.28/0.47 ( ( ( produc893821739n_game @ ( produc1149443391n_game @ X @ Y ) )
% 0.28/0.47 = A2 )
% 0.28/0.47 => ( X = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fst_eqD
% 0.28/0.47 thf(fact_260_fst__conv,axiom,
% 0.28/0.47 ! [X1: option_game,X22: option_game] :
% 0.28/0.47 ( ( produc1942569115n_game @ ( produc1111617711n_game @ X1 @ X22 ) )
% 0.28/0.47 = X1 ) ).
% 0.28/0.47
% 0.28/0.47 % fst_conv
% 0.28/0.47 thf(fact_261_fst__conv,axiom,
% 0.28/0.47 ! [X1: set_variable,X22: option_game] :
% 0.28/0.47 ( ( produc893821739n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.28/0.47 = X1 ) ).
% 0.28/0.47
% 0.28/0.47 % fst_conv
% 0.28/0.47 thf(fact_262_snd__eqD,axiom,
% 0.28/0.47 ! [X: option_game,Y: option_game,A2: option_game] :
% 0.28/0.47 ( ( ( produc279011037n_game @ ( produc1111617711n_game @ X @ Y ) )
% 0.28/0.47 = A2 )
% 0.28/0.47 => ( Y = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % snd_eqD
% 0.28/0.47 thf(fact_263_snd__eqD,axiom,
% 0.28/0.47 ! [X: set_variable,Y: option_game,A2: option_game] :
% 0.28/0.47 ( ( ( produc293487213n_game @ ( produc1149443391n_game @ X @ Y ) )
% 0.28/0.47 = A2 )
% 0.28/0.47 => ( Y = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % snd_eqD
% 0.28/0.47 thf(fact_264_snd__conv,axiom,
% 0.28/0.47 ! [X1: option_game,X22: option_game] :
% 0.28/0.47 ( ( produc279011037n_game @ ( produc1111617711n_game @ X1 @ X22 ) )
% 0.28/0.47 = X22 ) ).
% 0.28/0.47
% 0.28/0.47 % snd_conv
% 0.28/0.47 thf(fact_265_snd__conv,axiom,
% 0.28/0.47 ! [X1: set_variable,X22: option_game] :
% 0.28/0.47 ( ( produc293487213n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 0.28/0.47 = X22 ) ).
% 0.28/0.47
% 0.28/0.47 % snd_conv
% 0.28/0.47 thf(fact_266_prod_Oswap__def,axiom,
% 0.28/0.47 ( produc345397471riable
% 0.28/0.47 = ( ^ [P3: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ P3 ) @ ( produc884810027riable @ P3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.swap_def
% 0.28/0.47 thf(fact_267_prod_Oswap__def,axiom,
% 0.28/0.47 ( produc1696194127n_game
% 0.28/0.47 = ( ^ [P3: produc1016592119n_game] : ( produc1111617711n_game @ ( produc279011037n_game @ P3 ) @ ( produc1942569115n_game @ P3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.swap_def
% 0.28/0.47 thf(fact_268_prod_Oswap__def,axiom,
% 0.28/0.47 ( produc354409183n_game
% 0.28/0.47 = ( ^ [P3: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ P3 ) @ ( produc893821739n_game @ P3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.swap_def
% 0.28/0.47 thf(fact_269_fst__pair,axiom,
% 0.28/0.47 ! [A2: option_game,B2: option_game] :
% 0.28/0.47 ( ( produc1942569115n_game @ ( produc1111617711n_game @ A2 @ B2 ) )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % fst_pair
% 0.28/0.47 thf(fact_270_fst__pair,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: option_game] :
% 0.28/0.47 ( ( produc893821739n_game @ ( produc1149443391n_game @ A2 @ B2 ) )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % fst_pair
% 0.28/0.47 thf(fact_271_snd__pair,axiom,
% 0.28/0.47 ! [A2: option_game,B2: option_game] :
% 0.28/0.47 ( ( produc279011037n_game @ ( produc1111617711n_game @ A2 @ B2 ) )
% 0.28/0.47 = B2 ) ).
% 0.28/0.47
% 0.28/0.47 % snd_pair
% 0.28/0.47 thf(fact_272_snd__pair,axiom,
% 0.28/0.47 ! [A2: set_variable,B2: option_game] :
% 0.28/0.47 ( ( produc293487213n_game @ ( produc1149443391n_game @ A2 @ B2 ) )
% 0.28/0.47 = B2 ) ).
% 0.28/0.47
% 0.28/0.47 % snd_pair
% 0.28/0.47 thf(fact_273_surjective__pairing,axiom,
% 0.28/0.47 ! [T2: produc1016592119n_game] :
% 0.28/0.47 ( T2
% 0.28/0.47 = ( produc1111617711n_game @ ( produc1942569115n_game @ T2 ) @ ( produc279011037n_game @ T2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjective_pairing
% 0.28/0.47 thf(fact_274_surjective__pairing,axiom,
% 0.28/0.47 ! [T2: produc1078154247n_game] :
% 0.28/0.47 ( T2
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ T2 ) @ ( produc293487213n_game @ T2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjective_pairing
% 0.28/0.47 thf(fact_275_prod_Oexhaust__sel,axiom,
% 0.28/0.47 ! [Prod: produc1016592119n_game] :
% 0.28/0.47 ( Prod
% 0.28/0.47 = ( produc1111617711n_game @ ( produc1942569115n_game @ Prod ) @ ( produc279011037n_game @ Prod ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.exhaust_sel
% 0.28/0.47 thf(fact_276_prod_Oexhaust__sel,axiom,
% 0.28/0.47 ! [Prod: produc1078154247n_game] :
% 0.28/0.47 ( Prod
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.exhaust_sel
% 0.28/0.47 thf(fact_277_conjI__realizer,axiom,
% 0.28/0.47 ! [P: option_game > $o,P2: option_game,Q: option_game > $o,Q2: option_game] :
% 0.28/0.47 ( ( P @ P2 )
% 0.28/0.47 => ( ( Q @ Q2 )
% 0.28/0.47 => ( ( P @ ( produc1942569115n_game @ ( produc1111617711n_game @ P2 @ Q2 ) ) )
% 0.28/0.47 & ( Q @ ( produc279011037n_game @ ( produc1111617711n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conjI_realizer
% 0.28/0.47 thf(fact_278_conjI__realizer,axiom,
% 0.28/0.47 ! [P: set_variable > $o,P2: set_variable,Q: option_game > $o,Q2: option_game] :
% 0.28/0.47 ( ( P @ P2 )
% 0.28/0.47 => ( ( Q @ Q2 )
% 0.28/0.47 => ( ( P @ ( produc893821739n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) )
% 0.28/0.47 & ( Q @ ( produc293487213n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conjI_realizer
% 0.28/0.47 thf(fact_279_exI__realizer,axiom,
% 0.28/0.47 ! [P: option_game > option_game > $o,Y: option_game,X: option_game] :
% 0.28/0.47 ( ( P @ Y @ X )
% 0.28/0.47 => ( P @ ( produc279011037n_game @ ( produc1111617711n_game @ X @ Y ) ) @ ( produc1942569115n_game @ ( produc1111617711n_game @ X @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % exI_realizer
% 0.28/0.47 thf(fact_280_exI__realizer,axiom,
% 0.28/0.47 ! [P: option_game > set_variable > $o,Y: option_game,X: set_variable] :
% 0.28/0.47 ( ( P @ Y @ X )
% 0.28/0.47 => ( P @ ( produc293487213n_game @ ( produc1149443391n_game @ X @ Y ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ X @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % exI_realizer
% 0.28/0.47 thf(fact_281_Choiceo_Osimps_I2_J,axiom,
% 0.28/0.47 ! [Alpha: option_game] :
% 0.28/0.47 ( ( uSubst1484167963hoiceo @ Alpha @ none_game )
% 0.28/0.47 = none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Choiceo.simps(2)
% 0.28/0.47 thf(fact_282_Choiceo__undef,axiom,
% 0.28/0.47 ! [Alpha: option_game,Beta: option_game] :
% 0.28/0.47 ( ( ( uSubst1484167963hoiceo @ Alpha @ Beta )
% 0.28/0.47 = none_game )
% 0.28/0.47 = ( ( Alpha = none_game )
% 0.28/0.47 | ( Beta = none_game ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Choiceo_undef
% 0.28/0.47 thf(fact_283_usubstappp__compose,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst532817840mposeo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_compose
% 0.28/0.47 thf(fact_284_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.28/0.47 ! [P: option_game > option_game > $o,X: option_game,Y: option_game,A2: produc1016592119n_game] :
% 0.28/0.47 ( ( P @ X @ Y )
% 0.28/0.47 => ( ( A2
% 0.28/0.47 = ( produc1111617711n_game @ X @ Y ) )
% 0.28/0.47 => ( P @ ( produc1942569115n_game @ A2 ) @ ( produc279011037n_game @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.28/0.47 thf(fact_285_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.28/0.47 ! [P: set_variable > option_game > $o,X: set_variable,Y: option_game,A2: produc1078154247n_game] :
% 0.28/0.47 ( ( P @ X @ Y )
% 0.28/0.47 => ( ( A2
% 0.28/0.47 = ( produc1149443391n_game @ X @ Y ) )
% 0.28/0.47 => ( P @ ( produc893821739n_game @ A2 ) @ ( produc293487213n_game @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.28/0.47 thf(fact_286_Composeo__undef,axiom,
% 0.28/0.47 ! [Alpha: option_game,Beta: option_game] :
% 0.28/0.47 ( ( ( uSubst532817840mposeo @ Alpha @ Beta )
% 0.28/0.47 = none_game )
% 0.28/0.47 = ( ( Alpha = none_game )
% 0.28/0.47 | ( Beta = none_game ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo_undef
% 0.28/0.47 thf(fact_287_Composeo_Osimps_I2_J,axiom,
% 0.28/0.47 ! [Alpha: option_game] :
% 0.28/0.47 ( ( uSubst532817840mposeo @ Alpha @ none_game )
% 0.28/0.47 = none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.simps(2)
% 0.28/0.47 thf(fact_288_usubstappp__loop,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp_loop
% 0.28/0.47 thf(fact_289_eq__snd__iff,axiom,
% 0.28/0.47 ! [B2: option_game,P2: produc1016592119n_game] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( produc279011037n_game @ P2 ) )
% 0.28/0.47 = ( ? [A4: option_game] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1111617711n_game @ A4 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_snd_iff
% 0.28/0.47 thf(fact_290_eq__snd__iff,axiom,
% 0.28/0.47 ! [B2: option_game,P2: produc1078154247n_game] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( produc293487213n_game @ P2 ) )
% 0.28/0.47 = ( ? [A4: set_variable] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1149443391n_game @ A4 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_snd_iff
% 0.28/0.47 thf(fact_291_sndI,axiom,
% 0.28/0.47 ! [X: produc1016592119n_game,Y: option_game,Z: option_game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( produc1111617711n_game @ Y @ Z ) )
% 0.28/0.47 => ( ( produc279011037n_game @ X )
% 0.28/0.47 = Z ) ) ).
% 0.28/0.47
% 0.28/0.47 % sndI
% 0.28/0.47 thf(fact_292_sndI,axiom,
% 0.28/0.47 ! [X: produc1078154247n_game,Y: set_variable,Z: option_game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( produc1149443391n_game @ Y @ Z ) )
% 0.28/0.47 => ( ( produc293487213n_game @ X )
% 0.28/0.47 = Z ) ) ).
% 0.28/0.47
% 0.28/0.47 % sndI
% 0.28/0.47 thf(fact_293_Loopo_Osimps_I2_J,axiom,
% 0.28/0.47 ( ( uSubst23177304_Loopo @ none_game )
% 0.28/0.47 = none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo.simps(2)
% 0.28/0.47 thf(fact_294_Loopo__undef,axiom,
% 0.28/0.47 ! [Alpha: option_game] :
% 0.28/0.47 ( ( ( uSubst23177304_Loopo @ Alpha )
% 0.28/0.47 = none_game )
% 0.28/0.47 = ( Alpha = none_game ) ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo_undef
% 0.28/0.47 thf(fact_295_fstI,axiom,
% 0.28/0.47 ! [X: produc1016592119n_game,Y: option_game,Z: option_game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( produc1111617711n_game @ Y @ Z ) )
% 0.28/0.47 => ( ( produc1942569115n_game @ X )
% 0.28/0.47 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % fstI
% 0.28/0.47 thf(fact_296_fstI,axiom,
% 0.28/0.47 ! [X: produc1078154247n_game,Y: set_variable,Z: option_game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( produc1149443391n_game @ Y @ Z ) )
% 0.28/0.47 => ( ( produc893821739n_game @ X )
% 0.28/0.47 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % fstI
% 0.28/0.47 thf(fact_297_eq__fst__iff,axiom,
% 0.28/0.47 ! [A2: option_game,P2: produc1016592119n_game] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( produc1942569115n_game @ P2 ) )
% 0.28/0.47 = ( ? [B4: option_game] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1111617711n_game @ A2 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_fst_iff
% 0.28/0.47 thf(fact_298_eq__fst__iff,axiom,
% 0.28/0.47 ! [A2: set_variable,P2: produc1078154247n_game] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( produc893821739n_game @ P2 ) )
% 0.28/0.47 = ( ? [B4: option_game] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( produc1149443391n_game @ A2 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_fst_iff
% 0.28/0.47 thf(fact_299_relChain__def,axiom,
% 0.28/0.47 ( bNF_Ca1986151756riable
% 0.28/0.47 = ( ^ [R: set_Pr1625152599n_game,As: option_game > set_variable] :
% 0.28/0.47 ! [I: option_game,J: option_game] :
% 0.28/0.47 ( ( member191809696n_game @ ( produc1111617711n_game @ I @ J ) @ R )
% 0.28/0.47 => ( ord_le282106107riable @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % relChain_def
% 0.28/0.47 thf(fact_300_sndOp__def,axiom,
% 0.28/0.47 ( bNF_sn582998327n_game
% 0.28/0.47 = ( ^ [P4: set_variable > set_variable > $o,Q3: set_variable > option_game > $o,Ac: produc1078154247n_game] : ( produc1149443391n_game @ ( bNF_pi1813424679n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) @ ( produc293487213n_game @ Ac ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sndOp_def
% 0.28/0.47 thf(fact_301_sndOp__def,axiom,
% 0.28/0.47 ( bNF_sn1374695591n_game
% 0.28/0.47 = ( ^ [P4: set_variable > option_game > $o,Q3: option_game > option_game > $o,Ac: produc1078154247n_game] : ( produc1111617711n_game @ ( bNF_pi856525207n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) @ ( produc293487213n_game @ Ac ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sndOp_def
% 0.28/0.47 thf(fact_302_fstOp__def,axiom,
% 0.28/0.47 ( bNF_fs984229733n_game
% 0.28/0.47 = ( ^ [P4: set_variable > option_game > $o,Q3: option_game > option_game > $o,Ac: produc1078154247n_game] : ( produc1149443391n_game @ ( produc893821739n_game @ Ac ) @ ( bNF_pi856525207n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fstOp_def
% 0.28/0.47 thf(fact_303_usubstappp_Osimps_I4_J,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 0.28/0.47 = ( 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 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp.simps(4)
% 0.28/0.47 thf(fact_304_less__eq__set__def,axiom,
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ( ord_le1407353162able_o
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ A3 )
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_set_def
% 0.28/0.47 thf(fact_305_Collect__subset,axiom,
% 0.28/0.47 ! [A: set_variable,P: variable > $o] :
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A )
% 0.28/0.47 & ( P @ X2 ) ) )
% 0.28/0.47 @ A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_subset
% 0.28/0.47 thf(fact_306_Un__def,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A3 )
% 0.28/0.47 | ( member_variable @ X2 @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_def
% 0.28/0.47 thf(fact_307_sup__set__def,axiom,
% 0.28/0.47 ( sup_sup_set_variable
% 0.28/0.47 = ( ^ [A3: set_variable,B3: set_variable] :
% 0.28/0.47 ( collect_variable
% 0.28/0.47 @ ( sup_sup_variable_o
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ A3 )
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_set_def
% 0.28/0.47 thf(fact_308_Collect__disj__eq,axiom,
% 0.28/0.47 ! [P: variable > $o,Q: variable > $o] :
% 0.28/0.47 ( ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( P @ X2 )
% 0.28/0.47 | ( Q @ X2 ) ) )
% 0.28/0.47 = ( sup_sup_set_variable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_disj_eq
% 0.28/0.47 thf(fact_309_subset__CollectI,axiom,
% 0.28/0.47 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 0.28/0.47 ( ( ord_le282106107riable @ B @ A )
% 0.28/0.47 => ( ! [X3: variable] :
% 0.28/0.47 ( ( member_variable @ X3 @ B )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P @ X3 ) ) )
% 0.28/0.47 => ( ord_le282106107riable
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ B )
% 0.28/0.47 & ( Q @ X2 ) ) )
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A )
% 0.28/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_CollectI
% 0.28/0.47 thf(fact_310_subset__Collect__iff,axiom,
% 0.28/0.47 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 0.28/0.47 ( ( ord_le282106107riable @ B @ A )
% 0.28/0.47 => ( ( ord_le282106107riable @ B
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ A )
% 0.28/0.47 & ( P @ X2 ) ) ) )
% 0.28/0.47 = ( ! [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ B )
% 0.28/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Collect_iff
% 0.28/0.47 thf(fact_311_usubstappp_Osimps_I5_J,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst532817840mposeo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp.simps(5)
% 0.28/0.47 thf(fact_312_usubstappp_Osimps_I6_J,axiom,
% 0.28/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 0.28/0.47 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 0.28/0.47 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % usubstappp.simps(6)
% 0.28/0.47 thf(fact_313_sup__Un__eq,axiom,
% 0.28/0.47 ! [R2: set_variable,S2: set_variable] :
% 0.28/0.47 ( ( sup_sup_variable_o
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ R2 )
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ S2 ) )
% 0.28/0.47 = ( ^ [X2: variable] : ( member_variable @ X2 @ ( sup_sup_set_variable @ R2 @ S2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_Un_eq
% 0.28/0.47 thf(fact_314_subrelI,axiom,
% 0.28/0.47 ! [R3: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 0.28/0.47 ( ! [X3: set_variable,Y4: option_game] :
% 0.28/0.47 ( ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y4 ) @ R3 )
% 0.28/0.47 => ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y4 ) @ S3 ) )
% 0.28/0.47 => ( ord_le17855367n_game @ R3 @ S3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subrelI
% 0.28/0.47 thf(fact_315_subrelI,axiom,
% 0.28/0.47 ! [R3: set_Pr1625152599n_game,S3: set_Pr1625152599n_game] :
% 0.28/0.47 ( ! [X3: option_game,Y4: option_game] :
% 0.28/0.47 ( ( member191809696n_game @ ( produc1111617711n_game @ X3 @ Y4 ) @ R3 )
% 0.28/0.47 => ( member191809696n_game @ ( produc1111617711n_game @ X3 @ Y4 ) @ S3 ) )
% 0.28/0.47 => ( ord_le1780499447n_game @ R3 @ S3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subrelI
% 0.28/0.47 thf(fact_316_pred__equals__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 ) )
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) ) )
% 0.28/0.47 = ( R2 = S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_equals_eq2
% 0.28/0.47 thf(fact_317_pred__equals__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 ) )
% 0.28/0.47 = ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) ) )
% 0.28/0.47 = ( R2 = S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_equals_eq2
% 0.28/0.47 thf(fact_318_pred__subset__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( ord_le2134856704game_o
% 0.28/0.47 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 )
% 0.28/0.47 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) )
% 0.28/0.47 = ( ord_le17855367n_game @ R2 @ S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq2
% 0.28/0.47 thf(fact_319_pred__subset__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( ord_le707292176game_o
% 0.28/0.47 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 )
% 0.28/0.47 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) )
% 0.28/0.47 = ( ord_le1780499447n_game @ R2 @ S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq2
% 0.28/0.47 thf(fact_320_sup__Un__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 0.28/0.47 ( ( sup_su1227468340game_o
% 0.28/0.47 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 )
% 0.28/0.47 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) )
% 0.28/0.47 = ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ ( sup_su796825019n_game @ R2 @ S2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_Un_eq2
% 0.28/0.47 thf(fact_321_sup__Un__eq2,axiom,
% 0.28/0.47 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 0.28/0.47 ( ( sup_su169929796game_o
% 0.28/0.47 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 )
% 0.28/0.47 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) )
% 0.28/0.47 = ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ ( sup_su423136299n_game @ R2 @ S2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_Un_eq2
% 0.28/0.47 thf(fact_322_pred__subset__eq,axiom,
% 0.28/0.47 ! [R2: set_variable,S2: set_variable] :
% 0.28/0.47 ( ( ord_le1407353162able_o
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ R2 )
% 0.28/0.47 @ ^ [X2: variable] : ( member_variable @ X2 @ S2 ) )
% 0.28/0.47 = ( ord_le282106107riable @ R2 @ S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq
% 0.28/0.47 thf(fact_323_conj__subset__def,axiom,
% 0.28/0.47 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 0.28/0.47 ( ( ord_le282106107riable @ A
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( P @ X2 )
% 0.28/0.47 & ( Q @ X2 ) ) ) )
% 0.28/0.47 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 0.28/0.47 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conj_subset_def
% 0.28/0.47 thf(fact_324_prop__restrict,axiom,
% 0.28/0.47 ! [X: variable,Z4: set_variable,X4: set_variable,P: variable > $o] :
% 0.28/0.47 ( ( member_variable @ X @ Z4 )
% 0.28/0.47 => ( ( ord_le282106107riable @ Z4
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ X4 )
% 0.28/0.47 & ( P @ X2 ) ) ) )
% 0.28/0.47 => ( P @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prop_restrict
% 0.28/0.47 thf(fact_325_ssubst__Pair__rhs,axiom,
% 0.28/0.47 ! [R3: set_variable,S3: option_game,R2: set_Pr166476775n_game,S4: option_game] :
% 0.28/0.47 ( ( member171223600n_game @ ( produc1149443391n_game @ R3 @ S3 ) @ R2 )
% 0.28/0.47 => ( ( S4 = S3 )
% 0.28/0.47 => ( member171223600n_game @ ( produc1149443391n_game @ R3 @ S4 ) @ R2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ssubst_Pair_rhs
% 0.28/0.47 thf(fact_326_ssubst__Pair__rhs,axiom,
% 0.28/0.47 ! [R3: option_game,S3: option_game,R2: set_Pr1625152599n_game,S4: option_game] :
% 0.28/0.47 ( ( member191809696n_game @ ( produc1111617711n_game @ R3 @ S3 ) @ R2 )
% 0.28/0.47 => ( ( S4 = S3 )
% 0.28/0.47 => ( member191809696n_game @ ( produc1111617711n_game @ R3 @ S4 ) @ R2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ssubst_Pair_rhs
% 0.28/0.47 thf(fact_327_Collect__restrict,axiom,
% 0.28/0.47 ! [X4: set_variable,P: variable > $o] :
% 0.28/0.47 ( ord_le282106107riable
% 0.28/0.47 @ ( collect_variable
% 0.28/0.47 @ ^ [X2: variable] :
% 0.28/0.47 ( ( member_variable @ X2 @ X4 )
% 0.28/0.47 & ( P @ X2 ) ) )
% 0.28/0.47 @ X4 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_restrict
% 0.28/0.47 thf(fact_328_Loopo_Oelims,axiom,
% 0.28/0.47 ! [X: option_game,Y: option_game] :
% 0.28/0.47 ( ( ( uSubst23177304_Loopo @ X )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ! [Alpha2: game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( some_game @ Alpha2 ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 != ( some_game @ ( loop @ Alpha2 ) ) ) )
% 0.28/0.47 => ~ ( ( X = none_game )
% 0.28/0.47 => ( Y != none_game ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo.elims
% 0.28/0.47 thf(fact_329_option_Oinject,axiom,
% 0.28/0.47 ! [X22: game,Y22: game] :
% 0.28/0.47 ( ( ( some_game @ X22 )
% 0.28/0.47 = ( some_game @ Y22 ) )
% 0.28/0.47 = ( X22 = Y22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.inject
% 0.28/0.47 thf(fact_330_not__Some__eq,axiom,
% 0.28/0.47 ! [X: option_game] :
% 0.28/0.47 ( ( ! [Y3: game] :
% 0.28/0.47 ( X
% 0.28/0.47 != ( some_game @ Y3 ) ) )
% 0.28/0.47 = ( X = none_game ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_Some_eq
% 0.28/0.47 thf(fact_331_not__None__eq,axiom,
% 0.28/0.47 ! [X: option_game] :
% 0.28/0.47 ( ( X != none_game )
% 0.28/0.47 = ( ? [Y3: game] :
% 0.28/0.47 ( X
% 0.28/0.47 = ( some_game @ Y3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_None_eq
% 0.28/0.47 thf(fact_332_option_Ocollapse,axiom,
% 0.28/0.47 ! [Option: option_game] :
% 0.28/0.47 ( ( Option != none_game )
% 0.28/0.47 => ( ( some_game @ ( the_game @ Option ) )
% 0.28/0.47 = Option ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.collapse
% 0.28/0.47 thf(fact_333_Composeo_Ocases,axiom,
% 0.28/0.47 ! [X: produc1016592119n_game] :
% 0.28/0.47 ( ! [Alpha2: game,Beta2: game] :
% 0.28/0.47 ( X
% 0.28/0.47 != ( produc1111617711n_game @ ( some_game @ Alpha2 ) @ ( some_game @ Beta2 ) ) )
% 0.28/0.47 => ( ! [Alpha2: option_game] :
% 0.28/0.47 ( X
% 0.28/0.47 != ( produc1111617711n_game @ Alpha2 @ none_game ) )
% 0.28/0.47 => ~ ! [V2: game] :
% 0.28/0.47 ( X
% 0.28/0.47 != ( produc1111617711n_game @ none_game @ ( some_game @ V2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.cases
% 0.28/0.47 thf(fact_334_option_Oexhaust__sel,axiom,
% 0.28/0.47 ! [Option: option_game] :
% 0.28/0.47 ( ( Option != none_game )
% 0.28/0.47 => ( Option
% 0.28/0.47 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.exhaust_sel
% 0.28/0.47 thf(fact_335_combine__options__cases,axiom,
% 0.28/0.47 ! [X: option_game,P: option_game > option_game > $o,Y: option_game] :
% 0.28/0.47 ( ( ( X = none_game )
% 0.28/0.47 => ( P @ X @ Y ) )
% 0.28/0.47 => ( ( ( Y = none_game )
% 0.28/0.47 => ( P @ X @ Y ) )
% 0.28/0.47 => ( ! [A7: game,B7: game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( some_game @ A7 ) )
% 0.28/0.47 => ( ( Y
% 0.28/0.47 = ( some_game @ B7 ) )
% 0.28/0.47 => ( P @ X @ Y ) ) )
% 0.28/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % combine_options_cases
% 0.28/0.47 thf(fact_336_split__option__all,axiom,
% 0.28/0.47 ( ( ^ [P5: option_game > $o] :
% 0.28/0.47 ! [X5: option_game] : ( P5 @ X5 ) )
% 0.28/0.47 = ( ^ [P4: option_game > $o] :
% 0.28/0.47 ( ( P4 @ none_game )
% 0.28/0.47 & ! [X2: game] : ( P4 @ ( some_game @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_option_all
% 0.28/0.47 thf(fact_337_split__option__ex,axiom,
% 0.28/0.47 ( ( ^ [P5: option_game > $o] :
% 0.28/0.47 ? [X5: option_game] : ( P5 @ X5 ) )
% 0.28/0.47 = ( ^ [P4: option_game > $o] :
% 0.28/0.47 ( ( P4 @ none_game )
% 0.28/0.47 | ? [X2: game] : ( P4 @ ( some_game @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_option_ex
% 0.28/0.47 thf(fact_338_option_Oinducts,axiom,
% 0.28/0.47 ! [P: option_game > $o,Option: option_game] :
% 0.28/0.47 ( ( P @ none_game )
% 0.28/0.47 => ( ! [X3: game] : ( P @ ( some_game @ X3 ) )
% 0.28/0.47 => ( P @ Option ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.inducts
% 0.28/0.47 thf(fact_339_option_Oexhaust,axiom,
% 0.28/0.47 ! [Y: option_game] :
% 0.28/0.47 ( ( Y != none_game )
% 0.28/0.47 => ~ ! [X23: game] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( some_game @ X23 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.exhaust
% 0.28/0.47 thf(fact_340_option_OdiscI,axiom,
% 0.28/0.47 ! [Option: option_game,X22: game] :
% 0.28/0.47 ( ( Option
% 0.28/0.47 = ( some_game @ X22 ) )
% 0.28/0.47 => ( Option != none_game ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.discI
% 0.28/0.47 thf(fact_341_option_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [X22: game] :
% 0.28/0.47 ( none_game
% 0.28/0.47 != ( some_game @ X22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.distinct(1)
% 0.28/0.47 thf(fact_342_option_Osel,axiom,
% 0.28/0.47 ! [X22: game] :
% 0.28/0.47 ( ( the_game @ ( some_game @ X22 ) )
% 0.28/0.47 = X22 ) ).
% 0.28/0.47
% 0.28/0.47 % option.sel
% 0.28/0.47 thf(fact_343_Composeo_Oinduct,axiom,
% 0.28/0.47 ! [P: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 0.28/0.47 ( ! [Alpha2: game,Beta2: game] : ( P @ ( some_game @ Alpha2 ) @ ( some_game @ Beta2 ) )
% 0.28/0.47 => ( ! [Alpha2: option_game] : ( P @ Alpha2 @ none_game )
% 0.28/0.47 => ( ! [V2: game] : ( P @ none_game @ ( some_game @ V2 ) )
% 0.28/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.induct
% 0.28/0.47 thf(fact_344_undefg__equiv,axiom,
% 0.28/0.47 ! [Alpha: option_game] :
% 0.28/0.47 ( ( Alpha != none_game )
% 0.28/0.47 = ( ? [G: game] :
% 0.28/0.47 ( Alpha
% 0.28/0.47 = ( some_game @ G ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % undefg_equiv
% 0.28/0.47 thf(fact_345_Loopo_Oinduct,axiom,
% 0.28/0.47 ! [P: option_game > $o,A0: option_game] :
% 0.28/0.47 ( ! [Alpha2: game] : ( P @ ( some_game @ Alpha2 ) )
% 0.28/0.47 => ( ( P @ none_game )
% 0.28/0.47 => ( P @ A0 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo.induct
% 0.28/0.47 thf(fact_346_Loopo_Ocases,axiom,
% 0.28/0.47 ! [X: option_game] :
% 0.28/0.47 ( ! [Alpha2: game] :
% 0.28/0.47 ( X
% 0.28/0.47 != ( some_game @ Alpha2 ) )
% 0.28/0.47 => ( X = none_game ) ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo.cases
% 0.28/0.47 thf(fact_347_Loopo_Osimps_I1_J,axiom,
% 0.28/0.47 ! [Alpha: game] :
% 0.28/0.47 ( ( uSubst23177304_Loopo @ ( some_game @ Alpha ) )
% 0.28/0.47 = ( some_game @ ( loop @ Alpha ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Loopo.simps(1)
% 0.28/0.47 thf(fact_348_Choiceo_Osimps_I1_J,axiom,
% 0.28/0.47 ! [Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst1484167963hoiceo @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.28/0.47 = ( some_game @ ( choice @ Alpha @ Beta ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Choiceo.simps(1)
% 0.28/0.47 thf(fact_349_Composeo_Osimps_I1_J,axiom,
% 0.28/0.47 ! [Alpha: game,Beta: game] :
% 0.28/0.47 ( ( uSubst532817840mposeo @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.28/0.47 = ( some_game @ ( compose @ Alpha @ Beta ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.simps(1)
% 0.28/0.47 thf(fact_350_Composeo_Osimps_I3_J,axiom,
% 0.28/0.47 ! [V3: game] :
% 0.28/0.47 ( ( uSubst532817840mposeo @ none_game @ ( some_game @ V3 ) )
% 0.28/0.47 = none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.simps(3)
% 0.28/0.47 thf(fact_351_Choiceo_Osimps_I3_J,axiom,
% 0.28/0.47 ! [V3: game] :
% 0.28/0.47 ( ( uSubst1484167963hoiceo @ none_game @ ( some_game @ V3 ) )
% 0.28/0.47 = none_game ) ).
% 0.28/0.47
% 0.28/0.47 % Choiceo.simps(3)
% 0.28/0.47 thf(fact_352_Composeo_Oelims,axiom,
% 0.28/0.47 ! [X: option_game,Xa: option_game,Y: option_game] :
% 0.28/0.47 ( ( ( uSubst532817840mposeo @ X @ Xa )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ! [Alpha2: game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( some_game @ Alpha2 ) )
% 0.28/0.47 => ! [Beta2: game] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( some_game @ Beta2 ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 != ( some_game @ ( compose @ Alpha2 @ Beta2 ) ) ) ) )
% 0.28/0.47 => ( ( ( Xa = none_game )
% 0.28/0.47 => ( Y != none_game ) )
% 0.28/0.47 => ~ ( ( X = none_game )
% 0.28/0.47 => ( ? [V2: game] :
% 0.28/0.47 ( Xa
% 0.28/0.47 = ( some_game @ V2 ) )
% 0.28/0.47 => ( Y != none_game ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Composeo.elims
% 0.28/0.47 thf(fact_353_Choiceo_Oelims,axiom,
% 0.28/0.47 ! [X: option_game,Xa: option_game,Y: option_game] :
% 0.28/0.47 ( ( ( uSubst1484167963hoiceo @ X @ Xa )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ! [Alpha2: game] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( some_game @ Alpha2 ) )
% 0.28/0.47 => ! [Beta2: game] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( some_game @ Beta2 ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 != ( some_game @ ( choice @ Alpha2 @ Beta2 ) ) ) ) )
% 0.28/0.47 => ( ( ( Xa = none_game )
% 0.28/0.47 => ( Y != none_game ) )
% 0.28/0.47 => ~ ( ( X = none_game )
% 0.28/0.47 => ( ? [V2: game] :
% 0.28/0.47 ( Xa
% 0.28/0.47 = ( some_game @ V2 ) )
% 0.28/0.47 => ( Y != none_game ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Choiceo.elims
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.38/1.48 ---- Embedded in THF ---
% 2.38/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.38/1.49 %%% Generated on Tue Feb 24 08:29:58 EST 2026
% 2.38/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.38/1.49 %%% Logic specification used:
% 2.38/1.49 %%% thf(spec, logic, $$dhol).
% 2.38/1.49
% 2.38/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2DTF19725.p
% See solution above
% 2.38/1.49 ------------------------
% 2.66/1.54 ---- Cleaned THF ---
% 2.66/1.54 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,
% 2.66/1.54 produc1418842292n_game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 2.66/1.54 set_Pr1625152599n_game: $tType ).
% 2.66/1.54
% 2.66/1.54 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,
% 2.66/1.54 set_Pr166476775n_game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.66/1.54 produc1016592119n_game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.66/1.54 produc1078154247n_game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 2.66/1.54 produc735959047riable: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 option_game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 set_variable: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Syntax__Ovariable,type,
% 2.66/1.54 variable: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(ty_n_t__Syntax__Ogame,type,
% 2.66/1.54 game: $tType ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 bNF_Ca1986151756riable: set_Pr1625152599n_game > ( option_game > set_variable ) > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Def_OfstOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 bNF_fs984229733n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 bNF_pi856525207n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > set_variable > option_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Def_Opick__middlep_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 bNF_pi1813424679n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > set_variable > option_game > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 bNF_sn1374695591n_game: ( set_variable > option_game > $o ) > ( option_game > option_game > $o ) > produc1078154247n_game > produc1016592119n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 bNF_sn582998327n_game: ( set_variable > set_variable > $o ) > ( set_variable > option_game > $o ) > produc1078154247n_game > produc1078154247n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
% 2.66/1.54 sup_su169929796game_o: ( option_game > option_game > $o ) > ( option_game > option_game > $o ) > option_game > option_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J,type,
% 2.66/1.54 sup_su1229228248game_o: ( option_game > $o ) > ( option_game > $o ) > option_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
% 2.66/1.54 sup_su1227468340game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > set_variable > option_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 2.66/1.54 sup_sup_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001_Eo,type,
% 2.66/1.54 sup_sup_o: $o > $o > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 2.66/1.54 sup_su423136299n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > set_Pr1625152599n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 2.66/1.54 sup_su796825019n_game: set_Pr166476775n_game > set_Pr166476775n_game > set_Pr166476775n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 sup_sup_set_variable: set_variable > set_variable > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 2.66/1.54 none_game: option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 2.66/1.54 some_game: game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 2.66/1.54 the_game: option_game > game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ogame_J_M_Eo_J_J,type,
% 2.66/1.54 ord_le707292176game_o: ( option_game > option_game > $o ) > ( option_game > option_game > $o ) > $o ).
% 2.66/1.54
% 2.66/1.54 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,
% 2.66/1.54 ord_le2134856704game_o: ( set_variable > option_game > $o ) > ( set_variable > option_game > $o ) > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 2.66/1.54 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 2.66/1.54 ord_le1780499447n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > $o ).
% 2.66/1.54
% 2.66/1.54 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,
% 2.66/1.54 ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 ord_le282106107riable: set_variable > set_variable > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 order_272405634riable: ( set_variable > $o ) > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 produc1140431679riable: option_game > set_variable > produc735959047riable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc1149443391n_game: set_variable > option_game > produc1078154247n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc1942569115n_game: produc1016592119n_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 produc884810027riable: produc735959047riable > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc893821739n_game: produc1078154247n_game > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc279011037n_game: produc1016592119n_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 produc284475501riable: produc735959047riable > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc293487213n_game: produc1078154247n_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc1696194127n_game: produc1016592119n_game > produc1016592119n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.66/1.54 produc345397471riable: produc735959047riable > produc1078154247n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.66/1.54 produc354409183n_game: produc1078154247n_game > produc735959047riable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.66/1.54 collec884051426n_game: ( produc1016592119n_game > $o ) > set_Pr1625152599n_game ).
% 2.66/1.54
% 2.66/1.54 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,
% 2.66/1.54 collec1702522994n_game: ( produc1078154247n_game > $o ) > set_Pr166476775n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 2.66/1.54 collect_variable: ( variable > $o ) > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Static__Semantics_OBVG,type,
% 2.66/1.54 static_BVG: game > set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Syntax_Ogame_OChoice,type,
% 2.66/1.54 choice: game > game > game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Syntax_Ogame_OCompose,type,
% 2.66/1.54 compose: game > game > game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_Syntax_Ogame_OLoop,type,
% 2.66/1.54 loop: game > game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OChoiceo,type,
% 2.66/1.54 uSubst1484167963hoiceo: option_game > option_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OComposeo,type,
% 2.66/1.54 uSubst532817840mposeo: option_game > option_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OLoopo,type,
% 2.66/1.54 uSubst23177304_Loopo: option_game > option_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappp,type,
% 2.66/1.54 uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.66/1.54 member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.66/1.54 member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 2.66/1.54 member_variable: variable > set_variable > $o ).
% 2.66/1.54
% 2.66/1.54 thf(sy_v_Ua____,type,
% 2.66/1.54 ua: set_variable ).
% 2.66/1.54
% 2.66/1.54 thf(sy_v__092_060alpha_062_H____,type,
% 2.66/1.54 alpha: game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_v__092_060beta_062____,type,
% 2.66/1.54 beta: game ).
% 2.66/1.54
% 2.66/1.54 thf(sy_v__092_060sigma_062,type,
% 2.66/1.54 sigma: produc1418842292n_game ).
% 2.66/1.54
% 2.66/1.54 thf(fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062,axiom,
% 2.66/1.54 ord_le282106107riable @ ( sup_sup_set_variable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_1_fact,axiom,
% 2.66/1.54 ord_le282106107riable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) @ ( sup_sup_set_variable @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_2_IHa,axiom,
% 2.66/1.54 ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_3_IHb,axiom,
% 2.66/1.54 ord_le282106107riable @ ( sup_sup_set_variable @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_4_Compose_Oprems,axiom,
% 2.66/1.54 ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) )
% 2.66/1.54 != none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_5_usubst__taboos__mon,axiom,
% 2.66/1.54 ! [U: set_variable,Sigma: produc1418842292n_game,Alpha: game] : ( ord_le282106107riable @ U @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_6_usubstappp__fst__mon,axiom,
% 2.66/1.54 ! [U: set_variable,V: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 2.66/1.54 ( ( ord_le282106107riable @ U @ V )
% 2.66/1.54 => ( ord_le282106107riable @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_7_Compose_OIH_I2_J,axiom,
% 2.66/1.54 ! [U: set_variable] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ U @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ U @ beta ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_8_Compose_OIH_I1_J,axiom,
% 2.66/1.54 ! [U: set_variable] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ U @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ U @ alpha ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_9_Un__subset__iff,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ A @ B ) @ C )
% 2.66/1.54 = ( ( ord_le1780499447n_game @ A @ C )
% 2.66/1.54 & ( ord_le1780499447n_game @ B @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_10_Un__subset__iff,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ A @ B ) @ C )
% 2.66/1.54 = ( ( ord_le17855367n_game @ A @ C )
% 2.66/1.54 & ( ord_le17855367n_game @ B @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_11_Un__subset__iff,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,C: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C )
% 2.66/1.54 = ( ( ord_le282106107riable @ A @ C )
% 2.66/1.54 & ( ord_le282106107riable @ B @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_12_le__sup__iff,axiom,
% 2.66/1.54 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 2.66/1.54 ( ( ord_le1407353162able_o @ ( sup_sup_variable_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le1407353162able_o @ X @ Z )
% 2.66/1.54 & ( ord_le1407353162able_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_13_le__sup__iff,axiom,
% 2.66/1.54 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le1780499447n_game @ X @ Z )
% 2.66/1.54 & ( ord_le1780499447n_game @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_14_le__sup__iff,axiom,
% 2.66/1.54 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le17855367n_game @ X @ Z )
% 2.66/1.54 & ( ord_le17855367n_game @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_15_le__sup__iff,axiom,
% 2.66/1.54 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 2.66/1.54 ( ( ord_le707292176game_o @ ( sup_su169929796game_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le707292176game_o @ X @ Z )
% 2.66/1.54 & ( ord_le707292176game_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_16_le__sup__iff,axiom,
% 2.66/1.54 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 2.66/1.54 ( ( ord_le2134856704game_o @ ( sup_su1227468340game_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le2134856704game_o @ X @ Z )
% 2.66/1.54 & ( ord_le2134856704game_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_17_le__sup__iff,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.66/1.54 = ( ( ord_le282106107riable @ X @ Z )
% 2.66/1.54 & ( ord_le282106107riable @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_18_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: variable > $o,C2: variable > $o,A2: variable > $o] :
% 2.66/1.54 ( ( ord_le1407353162able_o @ ( sup_sup_variable_o @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le1407353162able_o @ B2 @ A2 )
% 2.66/1.54 & ( ord_le1407353162able_o @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_19_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game,A2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ ( sup_su423136299n_game @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le1780499447n_game @ B2 @ A2 )
% 2.66/1.54 & ( ord_le1780499447n_game @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_20_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: set_Pr166476775n_game,C2: set_Pr166476775n_game,A2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ ( sup_su796825019n_game @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le17855367n_game @ B2 @ A2 )
% 2.66/1.54 & ( ord_le17855367n_game @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_21_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: option_game > option_game > $o,C2: option_game > option_game > $o,A2: option_game > option_game > $o] :
% 2.66/1.54 ( ( ord_le707292176game_o @ ( sup_su169929796game_o @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le707292176game_o @ B2 @ A2 )
% 2.66/1.54 & ( ord_le707292176game_o @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_22_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: set_variable > option_game > $o,C2: set_variable > option_game > $o,A2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( ord_le2134856704game_o @ ( sup_su1227468340game_o @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le2134856704game_o @ B2 @ A2 )
% 2.66/1.54 & ( ord_le2134856704game_o @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_23_sup_Obounded__iff,axiom,
% 2.66/1.54 ! [B2: set_variable,C2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 )
% 2.66/1.54 = ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 & ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_24_BVG__compose,axiom,
% 2.66/1.54 ! [Alpha: game,Beta: game] : ( ord_le282106107riable @ ( static_BVG @ ( compose @ Alpha @ Beta ) ) @ ( sup_sup_set_variable @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_25_game_Oinject_I5_J,axiom,
% 2.66/1.54 ! [X51: game,X52: game,Y51: game,Y52: game] :
% 2.66/1.54 ( ( ( compose @ X51 @ X52 )
% 2.66/1.54 = ( compose @ Y51 @ Y52 ) )
% 2.66/1.54 = ( ( X51 = Y51 )
% 2.66/1.54 & ( X52 = Y52 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_26_UnCI,axiom,
% 2.66/1.54 ! [C2: produc1016592119n_game,B: set_Pr1625152599n_game,A: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ~ ( member191809696n_game @ C2 @ B )
% 2.66/1.54 => ( member191809696n_game @ C2 @ A ) )
% 2.66/1.54 => ( member191809696n_game @ C2 @ ( sup_su423136299n_game @ A @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_27_UnCI,axiom,
% 2.66/1.54 ! [C2: produc1078154247n_game,B: set_Pr166476775n_game,A: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ~ ( member171223600n_game @ C2 @ B )
% 2.66/1.54 => ( member171223600n_game @ C2 @ A ) )
% 2.66/1.54 => ( member171223600n_game @ C2 @ ( sup_su796825019n_game @ A @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_28_UnCI,axiom,
% 2.66/1.54 ! [C2: variable,B: set_variable,A: set_variable] :
% 2.66/1.54 ( ( ~ ( member_variable @ C2 @ B )
% 2.66/1.54 => ( member_variable @ C2 @ A ) )
% 2.66/1.54 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_29_union__or,axiom,
% 2.66/1.54 ! [C2: produc1016592119n_game,A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( member191809696n_game @ C2 @ ( sup_su423136299n_game @ A @ B ) )
% 2.66/1.54 = ( ( member191809696n_game @ C2 @ A )
% 2.66/1.54 | ( member191809696n_game @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_30_union__or,axiom,
% 2.66/1.54 ! [C2: produc1078154247n_game,A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ( member171223600n_game @ C2 @ ( sup_su796825019n_game @ A @ B ) )
% 2.66/1.54 = ( ( member171223600n_game @ C2 @ A )
% 2.66/1.54 | ( member171223600n_game @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_31_union__or,axiom,
% 2.66/1.54 ! [C2: variable,A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 = ( ( member_variable @ C2 @ A )
% 2.66/1.54 | ( member_variable @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_32_sup__apply,axiom,
% 2.66/1.54 ( sup_sup_variable_o
% 2.66/1.54 = ( ^ [F: variable > $o,G: variable > $o,X2: variable] : ( sup_sup_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_33_sup__apply,axiom,
% 2.66/1.54 ( sup_su169929796game_o
% 2.66/1.54 = ( ^ [F: option_game > option_game > $o,G: option_game > option_game > $o,X2: option_game] : ( sup_su1229228248game_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_34_sup__apply,axiom,
% 2.66/1.54 ( sup_su1227468340game_o
% 2.66/1.54 = ( ^ [F: set_variable > option_game > $o,G: set_variable > option_game > $o,X2: set_variable] : ( sup_su1229228248game_o @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_35_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_36_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_37_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_38_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_39_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_40_sup_Oidem,axiom,
% 2.66/1.54 ! [A2: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A2 @ A2 )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_41_sup__idem,axiom,
% 2.66/1.54 ! [X: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_42_sup__idem,axiom,
% 2.66/1.54 ! [X: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_43_sup__idem,axiom,
% 2.66/1.54 ! [X: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_44_sup__idem,axiom,
% 2.66/1.54 ! [X: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_45_sup__idem,axiom,
% 2.66/1.54 ! [X: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_46_sup__idem,axiom,
% 2.66/1.54 ! [X: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X @ X )
% 2.66/1.54 = X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_47_subset__antisym,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ A @ B )
% 2.66/1.54 => ( ( ord_le1780499447n_game @ B @ A )
% 2.66/1.54 => ( A = B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_48_subset__antisym,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ A @ B )
% 2.66/1.54 => ( ( ord_le17855367n_game @ B @ A )
% 2.66/1.54 => ( A = B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_49_subset__antisym,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ( ( ord_le282106107riable @ B @ A )
% 2.66/1.54 => ( A = B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_50_subsetI,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ! [X3: produc1016592119n_game] :
% 2.66/1.54 ( ( member191809696n_game @ X3 @ A )
% 2.66/1.54 => ( member191809696n_game @ X3 @ B ) )
% 2.66/1.54 => ( ord_le1780499447n_game @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_51_subsetI,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ! [X3: produc1078154247n_game] :
% 2.66/1.54 ( ( member171223600n_game @ X3 @ A )
% 2.66/1.54 => ( member171223600n_game @ X3 @ B ) )
% 2.66/1.54 => ( ord_le17855367n_game @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_52_subsetI,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ! [X3: variable] :
% 2.66/1.54 ( ( member_variable @ X3 @ A )
% 2.66/1.54 => ( member_variable @ X3 @ B ) )
% 2.66/1.54 => ( ord_le282106107riable @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_53_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: variable > $o,B2: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_sup_variable_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_54_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_su169929796game_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_55_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_su423136299n_game @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_56_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_su1227468340game_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_57_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_su796825019n_game @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_58_sup_Oright__idem,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B2 ) @ B2 )
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_59_sup__left__idem,axiom,
% 2.66/1.54 ! [X: variable > $o,Y: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ X @ Y ) )
% 2.66/1.54 = ( sup_sup_variable_o @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_60_sup__left__idem,axiom,
% 2.66/1.54 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ X @ Y ) )
% 2.66/1.54 = ( sup_su169929796game_o @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_61_sup__left__idem,axiom,
% 2.66/1.54 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ X @ Y ) )
% 2.66/1.54 = ( sup_su423136299n_game @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_62_sup__left__idem,axiom,
% 2.66/1.54 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ X @ Y ) )
% 2.66/1.54 = ( sup_su1227468340game_o @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_63_sup__left__idem,axiom,
% 2.66/1.54 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ X @ Y ) )
% 2.66/1.54 = ( sup_su796825019n_game @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_64_sup__left__idem,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 2.66/1.54 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_65_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: variable > $o,B2: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_sup_variable_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_66_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_su169929796game_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_67_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_su423136299n_game @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_68_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_su1227468340game_o @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_69_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_su796825019n_game @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_70_sup_Oleft__idem,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ A2 @ B2 ) )
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_71_usubstappp__det,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,V: set_variable] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_72_Collect__mono__iff,axiom,
% 2.66/1.54 ! [P: produc1016592119n_game > $o,Q: produc1016592119n_game > $o] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ ( collec884051426n_game @ P ) @ ( collec884051426n_game @ Q ) )
% 2.66/1.54 = ( ! [X2: produc1016592119n_game] :
% 2.66/1.54 ( ( P @ X2 )
% 2.66/1.54 => ( Q @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_73_Collect__mono__iff,axiom,
% 2.66/1.54 ! [P: produc1078154247n_game > $o,Q: produc1078154247n_game > $o] :
% 2.66/1.54 ( ( ord_le17855367n_game @ ( collec1702522994n_game @ P ) @ ( collec1702522994n_game @ Q ) )
% 2.66/1.54 = ( ! [X2: produc1078154247n_game] :
% 2.66/1.54 ( ( P @ X2 )
% 2.66/1.54 => ( Q @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_74_Collect__mono__iff,axiom,
% 2.66/1.54 ! [P: variable > $o,Q: variable > $o] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 2.66/1.54 = ( ! [X2: variable] :
% 2.66/1.54 ( ( P @ X2 )
% 2.66/1.54 => ( Q @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_75_set__eq__subset,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_Pr1625152599n_game,Z2: set_Pr1625152599n_game] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ A3 @ B3 )
% 2.66/1.54 & ( ord_le1780499447n_game @ B3 @ A3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_76_set__eq__subset,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_Pr166476775n_game,Z2: set_Pr166476775n_game] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ A3 @ B3 )
% 2.66/1.54 & ( ord_le17855367n_game @ B3 @ A3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_77_set__eq__subset,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A3 @ B3 )
% 2.66/1.54 & ( ord_le282106107riable @ B3 @ A3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_78_subset__trans,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ A @ B )
% 2.66/1.54 => ( ( ord_le1780499447n_game @ B @ C )
% 2.66/1.54 => ( ord_le1780499447n_game @ A @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_79_subset__trans,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ A @ B )
% 2.66/1.54 => ( ( ord_le17855367n_game @ B @ C )
% 2.66/1.54 => ( ord_le17855367n_game @ A @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_80_subset__trans,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,C: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ( ( ord_le282106107riable @ B @ C )
% 2.66/1.54 => ( ord_le282106107riable @ A @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_81_Collect__mono,axiom,
% 2.66/1.54 ! [P: produc1016592119n_game > $o,Q: produc1016592119n_game > $o] :
% 2.66/1.54 ( ! [X3: produc1016592119n_game] :
% 2.66/1.54 ( ( P @ X3 )
% 2.66/1.54 => ( Q @ X3 ) )
% 2.66/1.54 => ( ord_le1780499447n_game @ ( collec884051426n_game @ P ) @ ( collec884051426n_game @ Q ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_82_Collect__mono,axiom,
% 2.66/1.54 ! [P: produc1078154247n_game > $o,Q: produc1078154247n_game > $o] :
% 2.66/1.54 ( ! [X3: produc1078154247n_game] :
% 2.66/1.54 ( ( P @ X3 )
% 2.66/1.54 => ( Q @ X3 ) )
% 2.66/1.54 => ( ord_le17855367n_game @ ( collec1702522994n_game @ P ) @ ( collec1702522994n_game @ Q ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_83_Collect__mono,axiom,
% 2.66/1.54 ! [P: variable > $o,Q: variable > $o] :
% 2.66/1.54 ( ! [X3: variable] :
% 2.66/1.54 ( ( P @ X3 )
% 2.66/1.54 => ( Q @ X3 ) )
% 2.66/1.54 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_84_subset__refl,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game] : ( ord_le1780499447n_game @ A @ A ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_85_subset__refl,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game] : ( ord_le17855367n_game @ A @ A ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_86_subset__refl,axiom,
% 2.66/1.54 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_87_subset__iff,axiom,
% 2.66/1.54 ( ord_le1780499447n_game
% 2.66/1.54 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 2.66/1.54 ! [T: produc1016592119n_game] :
% 2.66/1.54 ( ( member191809696n_game @ T @ A3 )
% 2.66/1.54 => ( member191809696n_game @ T @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_88_subset__iff,axiom,
% 2.66/1.54 ( ord_le17855367n_game
% 2.66/1.54 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 2.66/1.54 ! [T: produc1078154247n_game] :
% 2.66/1.54 ( ( member171223600n_game @ T @ A3 )
% 2.66/1.54 => ( member171223600n_game @ T @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_89_subset__iff,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ! [T: variable] :
% 2.66/1.54 ( ( member_variable @ T @ A3 )
% 2.66/1.54 => ( member_variable @ T @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_90_equalityD2,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le1780499447n_game @ B @ A ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_91_equalityD2,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le17855367n_game @ B @ A ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_92_equalityD2,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le282106107riable @ B @ A ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_93_equalityD1,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le1780499447n_game @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_94_equalityD1,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le17855367n_game @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_95_equalityD1,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ( ord_le282106107riable @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_96_subset__eq,axiom,
% 2.66/1.54 ( ord_le1780499447n_game
% 2.66/1.54 = ( ^ [A3: set_Pr1625152599n_game,B3: set_Pr1625152599n_game] :
% 2.66/1.54 ! [X2: produc1016592119n_game] :
% 2.66/1.54 ( ( member191809696n_game @ X2 @ A3 )
% 2.66/1.54 => ( member191809696n_game @ X2 @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_97_subset__eq,axiom,
% 2.66/1.54 ( ord_le17855367n_game
% 2.66/1.54 = ( ^ [A3: set_Pr166476775n_game,B3: set_Pr166476775n_game] :
% 2.66/1.54 ! [X2: produc1078154247n_game] :
% 2.66/1.54 ( ( member171223600n_game @ X2 @ A3 )
% 2.66/1.54 => ( member171223600n_game @ X2 @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_98_subset__eq,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ! [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A3 )
% 2.66/1.54 => ( member_variable @ X2 @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_99_equalityE,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ~ ( ( ord_le1780499447n_game @ A @ B )
% 2.66/1.54 => ~ ( ord_le1780499447n_game @ B @ A ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_100_equalityE,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ~ ( ( ord_le17855367n_game @ A @ B )
% 2.66/1.54 => ~ ( ord_le17855367n_game @ B @ A ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_101_equalityE,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( A = B )
% 2.66/1.54 => ~ ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_102_subsetD,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,C2: produc1016592119n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ A @ B )
% 2.66/1.54 => ( ( member191809696n_game @ C2 @ A )
% 2.66/1.54 => ( member191809696n_game @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_103_subsetD,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,C2: produc1078154247n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ A @ B )
% 2.66/1.54 => ( ( member171223600n_game @ C2 @ A )
% 2.66/1.54 => ( member171223600n_game @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_104_subsetD,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,C2: variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ( ( member_variable @ C2 @ A )
% 2.66/1.54 => ( member_variable @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_105_in__mono,axiom,
% 2.66/1.54 ! [A: set_Pr1625152599n_game,B: set_Pr1625152599n_game,X: produc1016592119n_game] :
% 2.66/1.54 ( ( ord_le1780499447n_game @ A @ B )
% 2.66/1.54 => ( ( member191809696n_game @ X @ A )
% 2.66/1.54 => ( member191809696n_game @ X @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_106_in__mono,axiom,
% 2.66/1.54 ! [A: set_Pr166476775n_game,B: set_Pr166476775n_game,X: produc1078154247n_game] :
% 2.66/1.54 ( ( ord_le17855367n_game @ A @ B )
% 2.66/1.54 => ( ( member171223600n_game @ X @ A )
% 2.66/1.54 => ( member171223600n_game @ X @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_107_in__mono,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,X: variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ( ( member_variable @ X @ A )
% 2.66/1.54 => ( member_variable @ X @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_108_sup__left__commute,axiom,
% 2.66/1.54 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ Y @ Z ) )
% 2.66/1.54 = ( sup_sup_variable_o @ Y @ ( sup_sup_variable_o @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_109_sup__left__commute,axiom,
% 2.66/1.54 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ Y @ Z ) )
% 2.66/1.54 = ( sup_su169929796game_o @ Y @ ( sup_su169929796game_o @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_110_sup__left__commute,axiom,
% 2.66/1.54 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ Y @ Z ) )
% 2.66/1.54 = ( sup_su423136299n_game @ Y @ ( sup_su423136299n_game @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_111_sup__left__commute,axiom,
% 2.66/1.54 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ Y @ Z ) )
% 2.66/1.54 = ( sup_su1227468340game_o @ Y @ ( sup_su1227468340game_o @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_112_sup__left__commute,axiom,
% 2.66/1.54 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ Y @ Z ) )
% 2.66/1.54 = ( sup_su796825019n_game @ Y @ ( sup_su796825019n_game @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_113_sup__left__commute,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 2.66/1.54 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_114_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: variable > $o,A2: variable > $o,C2: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ B2 @ ( sup_sup_variable_o @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_115_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: option_game > option_game > $o,A2: option_game > option_game > $o,C2: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ B2 @ ( sup_su169929796game_o @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_116_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: set_Pr1625152599n_game,A2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ B2 @ ( sup_su423136299n_game @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_117_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: set_variable > option_game > $o,A2: set_variable > option_game > $o,C2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ B2 @ ( sup_su1227468340game_o @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_118_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: set_Pr166476775n_game,A2: set_Pr166476775n_game,C2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ B2 @ ( sup_su796825019n_game @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_119_sup_Oleft__commute,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A2 @ C2 ) )
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_120_sup__commute,axiom,
% 2.66/1.54 ( sup_sup_variable_o
% 2.66/1.54 = ( ^ [X2: variable > $o,Y3: variable > $o] : ( sup_sup_variable_o @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_121_sup__commute,axiom,
% 2.66/1.54 ( sup_su169929796game_o
% 2.66/1.54 = ( ^ [X2: option_game > option_game > $o,Y3: option_game > option_game > $o] : ( sup_su169929796game_o @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_122_sup__commute,axiom,
% 2.66/1.54 ( sup_su423136299n_game
% 2.66/1.54 = ( ^ [X2: set_Pr1625152599n_game,Y3: set_Pr1625152599n_game] : ( sup_su423136299n_game @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_123_sup__commute,axiom,
% 2.66/1.54 ( sup_su1227468340game_o
% 2.66/1.54 = ( ^ [X2: set_variable > option_game > $o,Y3: set_variable > option_game > $o] : ( sup_su1227468340game_o @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_124_sup__commute,axiom,
% 2.66/1.54 ( sup_su796825019n_game
% 2.66/1.54 = ( ^ [X2: set_Pr166476775n_game,Y3: set_Pr166476775n_game] : ( sup_su796825019n_game @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_125_sup__commute,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_126_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_sup_variable_o
% 2.66/1.54 = ( ^ [A4: variable > $o,B4: variable > $o] : ( sup_sup_variable_o @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_127_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_su169929796game_o
% 2.66/1.54 = ( ^ [A4: option_game > option_game > $o,B4: option_game > option_game > $o] : ( sup_su169929796game_o @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_128_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_su423136299n_game
% 2.66/1.54 = ( ^ [A4: set_Pr1625152599n_game,B4: set_Pr1625152599n_game] : ( sup_su423136299n_game @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_129_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_su1227468340game_o
% 2.66/1.54 = ( ^ [A4: set_variable > option_game > $o,B4: set_variable > option_game > $o] : ( sup_su1227468340game_o @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_130_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_su796825019n_game
% 2.66/1.54 = ( ^ [A4: set_Pr166476775n_game,B4: set_Pr166476775n_game] : ( sup_su796825019n_game @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_131_sup_Ocommute,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [A4: set_variable,B4: set_variable] : ( sup_sup_set_variable @ B4 @ A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_132_sup__assoc,axiom,
% 2.66/1.54 ! [X: variable > $o,Y: variable > $o,Z: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_sup_variable_o @ X @ ( sup_sup_variable_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_133_sup__assoc,axiom,
% 2.66/1.54 ! [X: option_game > option_game > $o,Y: option_game > option_game > $o,Z: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_su169929796game_o @ X @ ( sup_su169929796game_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_134_sup__assoc,axiom,
% 2.66/1.54 ! [X: set_Pr1625152599n_game,Y: set_Pr1625152599n_game,Z: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_su423136299n_game @ X @ ( sup_su423136299n_game @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_135_sup__assoc,axiom,
% 2.66/1.54 ! [X: set_variable > option_game > $o,Y: set_variable > option_game > $o,Z: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_su1227468340game_o @ X @ ( sup_su1227468340game_o @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_136_sup__assoc,axiom,
% 2.66/1.54 ! [X: set_Pr166476775n_game,Y: set_Pr166476775n_game,Z: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_su796825019n_game @ X @ ( sup_su796825019n_game @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_137_sup__assoc,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_138_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: variable > $o,B2: variable > $o,C2: variable > $o] :
% 2.66/1.54 ( ( sup_sup_variable_o @ ( sup_sup_variable_o @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_sup_variable_o @ A2 @ ( sup_sup_variable_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_139_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: option_game > option_game > $o,B2: option_game > option_game > $o,C2: option_game > option_game > $o] :
% 2.66/1.54 ( ( sup_su169929796game_o @ ( sup_su169929796game_o @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_su169929796game_o @ A2 @ ( sup_su169929796game_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_140_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: set_Pr1625152599n_game,B2: set_Pr1625152599n_game,C2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su423136299n_game @ ( sup_su423136299n_game @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_su423136299n_game @ A2 @ ( sup_su423136299n_game @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_141_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: set_variable > option_game > $o,B2: set_variable > option_game > $o,C2: set_variable > option_game > $o] :
% 2.66/1.54 ( ( sup_su1227468340game_o @ ( sup_su1227468340game_o @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_su1227468340game_o @ A2 @ ( sup_su1227468340game_o @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_142_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: set_Pr166476775n_game,B2: set_Pr166476775n_game,C2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su796825019n_game @ ( sup_su796825019n_game @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_su796825019n_game @ A2 @ ( sup_su796825019n_game @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_143_sup_Oassoc,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B2 ) @ C2 )
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_144_boolean__algebra__cancel_Osup2,axiom,
% 2.66/1.54 ! [B: set_Pr166476775n_game,K: set_Pr166476775n_game,B2: set_Pr166476775n_game,A2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( B
% 2.66/1.54 = ( sup_su796825019n_game @ K @ B2 ) )
% 2.66/1.54 => ( ( sup_su796825019n_game @ A2 @ B )
% 2.66/1.54 = ( sup_su796825019n_game @ K @ ( sup_su796825019n_game @ A2 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_145_boolean__algebra__cancel_Osup2,axiom,
% 2.66/1.54 ! [B: set_variable,K: set_variable,B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( B
% 2.66/1.54 = ( sup_sup_set_variable @ K @ B2 ) )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A2 @ B )
% 2.66/1.54 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_146_boolean__algebra__cancel_Osup1,axiom,
% 2.66/1.54 ! [A: set_variable,K: set_variable,A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( A
% 2.66/1.54 = ( sup_sup_set_variable @ K @ A2 ) )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A @ B2 )
% 2.66/1.54 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_147_inf__sup__aci_I5_J,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_148_inf__sup__aci_I6_J,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.66/1.54 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_149_inf__sup__aci_I7_J,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 2.66/1.54 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_150_inf__sup__aci_I8_J,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 2.66/1.54 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_151_not__union__or,axiom,
% 2.66/1.54 ! [X: variable,A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( ~ ( member_variable @ X @ ( sup_sup_set_variable @ A @ B ) ) )
% 2.66/1.54 = ( ~ ( member_variable @ X @ A )
% 2.66/1.54 & ~ ( member_variable @ X @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_152_Un__left__commute,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,C: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) )
% 2.66/1.54 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_153_Un__left__absorb,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 = ( sup_sup_set_variable @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_154_Un__commute,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] : ( sup_sup_set_variable @ B3 @ A3 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_155_Un__absorb,axiom,
% 2.66/1.54 ! [A: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A @ A )
% 2.66/1.54 = A ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_156_Un__assoc,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,C: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B ) @ C )
% 2.66/1.54 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_157_ball__Un,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 2.66/1.54 ( ( ! [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 => ( P @ X2 ) ) )
% 2.66/1.54 = ( ! [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A )
% 2.66/1.54 => ( P @ X2 ) )
% 2.66/1.54 & ! [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ B )
% 2.66/1.54 => ( P @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_158_bex__Un,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable,P: variable > $o] :
% 2.66/1.54 ( ( ? [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 & ( P @ X2 ) ) )
% 2.66/1.54 = ( ? [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A )
% 2.66/1.54 & ( P @ X2 ) )
% 2.66/1.54 | ? [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ B )
% 2.66/1.54 & ( P @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_159_UnI2,axiom,
% 2.66/1.54 ! [C2: variable,B: set_variable,A: set_variable] :
% 2.66/1.54 ( ( member_variable @ C2 @ B )
% 2.66/1.54 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_160_UnI1,axiom,
% 2.66/1.54 ! [C2: variable,A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( member_variable @ C2 @ A )
% 2.66/1.54 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_161_UnE,axiom,
% 2.66/1.54 ! [C2: variable,A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 => ( ~ ( member_variable @ C2 @ A )
% 2.66/1.54 => ( member_variable @ C2 @ B ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_162_usubstappp__antimon,axiom,
% 2.66/1.54 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Alpha: game] :
% 2.66/1.54 ( ( ord_le282106107riable @ V @ U )
% 2.66/1.54 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 = ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ V @ Alpha ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_163_sup_OcoboundedI2,axiom,
% 2.66/1.54 ! [C2: set_variable,B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ C2 @ B2 )
% 2.66/1.54 => ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_164_sup_OcoboundedI1,axiom,
% 2.66/1.54 ! [C2: set_variable,A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ C2 @ A2 )
% 2.66/1.54 => ( ord_le282106107riable @ C2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_165_sup_Oabsorb__iff2,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [A4: set_variable,B4: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A4 @ B4 )
% 2.66/1.54 = B4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_166_sup_Oabsorb__iff1,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [B4: set_variable,A4: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A4 @ B4 )
% 2.66/1.54 = A4 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_167_sup_Ocobounded2,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable] : ( ord_le282106107riable @ B2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_168_sup_Ocobounded1,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] : ( ord_le282106107riable @ A2 @ ( sup_sup_set_variable @ A2 @ B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_169_sup_Oorder__iff,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [B4: set_variable,A4: set_variable] :
% 2.66/1.54 ( A4
% 2.66/1.54 = ( sup_sup_set_variable @ A4 @ B4 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_170_sup_OboundedI,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ C2 @ A2 )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_171_sup_OboundedE,axiom,
% 2.66/1.54 ! [B2: set_variable,C2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A2 )
% 2.66/1.54 => ~ ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ~ ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_172_sup__absorb2,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X @ Y )
% 2.66/1.54 => ( ( sup_sup_set_variable @ X @ Y )
% 2.66/1.54 = Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_173_sup__absorb1,axiom,
% 2.66/1.54 ! [Y: set_variable,X: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ Y @ X )
% 2.66/1.54 => ( ( sup_sup_set_variable @ X @ Y )
% 2.66/1.54 = X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_174_sup_Oabsorb2,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 2.66/1.54 = B2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_175_sup_Oabsorb1,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 2.66/1.54 = A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_176_sup__unique,axiom,
% 2.66/1.54 ! [F2: set_variable > set_variable > set_variable,X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ! [X3: set_variable,Y4: set_variable] : ( ord_le282106107riable @ X3 @ ( F2 @ X3 @ Y4 ) )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable] : ( ord_le282106107riable @ Y4 @ ( F2 @ X3 @ Y4 ) )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable,Z3: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ Y4 @ X3 )
% 2.66/1.54 => ( ( ord_le282106107riable @ Z3 @ X3 )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ Y4 @ Z3 ) @ X3 ) ) )
% 2.66/1.54 => ( ( sup_sup_set_variable @ X @ Y )
% 2.66/1.54 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_177_sup_OorderI,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( A2
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ B2 ) )
% 2.66/1.54 => ( ord_le282106107riable @ B2 @ A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_178_sup_OorderE,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( A2
% 2.66/1.54 = ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_179_le__iff__sup,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ X2 @ Y3 )
% 2.66/1.54 = Y3 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_180_sup__least,axiom,
% 2.66/1.54 ! [Y: set_variable,X: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ Y @ X )
% 2.66/1.54 => ( ( ord_le282106107riable @ Z @ X )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ Y @ Z ) @ X ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_181_sup__mono,axiom,
% 2.66/1.54 ! [A2: set_variable,C2: set_variable,B2: set_variable,D: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ C2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ D )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ ( sup_sup_set_variable @ C2 @ D ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_182_sup_Omono,axiom,
% 2.66/1.54 ! [C2: set_variable,A2: set_variable,D: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ C2 @ A2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ D @ B2 )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ C2 @ D ) @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_183_le__supI2,axiom,
% 2.66/1.54 ! [X: set_variable,B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X @ B2 )
% 2.66/1.54 => ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_184_le__supI1,axiom,
% 2.66/1.54 ! [X: set_variable,A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X @ A2 )
% 2.66/1.54 => ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ A2 @ B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_185_sup__ge2,axiom,
% 2.66/1.54 ! [Y: set_variable,X: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_186_sup__ge1,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] : ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_187_le__supI,axiom,
% 2.66/1.54 ! [A2: set_variable,X: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ X )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ X )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ X ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_188_le__supE,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,X: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ A2 @ B2 ) @ X )
% 2.66/1.54 => ~ ( ( ord_le282106107riable @ A2 @ X )
% 2.66/1.54 => ~ ( ord_le282106107riable @ B2 @ X ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_189_inf__sup__ord_I3_J,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] : ( ord_le282106107riable @ X @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_190_inf__sup__ord_I4_J,axiom,
% 2.66/1.54 ! [Y: set_variable,X: set_variable] : ( ord_le282106107riable @ Y @ ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_191_subset__Un__eq,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ( ( sup_sup_set_variable @ A3 @ B3 )
% 2.66/1.54 = B3 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_192_subset__UnE,axiom,
% 2.66/1.54 ! [C: set_variable,A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ C @ ( sup_sup_set_variable @ A @ B ) )
% 2.66/1.54 => ~ ! [A5: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A5 @ A )
% 2.66/1.54 => ! [B5: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B5 @ B )
% 2.66/1.54 => ( C
% 2.66/1.54 != ( sup_sup_set_variable @ A5 @ B5 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_193_Un__absorb2,axiom,
% 2.66/1.54 ! [B: set_variable,A: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B @ A )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A @ B )
% 2.66/1.54 = A ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_194_Un__absorb1,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ B )
% 2.66/1.54 => ( ( sup_sup_set_variable @ A @ B )
% 2.66/1.54 = B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_195_Un__upper2,axiom,
% 2.66/1.54 ! [B: set_variable,A: set_variable] : ( ord_le282106107riable @ B @ ( sup_sup_set_variable @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_196_Un__upper1,axiom,
% 2.66/1.54 ! [A: set_variable,B: set_variable] : ( ord_le282106107riable @ A @ ( sup_sup_set_variable @ A @ B ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_197_Un__least,axiom,
% 2.66/1.54 ! [A: set_variable,C: set_variable,B: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ C )
% 2.66/1.54 => ( ( ord_le282106107riable @ B @ C )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ C ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_198_Un__mono,axiom,
% 2.66/1.54 ! [A: set_variable,C: set_variable,B: set_variable,D2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A @ C )
% 2.66/1.54 => ( ( ord_le282106107riable @ B @ D2 )
% 2.66/1.54 => ( ord_le282106107riable @ ( sup_sup_set_variable @ A @ B ) @ ( sup_sup_set_variable @ C @ D2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_199_order__refl,axiom,
% 2.66/1.54 ! [X: set_variable] : ( ord_le282106107riable @ X @ X ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_200_option_Oexpand,axiom,
% 2.66/1.54 ! [Option: option_game,Option2: option_game] :
% 2.66/1.54 ( ( ( Option = none_game )
% 2.66/1.54 = ( Option2 = none_game ) )
% 2.66/1.54 => ( ( ( Option != none_game )
% 2.66/1.54 => ( ( Option2 != none_game )
% 2.66/1.54 => ( ( the_game @ Option )
% 2.66/1.54 = ( the_game @ Option2 ) ) ) )
% 2.66/1.54 => ( Option = Option2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_201_prod__eq__iff,axiom,
% 2.66/1.54 ( ( ^ [Y2: produc1078154247n_game,Z2: produc1078154247n_game] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [S: produc1078154247n_game,T: produc1078154247n_game] :
% 2.66/1.54 ( ( ( produc893821739n_game @ S )
% 2.66/1.54 = ( produc893821739n_game @ T ) )
% 2.66/1.54 & ( ( produc293487213n_game @ S )
% 2.66/1.54 = ( produc293487213n_game @ T ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_202_prod_Oexpand,axiom,
% 2.66/1.54 ! [Prod: produc1078154247n_game,Prod2: produc1078154247n_game] :
% 2.66/1.54 ( ( ( ( produc893821739n_game @ Prod )
% 2.66/1.54 = ( produc893821739n_game @ Prod2 ) )
% 2.66/1.54 & ( ( produc293487213n_game @ Prod )
% 2.66/1.54 = ( produc293487213n_game @ Prod2 ) ) )
% 2.66/1.54 => ( Prod = Prod2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_203_exE__realizer_H,axiom,
% 2.66/1.54 ! [P: option_game > set_variable > $o,P2: produc1078154247n_game] :
% 2.66/1.54 ( ( P @ ( produc293487213n_game @ P2 ) @ ( produc893821739n_game @ P2 ) )
% 2.66/1.54 => ~ ! [X3: set_variable,Y4: option_game] :
% 2.66/1.54 ~ ( P @ Y4 @ X3 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_204_prod__eqI,axiom,
% 2.66/1.54 ! [P2: produc1078154247n_game,Q2: produc1078154247n_game] :
% 2.66/1.54 ( ( ( produc893821739n_game @ P2 )
% 2.66/1.54 = ( produc893821739n_game @ Q2 ) )
% 2.66/1.54 => ( ( ( produc293487213n_game @ P2 )
% 2.66/1.54 = ( produc293487213n_game @ Q2 ) )
% 2.66/1.54 => ( P2 = Q2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_205_usubstappp__loop__conv,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) )
% 2.66/1.54 != none_game ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_206_BVG__choice,axiom,
% 2.66/1.54 ! [Alpha: game,Beta: game] : ( ord_le282106107riable @ ( static_BVG @ ( choice @ Alpha @ Beta ) ) @ ( sup_sup_set_variable @ ( static_BVG @ Alpha ) @ ( static_BVG @ Beta ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_207_usubstappp__choice__conv,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 => ( ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) )
% 2.66/1.54 != none_game )
% 2.66/1.54 & ( ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Beta ) )
% 2.66/1.54 != none_game ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_208_game_Oinject_I6_J,axiom,
% 2.66/1.54 ! [X6: game,Y6: game] :
% 2.66/1.54 ( ( ( loop @ X6 )
% 2.66/1.54 = ( loop @ Y6 ) )
% 2.66/1.54 = ( X6 = Y6 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_209_game_Oinject_I4_J,axiom,
% 2.66/1.54 ! [X41: game,X42: game,Y41: game,Y42: game] :
% 2.66/1.54 ( ( ( choice @ X41 @ X42 )
% 2.66/1.54 = ( choice @ Y41 @ Y42 ) )
% 2.66/1.54 = ( ( X41 = Y41 )
% 2.66/1.54 & ( X42 = Y42 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_210_game_Odistinct_I39_J,axiom,
% 2.66/1.54 ! [X41: game,X42: game,X6: game] :
% 2.66/1.54 ( ( choice @ X41 @ X42 )
% 2.66/1.54 != ( loop @ X6 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_211_game_Odistinct_I45_J,axiom,
% 2.66/1.54 ! [X51: game,X52: game,X6: game] :
% 2.66/1.54 ( ( compose @ X51 @ X52 )
% 2.66/1.54 != ( loop @ X6 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_212_game_Odistinct_I37_J,axiom,
% 2.66/1.54 ! [X41: game,X42: game,X51: game,X52: game] :
% 2.66/1.54 ( ( choice @ X41 @ X42 )
% 2.66/1.54 != ( compose @ X51 @ X52 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_213_BVG__loop,axiom,
% 2.66/1.54 ! [Alpha: game] : ( ord_le282106107riable @ ( static_BVG @ ( loop @ Alpha ) ) @ ( static_BVG @ Alpha ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_214_order__subst1,axiom,
% 2.66/1.54 ! [A2: set_variable,F2: set_variable > set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ ( F2 @ B2 ) )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ C2 )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X3 @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 2.66/1.54 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_215_order__subst2,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ ( F2 @ B2 ) @ C2 )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X3 @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_216_ord__eq__le__subst,axiom,
% 2.66/1.54 ! [A2: set_variable,F2: set_variable > set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( A2
% 2.66/1.54 = ( F2 @ B2 ) )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ C2 )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X3 @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 2.66/1.54 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_217_ord__le__eq__subst,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( ( F2 @ B2 )
% 2.66/1.54 = C2 )
% 2.66/1.54 => ( ! [X3: set_variable,Y4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X3 @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) )
% 2.66/1.54 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_218_eq__iff,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X2 @ Y3 )
% 2.66/1.54 & ( ord_le282106107riable @ Y3 @ X2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_219_antisym,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X @ Y )
% 2.66/1.54 => ( ( ord_le282106107riable @ Y @ X )
% 2.66/1.54 => ( X = Y ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_220_eq__refl,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable] :
% 2.66/1.54 ( ( X = Y )
% 2.66/1.54 => ( ord_le282106107riable @ X @ Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_221_order_Otrans,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ C2 )
% 2.66/1.54 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_222_antisym__conv,axiom,
% 2.66/1.54 ! [Y: set_variable,X: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ Y @ X )
% 2.66/1.54 => ( ( ord_le282106107riable @ X @ Y )
% 2.66/1.54 = ( X = Y ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_223_order__class_Oorder_Oeq__iff,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [A4: set_variable,B4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A4 @ B4 )
% 2.66/1.54 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_224_ord__eq__le__trans,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( A2 = B2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ C2 )
% 2.66/1.54 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_225_ord__le__eq__trans,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( B2 = C2 )
% 2.66/1.54 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_226_order__class_Oorder_Oantisym,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( A2 = B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_227_order__trans,axiom,
% 2.66/1.54 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ X @ Y )
% 2.66/1.54 => ( ( ord_le282106107riable @ Y @ Z )
% 2.66/1.54 => ( ord_le282106107riable @ X @ Z ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_228_dual__order_Orefl,axiom,
% 2.66/1.54 ! [A2: set_variable] : ( ord_le282106107riable @ A2 @ A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_229_dual__order_Otrans,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable,C2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ C2 @ B2 )
% 2.66/1.54 => ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_230_dual__order_Oeq__iff,axiom,
% 2.66/1.54 ( ( ^ [Y2: set_variable,Z2: set_variable] : ( Y2 = Z2 ) )
% 2.66/1.54 = ( ^ [A4: set_variable,B4: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B4 @ A4 )
% 2.66/1.54 & ( ord_le282106107riable @ A4 @ B4 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_231_dual__order_Oantisym,axiom,
% 2.66/1.54 ! [B2: set_variable,A2: set_variable] :
% 2.66/1.54 ( ( ord_le282106107riable @ B2 @ A2 )
% 2.66/1.54 => ( ( ord_le282106107riable @ A2 @ B2 )
% 2.66/1.54 => ( A2 = B2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_232_fst__swap,axiom,
% 2.66/1.54 ! [X: produc735959047riable] :
% 2.66/1.54 ( ( produc893821739n_game @ ( produc345397471riable @ X ) )
% 2.66/1.54 = ( produc284475501riable @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_233_fst__swap,axiom,
% 2.66/1.54 ! [X: produc1078154247n_game] :
% 2.66/1.54 ( ( produc884810027riable @ ( produc354409183n_game @ X ) )
% 2.66/1.54 = ( produc293487213n_game @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_234_snd__swap,axiom,
% 2.66/1.54 ! [X: produc1078154247n_game] :
% 2.66/1.54 ( ( produc284475501riable @ ( produc354409183n_game @ X ) )
% 2.66/1.54 = ( produc893821739n_game @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_235_snd__swap,axiom,
% 2.66/1.54 ! [X: produc735959047riable] :
% 2.66/1.54 ( ( produc293487213n_game @ ( produc345397471riable @ X ) )
% 2.66/1.54 = ( produc884810027riable @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_236_usubstappp__choice,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 2.66/1.54 = ( 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 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_237_GreatestI2__order,axiom,
% 2.66/1.54 ! [P: set_variable > $o,X: set_variable,Q: set_variable > $o] :
% 2.66/1.54 ( ( P @ X )
% 2.66/1.54 => ( ! [Y4: set_variable] :
% 2.66/1.54 ( ( P @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ Y4 @ X ) )
% 2.66/1.54 => ( ! [X3: set_variable] :
% 2.66/1.54 ( ( P @ X3 )
% 2.66/1.54 => ( ! [Y5: set_variable] :
% 2.66/1.54 ( ( P @ Y5 )
% 2.66/1.54 => ( ord_le282106107riable @ Y5 @ X3 ) )
% 2.66/1.54 => ( Q @ X3 ) ) )
% 2.66/1.54 => ( Q @ ( order_272405634riable @ P ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_238_Greatest__equality,axiom,
% 2.66/1.54 ! [P: set_variable > $o,X: set_variable] :
% 2.66/1.54 ( ( P @ X )
% 2.66/1.54 => ( ! [Y4: set_variable] :
% 2.66/1.54 ( ( P @ Y4 )
% 2.66/1.54 => ( ord_le282106107riable @ Y4 @ X ) )
% 2.66/1.54 => ( ( order_272405634riable @ P )
% 2.66/1.54 = X ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_239_old_Oprod_Oinject,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: option_game,A6: set_variable,B6: option_game] :
% 2.66/1.54 ( ( ( produc1149443391n_game @ A2 @ B2 )
% 2.66/1.54 = ( produc1149443391n_game @ A6 @ B6 ) )
% 2.66/1.54 = ( ( A2 = A6 )
% 2.66/1.54 & ( B2 = B6 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_240_old_Oprod_Oinject,axiom,
% 2.66/1.54 ! [A2: option_game,B2: option_game,A6: option_game,B6: option_game] :
% 2.66/1.54 ( ( ( produc1111617711n_game @ A2 @ B2 )
% 2.66/1.54 = ( produc1111617711n_game @ A6 @ B6 ) )
% 2.66/1.54 = ( ( A2 = A6 )
% 2.66/1.54 & ( B2 = B6 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_241_prod_Oinject,axiom,
% 2.66/1.54 ! [X1: set_variable,X22: option_game,Y1: set_variable,Y22: option_game] :
% 2.66/1.54 ( ( ( produc1149443391n_game @ X1 @ X22 )
% 2.66/1.54 = ( produc1149443391n_game @ Y1 @ Y22 ) )
% 2.66/1.54 = ( ( X1 = Y1 )
% 2.66/1.54 & ( X22 = Y22 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_242_prod_Oinject,axiom,
% 2.66/1.54 ! [X1: option_game,X22: option_game,Y1: option_game,Y22: option_game] :
% 2.66/1.54 ( ( ( produc1111617711n_game @ X1 @ X22 )
% 2.66/1.54 = ( produc1111617711n_game @ Y1 @ Y22 ) )
% 2.66/1.54 = ( ( X1 = Y1 )
% 2.66/1.54 & ( X22 = Y22 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_243_swap__simp,axiom,
% 2.66/1.54 ! [X: option_game,Y: set_variable] :
% 2.66/1.54 ( ( produc345397471riable @ ( produc1140431679riable @ X @ Y ) )
% 2.66/1.54 = ( produc1149443391n_game @ Y @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_244_swap__simp,axiom,
% 2.66/1.54 ! [X: set_variable,Y: option_game] :
% 2.66/1.54 ( ( produc354409183n_game @ ( produc1149443391n_game @ X @ Y ) )
% 2.66/1.54 = ( produc1140431679riable @ Y @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_245_swap__simp,axiom,
% 2.66/1.54 ! [X: option_game,Y: option_game] :
% 2.66/1.54 ( ( produc1696194127n_game @ ( produc1111617711n_game @ X @ Y ) )
% 2.66/1.54 = ( produc1111617711n_game @ Y @ X ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_246_prod_Ocollapse,axiom,
% 2.66/1.54 ! [Prod: produc1016592119n_game] :
% 2.66/1.54 ( ( produc1111617711n_game @ ( produc1942569115n_game @ Prod ) @ ( produc279011037n_game @ Prod ) )
% 2.66/1.54 = Prod ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_247_prod_Ocollapse,axiom,
% 2.66/1.54 ! [Prod: produc1078154247n_game] :
% 2.66/1.54 ( ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) )
% 2.66/1.54 = Prod ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_248_old_Oprod_Oinducts,axiom,
% 2.66/1.54 ! [P: produc1078154247n_game > $o,Prod: produc1078154247n_game] :
% 2.66/1.54 ( ! [A7: set_variable,B7: option_game] : ( P @ ( produc1149443391n_game @ A7 @ B7 ) )
% 2.66/1.54 => ( P @ Prod ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_249_old_Oprod_Oinducts,axiom,
% 2.66/1.54 ! [P: produc1016592119n_game > $o,Prod: produc1016592119n_game] :
% 2.66/1.54 ( ! [A7: option_game,B7: option_game] : ( P @ ( produc1111617711n_game @ A7 @ B7 ) )
% 2.66/1.54 => ( P @ Prod ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_250_old_Oprod_Oexhaust,axiom,
% 2.66/1.54 ! [Y: produc1078154247n_game] :
% 2.66/1.54 ~ ! [A7: set_variable,B7: option_game] :
% 2.66/1.54 ( Y
% 2.66/1.54 != ( produc1149443391n_game @ A7 @ B7 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_251_old_Oprod_Oexhaust,axiom,
% 2.66/1.54 ! [Y: produc1016592119n_game] :
% 2.66/1.54 ~ ! [A7: option_game,B7: option_game] :
% 2.66/1.54 ( Y
% 2.66/1.54 != ( produc1111617711n_game @ A7 @ B7 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_252_Pair__inject,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: option_game,A6: set_variable,B6: option_game] :
% 2.66/1.54 ( ( ( produc1149443391n_game @ A2 @ B2 )
% 2.66/1.54 = ( produc1149443391n_game @ A6 @ B6 ) )
% 2.66/1.54 => ~ ( ( A2 = A6 )
% 2.66/1.54 => ( B2 != B6 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_253_Pair__inject,axiom,
% 2.66/1.54 ! [A2: option_game,B2: option_game,A6: option_game,B6: option_game] :
% 2.66/1.54 ( ( ( produc1111617711n_game @ A2 @ B2 )
% 2.66/1.54 = ( produc1111617711n_game @ A6 @ B6 ) )
% 2.66/1.54 => ~ ( ( A2 = A6 )
% 2.66/1.54 => ( B2 != B6 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_254_prod__cases,axiom,
% 2.66/1.54 ! [P: produc1078154247n_game > $o,P2: produc1078154247n_game] :
% 2.66/1.54 ( ! [A7: set_variable,B7: option_game] : ( P @ ( produc1149443391n_game @ A7 @ B7 ) )
% 2.66/1.54 => ( P @ P2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_255_prod__cases,axiom,
% 2.66/1.54 ! [P: produc1016592119n_game > $o,P2: produc1016592119n_game] :
% 2.66/1.54 ( ! [A7: option_game,B7: option_game] : ( P @ ( produc1111617711n_game @ A7 @ B7 ) )
% 2.66/1.54 => ( P @ P2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_256_surj__pair,axiom,
% 2.66/1.54 ! [P2: produc1078154247n_game] :
% 2.66/1.54 ? [X3: set_variable,Y4: option_game] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1149443391n_game @ X3 @ Y4 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_257_surj__pair,axiom,
% 2.66/1.54 ! [P2: produc1016592119n_game] :
% 2.66/1.54 ? [X3: option_game,Y4: option_game] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1111617711n_game @ X3 @ Y4 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_258_fst__eqD,axiom,
% 2.66/1.54 ! [X: option_game,Y: option_game,A2: option_game] :
% 2.66/1.54 ( ( ( produc1942569115n_game @ ( produc1111617711n_game @ X @ Y ) )
% 2.66/1.54 = A2 )
% 2.66/1.54 => ( X = A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_259_fst__eqD,axiom,
% 2.66/1.54 ! [X: set_variable,Y: option_game,A2: set_variable] :
% 2.66/1.54 ( ( ( produc893821739n_game @ ( produc1149443391n_game @ X @ Y ) )
% 2.66/1.54 = A2 )
% 2.66/1.54 => ( X = A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_260_fst__conv,axiom,
% 2.66/1.54 ! [X1: option_game,X22: option_game] :
% 2.66/1.54 ( ( produc1942569115n_game @ ( produc1111617711n_game @ X1 @ X22 ) )
% 2.66/1.54 = X1 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_261_fst__conv,axiom,
% 2.66/1.54 ! [X1: set_variable,X22: option_game] :
% 2.66/1.54 ( ( produc893821739n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 2.66/1.54 = X1 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_262_snd__eqD,axiom,
% 2.66/1.54 ! [X: option_game,Y: option_game,A2: option_game] :
% 2.66/1.54 ( ( ( produc279011037n_game @ ( produc1111617711n_game @ X @ Y ) )
% 2.66/1.54 = A2 )
% 2.66/1.54 => ( Y = A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_263_snd__eqD,axiom,
% 2.66/1.54 ! [X: set_variable,Y: option_game,A2: option_game] :
% 2.66/1.54 ( ( ( produc293487213n_game @ ( produc1149443391n_game @ X @ Y ) )
% 2.66/1.54 = A2 )
% 2.66/1.54 => ( Y = A2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_264_snd__conv,axiom,
% 2.66/1.54 ! [X1: option_game,X22: option_game] :
% 2.66/1.54 ( ( produc279011037n_game @ ( produc1111617711n_game @ X1 @ X22 ) )
% 2.66/1.54 = X22 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_265_snd__conv,axiom,
% 2.66/1.54 ! [X1: set_variable,X22: option_game] :
% 2.66/1.54 ( ( produc293487213n_game @ ( produc1149443391n_game @ X1 @ X22 ) )
% 2.66/1.54 = X22 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_266_prod_Oswap__def,axiom,
% 2.66/1.54 ( produc345397471riable
% 2.66/1.54 = ( ^ [P3: produc735959047riable] : ( produc1149443391n_game @ ( produc284475501riable @ P3 ) @ ( produc884810027riable @ P3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_267_prod_Oswap__def,axiom,
% 2.66/1.54 ( produc1696194127n_game
% 2.66/1.54 = ( ^ [P3: produc1016592119n_game] : ( produc1111617711n_game @ ( produc279011037n_game @ P3 ) @ ( produc1942569115n_game @ P3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_268_prod_Oswap__def,axiom,
% 2.66/1.54 ( produc354409183n_game
% 2.66/1.54 = ( ^ [P3: produc1078154247n_game] : ( produc1140431679riable @ ( produc293487213n_game @ P3 ) @ ( produc893821739n_game @ P3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_269_fst__pair,axiom,
% 2.66/1.54 ! [A2: option_game,B2: option_game] :
% 2.66/1.54 ( ( produc1942569115n_game @ ( produc1111617711n_game @ A2 @ B2 ) )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_270_fst__pair,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: option_game] :
% 2.66/1.54 ( ( produc893821739n_game @ ( produc1149443391n_game @ A2 @ B2 ) )
% 2.66/1.54 = A2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_271_snd__pair,axiom,
% 2.66/1.54 ! [A2: option_game,B2: option_game] :
% 2.66/1.54 ( ( produc279011037n_game @ ( produc1111617711n_game @ A2 @ B2 ) )
% 2.66/1.54 = B2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_272_snd__pair,axiom,
% 2.66/1.54 ! [A2: set_variable,B2: option_game] :
% 2.66/1.54 ( ( produc293487213n_game @ ( produc1149443391n_game @ A2 @ B2 ) )
% 2.66/1.54 = B2 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_273_surjective__pairing,axiom,
% 2.66/1.54 ! [T2: produc1016592119n_game] :
% 2.66/1.54 ( T2
% 2.66/1.54 = ( produc1111617711n_game @ ( produc1942569115n_game @ T2 ) @ ( produc279011037n_game @ T2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_274_surjective__pairing,axiom,
% 2.66/1.54 ! [T2: produc1078154247n_game] :
% 2.66/1.54 ( T2
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ T2 ) @ ( produc293487213n_game @ T2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_275_prod_Oexhaust__sel,axiom,
% 2.66/1.54 ! [Prod: produc1016592119n_game] :
% 2.66/1.54 ( Prod
% 2.66/1.54 = ( produc1111617711n_game @ ( produc1942569115n_game @ Prod ) @ ( produc279011037n_game @ Prod ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_276_prod_Oexhaust__sel,axiom,
% 2.66/1.54 ! [Prod: produc1078154247n_game] :
% 2.66/1.54 ( Prod
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ Prod ) @ ( produc293487213n_game @ Prod ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_277_conjI__realizer,axiom,
% 2.66/1.54 ! [P: option_game > $o,P2: option_game,Q: option_game > $o,Q2: option_game] :
% 2.66/1.54 ( ( P @ P2 )
% 2.66/1.54 => ( ( Q @ Q2 )
% 2.66/1.54 => ( ( P @ ( produc1942569115n_game @ ( produc1111617711n_game @ P2 @ Q2 ) ) )
% 2.66/1.54 & ( Q @ ( produc279011037n_game @ ( produc1111617711n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_278_conjI__realizer,axiom,
% 2.66/1.54 ! [P: set_variable > $o,P2: set_variable,Q: option_game > $o,Q2: option_game] :
% 2.66/1.54 ( ( P @ P2 )
% 2.66/1.54 => ( ( Q @ Q2 )
% 2.66/1.54 => ( ( P @ ( produc893821739n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) )
% 2.66/1.54 & ( Q @ ( produc293487213n_game @ ( produc1149443391n_game @ P2 @ Q2 ) ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_279_exI__realizer,axiom,
% 2.66/1.54 ! [P: option_game > option_game > $o,Y: option_game,X: option_game] :
% 2.66/1.54 ( ( P @ Y @ X )
% 2.66/1.54 => ( P @ ( produc279011037n_game @ ( produc1111617711n_game @ X @ Y ) ) @ ( produc1942569115n_game @ ( produc1111617711n_game @ X @ Y ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_280_exI__realizer,axiom,
% 2.66/1.54 ! [P: option_game > set_variable > $o,Y: option_game,X: set_variable] :
% 2.66/1.54 ( ( P @ Y @ X )
% 2.66/1.54 => ( P @ ( produc293487213n_game @ ( produc1149443391n_game @ X @ Y ) ) @ ( produc893821739n_game @ ( produc1149443391n_game @ X @ Y ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_281_Choiceo_Osimps_I2_J,axiom,
% 2.66/1.54 ! [Alpha: option_game] :
% 2.66/1.54 ( ( uSubst1484167963hoiceo @ Alpha @ none_game )
% 2.66/1.54 = none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_282_Choiceo__undef,axiom,
% 2.66/1.54 ! [Alpha: option_game,Beta: option_game] :
% 2.66/1.54 ( ( ( uSubst1484167963hoiceo @ Alpha @ Beta )
% 2.66/1.54 = none_game )
% 2.66/1.54 = ( ( Alpha = none_game )
% 2.66/1.54 | ( Beta = none_game ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_283_usubstappp__compose,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst532817840mposeo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_284_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.66/1.54 ! [P: option_game > option_game > $o,X: option_game,Y: option_game,A2: produc1016592119n_game] :
% 2.66/1.54 ( ( P @ X @ Y )
% 2.66/1.54 => ( ( A2
% 2.66/1.54 = ( produc1111617711n_game @ X @ Y ) )
% 2.66/1.54 => ( P @ ( produc1942569115n_game @ A2 ) @ ( produc279011037n_game @ A2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_285_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.66/1.54 ! [P: set_variable > option_game > $o,X: set_variable,Y: option_game,A2: produc1078154247n_game] :
% 2.66/1.54 ( ( P @ X @ Y )
% 2.66/1.54 => ( ( A2
% 2.66/1.54 = ( produc1149443391n_game @ X @ Y ) )
% 2.66/1.54 => ( P @ ( produc893821739n_game @ A2 ) @ ( produc293487213n_game @ A2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_286_Composeo__undef,axiom,
% 2.66/1.54 ! [Alpha: option_game,Beta: option_game] :
% 2.66/1.54 ( ( ( uSubst532817840mposeo @ Alpha @ Beta )
% 2.66/1.54 = none_game )
% 2.66/1.54 = ( ( Alpha = none_game )
% 2.66/1.54 | ( Beta = none_game ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_287_Composeo_Osimps_I2_J,axiom,
% 2.66/1.54 ! [Alpha: option_game] :
% 2.66/1.54 ( ( uSubst532817840mposeo @ Alpha @ none_game )
% 2.66/1.54 = none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_288_usubstappp__loop,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_289_eq__snd__iff,axiom,
% 2.66/1.54 ! [B2: option_game,P2: produc1016592119n_game] :
% 2.66/1.54 ( ( B2
% 2.66/1.54 = ( produc279011037n_game @ P2 ) )
% 2.66/1.54 = ( ? [A4: option_game] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1111617711n_game @ A4 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_290_eq__snd__iff,axiom,
% 2.66/1.54 ! [B2: option_game,P2: produc1078154247n_game] :
% 2.66/1.54 ( ( B2
% 2.66/1.54 = ( produc293487213n_game @ P2 ) )
% 2.66/1.54 = ( ? [A4: set_variable] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1149443391n_game @ A4 @ B2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_291_sndI,axiom,
% 2.66/1.54 ! [X: produc1016592119n_game,Y: option_game,Z: option_game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( produc1111617711n_game @ Y @ Z ) )
% 2.66/1.54 => ( ( produc279011037n_game @ X )
% 2.66/1.54 = Z ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_292_sndI,axiom,
% 2.66/1.54 ! [X: produc1078154247n_game,Y: set_variable,Z: option_game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( produc1149443391n_game @ Y @ Z ) )
% 2.66/1.54 => ( ( produc293487213n_game @ X )
% 2.66/1.54 = Z ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_293_Loopo_Osimps_I2_J,axiom,
% 2.66/1.54 ( ( uSubst23177304_Loopo @ none_game )
% 2.66/1.54 = none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_294_Loopo__undef,axiom,
% 2.66/1.54 ! [Alpha: option_game] :
% 2.66/1.54 ( ( ( uSubst23177304_Loopo @ Alpha )
% 2.66/1.54 = none_game )
% 2.66/1.54 = ( Alpha = none_game ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_295_fstI,axiom,
% 2.66/1.54 ! [X: produc1016592119n_game,Y: option_game,Z: option_game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( produc1111617711n_game @ Y @ Z ) )
% 2.66/1.54 => ( ( produc1942569115n_game @ X )
% 2.66/1.54 = Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_296_fstI,axiom,
% 2.66/1.54 ! [X: produc1078154247n_game,Y: set_variable,Z: option_game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( produc1149443391n_game @ Y @ Z ) )
% 2.66/1.54 => ( ( produc893821739n_game @ X )
% 2.66/1.54 = Y ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_297_eq__fst__iff,axiom,
% 2.66/1.54 ! [A2: option_game,P2: produc1016592119n_game] :
% 2.66/1.54 ( ( A2
% 2.66/1.54 = ( produc1942569115n_game @ P2 ) )
% 2.66/1.54 = ( ? [B4: option_game] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1111617711n_game @ A2 @ B4 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_298_eq__fst__iff,axiom,
% 2.66/1.54 ! [A2: set_variable,P2: produc1078154247n_game] :
% 2.66/1.54 ( ( A2
% 2.66/1.54 = ( produc893821739n_game @ P2 ) )
% 2.66/1.54 = ( ? [B4: option_game] :
% 2.66/1.54 ( P2
% 2.66/1.54 = ( produc1149443391n_game @ A2 @ B4 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_299_relChain__def,axiom,
% 2.66/1.54 ( bNF_Ca1986151756riable
% 2.66/1.54 = ( ^ [R: set_Pr1625152599n_game,As: option_game > set_variable] :
% 2.66/1.54 ! [I: option_game,J: option_game] :
% 2.66/1.54 ( ( member191809696n_game @ ( produc1111617711n_game @ I @ J ) @ R )
% 2.66/1.54 => ( ord_le282106107riable @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_300_sndOp__def,axiom,
% 2.66/1.54 ( bNF_sn582998327n_game
% 2.66/1.54 = ( ^ [P4: set_variable > set_variable > $o,Q3: set_variable > option_game > $o,Ac: produc1078154247n_game] : ( produc1149443391n_game @ ( bNF_pi1813424679n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) @ ( produc293487213n_game @ Ac ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_301_sndOp__def,axiom,
% 2.66/1.54 ( bNF_sn1374695591n_game
% 2.66/1.54 = ( ^ [P4: set_variable > option_game > $o,Q3: option_game > option_game > $o,Ac: produc1078154247n_game] : ( produc1111617711n_game @ ( bNF_pi856525207n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) @ ( produc293487213n_game @ Ac ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_302_fstOp__def,axiom,
% 2.66/1.54 ( bNF_fs984229733n_game
% 2.66/1.54 = ( ^ [P4: set_variable > option_game > $o,Q3: option_game > option_game > $o,Ac: produc1078154247n_game] : ( produc1149443391n_game @ ( produc893821739n_game @ Ac ) @ ( bNF_pi856525207n_game @ P4 @ Q3 @ ( produc893821739n_game @ Ac ) @ ( produc293487213n_game @ Ac ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_303_usubstappp_Osimps_I4_J,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( choice @ Alpha @ Beta ) )
% 2.66/1.54 = ( 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 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_304_less__eq__set__def,axiom,
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ( ord_le1407353162able_o
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ A3 )
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ B3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_305_Collect__subset,axiom,
% 2.66/1.54 ! [A: set_variable,P: variable > $o] :
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A )
% 2.66/1.54 & ( P @ X2 ) ) )
% 2.66/1.54 @ A ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_306_Un__def,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A3 )
% 2.66/1.54 | ( member_variable @ X2 @ B3 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_307_sup__set__def,axiom,
% 2.66/1.54 ( sup_sup_set_variable
% 2.66/1.54 = ( ^ [A3: set_variable,B3: set_variable] :
% 2.66/1.54 ( collect_variable
% 2.66/1.54 @ ( sup_sup_variable_o
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ A3 )
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ B3 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_308_Collect__disj__eq,axiom,
% 2.66/1.54 ! [P: variable > $o,Q: variable > $o] :
% 2.66/1.54 ( ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( P @ X2 )
% 2.66/1.54 | ( Q @ X2 ) ) )
% 2.66/1.54 = ( sup_sup_set_variable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_309_subset__CollectI,axiom,
% 2.66/1.54 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 2.66/1.54 ( ( ord_le282106107riable @ B @ A )
% 2.66/1.54 => ( ! [X3: variable] :
% 2.66/1.54 ( ( member_variable @ X3 @ B )
% 2.66/1.54 => ( ( Q @ X3 )
% 2.66/1.54 => ( P @ X3 ) ) )
% 2.66/1.54 => ( ord_le282106107riable
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ B )
% 2.66/1.54 & ( Q @ X2 ) ) )
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A )
% 2.66/1.54 & ( P @ X2 ) ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_310_subset__Collect__iff,axiom,
% 2.66/1.54 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 2.66/1.54 ( ( ord_le282106107riable @ B @ A )
% 2.66/1.54 => ( ( ord_le282106107riable @ B
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ A )
% 2.66/1.54 & ( P @ X2 ) ) ) )
% 2.66/1.54 = ( ! [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ B )
% 2.66/1.54 => ( P @ X2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_311_usubstappp_Osimps_I5_J,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( compose @ Alpha @ Beta ) )
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) @ ( uSubst532817840mposeo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Beta ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_312_usubstappp_Osimps_I6_J,axiom,
% 2.66/1.54 ! [Sigma: produc1418842292n_game,U: set_variable,Alpha: game] :
% 2.66/1.54 ( ( uSubst516392814stappp @ Sigma @ U @ ( loop @ Alpha ) )
% 2.66/1.54 = ( produc1149443391n_game @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ ( uSubst23177304_Loopo @ ( produc293487213n_game @ ( uSubst516392814stappp @ Sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ Sigma @ U @ Alpha ) ) @ Alpha ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_313_sup__Un__eq,axiom,
% 2.66/1.54 ! [R2: set_variable,S2: set_variable] :
% 2.66/1.54 ( ( sup_sup_variable_o
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ R2 )
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ S2 ) )
% 2.66/1.54 = ( ^ [X2: variable] : ( member_variable @ X2 @ ( sup_sup_set_variable @ R2 @ S2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_314_subrelI,axiom,
% 2.66/1.54 ! [R3: set_Pr166476775n_game,S3: set_Pr166476775n_game] :
% 2.66/1.54 ( ! [X3: set_variable,Y4: option_game] :
% 2.66/1.54 ( ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y4 ) @ R3 )
% 2.66/1.54 => ( member171223600n_game @ ( produc1149443391n_game @ X3 @ Y4 ) @ S3 ) )
% 2.66/1.54 => ( ord_le17855367n_game @ R3 @ S3 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_315_subrelI,axiom,
% 2.66/1.54 ! [R3: set_Pr1625152599n_game,S3: set_Pr1625152599n_game] :
% 2.66/1.54 ( ! [X3: option_game,Y4: option_game] :
% 2.66/1.54 ( ( member191809696n_game @ ( produc1111617711n_game @ X3 @ Y4 ) @ R3 )
% 2.66/1.54 => ( member191809696n_game @ ( produc1111617711n_game @ X3 @ Y4 ) @ S3 ) )
% 2.66/1.54 => ( ord_le1780499447n_game @ R3 @ S3 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_316_pred__equals__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 ) )
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) ) )
% 2.66/1.54 = ( R2 = S2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_317_pred__equals__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 ) )
% 2.66/1.54 = ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) ) )
% 2.66/1.54 = ( R2 = S2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_318_pred__subset__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( ord_le2134856704game_o
% 2.66/1.54 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 )
% 2.66/1.54 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) )
% 2.66/1.54 = ( ord_le17855367n_game @ R2 @ S2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_319_pred__subset__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( ord_le707292176game_o
% 2.66/1.54 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 )
% 2.66/1.54 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) )
% 2.66/1.54 = ( ord_le1780499447n_game @ R2 @ S2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_320_sup__Un__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr166476775n_game,S2: set_Pr166476775n_game] :
% 2.66/1.54 ( ( sup_su1227468340game_o
% 2.66/1.54 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ R2 )
% 2.66/1.54 @ ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ S2 ) )
% 2.66/1.54 = ( ^ [X2: set_variable,Y3: option_game] : ( member171223600n_game @ ( produc1149443391n_game @ X2 @ Y3 ) @ ( sup_su796825019n_game @ R2 @ S2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_321_sup__Un__eq2,axiom,
% 2.66/1.54 ! [R2: set_Pr1625152599n_game,S2: set_Pr1625152599n_game] :
% 2.66/1.54 ( ( sup_su169929796game_o
% 2.66/1.54 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ R2 )
% 2.66/1.54 @ ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ S2 ) )
% 2.66/1.54 = ( ^ [X2: option_game,Y3: option_game] : ( member191809696n_game @ ( produc1111617711n_game @ X2 @ Y3 ) @ ( sup_su423136299n_game @ R2 @ S2 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_322_pred__subset__eq,axiom,
% 2.66/1.54 ! [R2: set_variable,S2: set_variable] :
% 2.66/1.54 ( ( ord_le1407353162able_o
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ R2 )
% 2.66/1.54 @ ^ [X2: variable] : ( member_variable @ X2 @ S2 ) )
% 2.66/1.54 = ( ord_le282106107riable @ R2 @ S2 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_323_conj__subset__def,axiom,
% 2.66/1.54 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 2.66/1.54 ( ( ord_le282106107riable @ A
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( P @ X2 )
% 2.66/1.54 & ( Q @ X2 ) ) ) )
% 2.66/1.54 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 2.66/1.54 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_324_prop__restrict,axiom,
% 2.66/1.54 ! [X: variable,Z4: set_variable,X4: set_variable,P: variable > $o] :
% 2.66/1.54 ( ( member_variable @ X @ Z4 )
% 2.66/1.54 => ( ( ord_le282106107riable @ Z4
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ X4 )
% 2.66/1.54 & ( P @ X2 ) ) ) )
% 2.66/1.54 => ( P @ X ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_325_ssubst__Pair__rhs,axiom,
% 2.66/1.54 ! [R3: set_variable,S3: option_game,R2: set_Pr166476775n_game,S4: option_game] :
% 2.66/1.54 ( ( member171223600n_game @ ( produc1149443391n_game @ R3 @ S3 ) @ R2 )
% 2.66/1.54 => ( ( S4 = S3 )
% 2.66/1.54 => ( member171223600n_game @ ( produc1149443391n_game @ R3 @ S4 ) @ R2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_326_ssubst__Pair__rhs,axiom,
% 2.66/1.54 ! [R3: option_game,S3: option_game,R2: set_Pr1625152599n_game,S4: option_game] :
% 2.66/1.54 ( ( member191809696n_game @ ( produc1111617711n_game @ R3 @ S3 ) @ R2 )
% 2.66/1.54 => ( ( S4 = S3 )
% 2.66/1.54 => ( member191809696n_game @ ( produc1111617711n_game @ R3 @ S4 ) @ R2 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_327_Collect__restrict,axiom,
% 2.66/1.54 ! [X4: set_variable,P: variable > $o] :
% 2.66/1.54 ( ord_le282106107riable
% 2.66/1.54 @ ( collect_variable
% 2.66/1.54 @ ^ [X2: variable] :
% 2.66/1.54 ( ( member_variable @ X2 @ X4 )
% 2.66/1.54 & ( P @ X2 ) ) )
% 2.66/1.54 @ X4 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_328_Loopo_Oelims,axiom,
% 2.66/1.54 ! [X: option_game,Y: option_game] :
% 2.66/1.54 ( ( ( uSubst23177304_Loopo @ X )
% 2.66/1.54 = Y )
% 2.66/1.54 => ( ! [Alpha2: game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( some_game @ Alpha2 ) )
% 2.66/1.54 => ( Y
% 2.66/1.54 != ( some_game @ ( loop @ Alpha2 ) ) ) )
% 2.66/1.54 => ~ ( ( X = none_game )
% 2.66/1.54 => ( Y != none_game ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_329_option_Oinject,axiom,
% 2.66/1.54 ! [X22: game,Y22: game] :
% 2.66/1.54 ( ( ( some_game @ X22 )
% 2.66/1.54 = ( some_game @ Y22 ) )
% 2.66/1.54 = ( X22 = Y22 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_330_not__Some__eq,axiom,
% 2.66/1.54 ! [X: option_game] :
% 2.66/1.54 ( ( ! [Y3: game] :
% 2.66/1.54 ( X
% 2.66/1.54 != ( some_game @ Y3 ) ) )
% 2.66/1.54 = ( X = none_game ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_331_not__None__eq,axiom,
% 2.66/1.54 ! [X: option_game] :
% 2.66/1.54 ( ( X != none_game )
% 2.66/1.54 = ( ? [Y3: game] :
% 2.66/1.54 ( X
% 2.66/1.54 = ( some_game @ Y3 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_332_option_Ocollapse,axiom,
% 2.66/1.54 ! [Option: option_game] :
% 2.66/1.54 ( ( Option != none_game )
% 2.66/1.54 => ( ( some_game @ ( the_game @ Option ) )
% 2.66/1.54 = Option ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_333_Composeo_Ocases,axiom,
% 2.66/1.54 ! [X: produc1016592119n_game] :
% 2.66/1.54 ( ! [Alpha2: game,Beta2: game] :
% 2.66/1.54 ( X
% 2.66/1.54 != ( produc1111617711n_game @ ( some_game @ Alpha2 ) @ ( some_game @ Beta2 ) ) )
% 2.66/1.54 => ( ! [Alpha2: option_game] :
% 2.66/1.54 ( X
% 2.66/1.54 != ( produc1111617711n_game @ Alpha2 @ none_game ) )
% 2.66/1.54 => ~ ! [V2: game] :
% 2.66/1.54 ( X
% 2.66/1.54 != ( produc1111617711n_game @ none_game @ ( some_game @ V2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_334_option_Oexhaust__sel,axiom,
% 2.66/1.54 ! [Option: option_game] :
% 2.66/1.54 ( ( Option != none_game )
% 2.66/1.54 => ( Option
% 2.66/1.54 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_335_combine__options__cases,axiom,
% 2.66/1.54 ! [X: option_game,P: option_game > option_game > $o,Y: option_game] :
% 2.66/1.54 ( ( ( X = none_game )
% 2.66/1.54 => ( P @ X @ Y ) )
% 2.66/1.54 => ( ( ( Y = none_game )
% 2.66/1.54 => ( P @ X @ Y ) )
% 2.66/1.54 => ( ! [A7: game,B7: game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( some_game @ A7 ) )
% 2.66/1.54 => ( ( Y
% 2.66/1.54 = ( some_game @ B7 ) )
% 2.66/1.54 => ( P @ X @ Y ) ) )
% 2.66/1.54 => ( P @ X @ Y ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_336_split__option__all,axiom,
% 2.66/1.54 ( ( ^ [P5: option_game > $o] :
% 2.66/1.54 ! [X5: option_game] : ( P5 @ X5 ) )
% 2.66/1.54 = ( ^ [P4: option_game > $o] :
% 2.66/1.54 ( ( P4 @ none_game )
% 2.66/1.54 & ! [X2: game] : ( P4 @ ( some_game @ X2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_337_split__option__ex,axiom,
% 2.66/1.54 ( ( ^ [P5: option_game > $o] :
% 2.66/1.54 ? [X5: option_game] : ( P5 @ X5 ) )
% 2.66/1.54 = ( ^ [P4: option_game > $o] :
% 2.66/1.54 ( ( P4 @ none_game )
% 2.66/1.54 | ? [X2: game] : ( P4 @ ( some_game @ X2 ) ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_338_option_Oinducts,axiom,
% 2.66/1.54 ! [P: option_game > $o,Option: option_game] :
% 2.66/1.54 ( ( P @ none_game )
% 2.66/1.54 => ( ! [X3: game] : ( P @ ( some_game @ X3 ) )
% 2.66/1.54 => ( P @ Option ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_339_option_Oexhaust,axiom,
% 2.66/1.54 ! [Y: option_game] :
% 2.66/1.54 ( ( Y != none_game )
% 2.66/1.54 => ~ ! [X23: game] :
% 2.66/1.54 ( Y
% 2.66/1.54 != ( some_game @ X23 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_340_option_OdiscI,axiom,
% 2.66/1.54 ! [Option: option_game,X22: game] :
% 2.66/1.54 ( ( Option
% 2.66/1.54 = ( some_game @ X22 ) )
% 2.66/1.54 => ( Option != none_game ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_341_option_Odistinct_I1_J,axiom,
% 2.66/1.54 ! [X22: game] :
% 2.66/1.54 ( none_game
% 2.66/1.54 != ( some_game @ X22 ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_342_option_Osel,axiom,
% 2.66/1.54 ! [X22: game] :
% 2.66/1.54 ( ( the_game @ ( some_game @ X22 ) )
% 2.66/1.54 = X22 ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_343_Composeo_Oinduct,axiom,
% 2.66/1.54 ! [P: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 2.66/1.54 ( ! [Alpha2: game,Beta2: game] : ( P @ ( some_game @ Alpha2 ) @ ( some_game @ Beta2 ) )
% 2.66/1.54 => ( ! [Alpha2: option_game] : ( P @ Alpha2 @ none_game )
% 2.66/1.54 => ( ! [V2: game] : ( P @ none_game @ ( some_game @ V2 ) )
% 2.66/1.54 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_344_undefg__equiv,axiom,
% 2.66/1.54 ! [Alpha: option_game] :
% 2.66/1.54 ( ( Alpha != none_game )
% 2.66/1.54 = ( ? [G: game] :
% 2.66/1.54 ( Alpha
% 2.66/1.54 = ( some_game @ G ) ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_345_Loopo_Oinduct,axiom,
% 2.66/1.54 ! [P: option_game > $o,A0: option_game] :
% 2.66/1.54 ( ! [Alpha2: game] : ( P @ ( some_game @ Alpha2 ) )
% 2.66/1.54 => ( ( P @ none_game )
% 2.66/1.54 => ( P @ A0 ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_346_Loopo_Ocases,axiom,
% 2.66/1.54 ! [X: option_game] :
% 2.66/1.54 ( ! [Alpha2: game] :
% 2.66/1.54 ( X
% 2.66/1.54 != ( some_game @ Alpha2 ) )
% 2.66/1.54 => ( X = none_game ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_347_Loopo_Osimps_I1_J,axiom,
% 2.66/1.54 ! [Alpha: game] :
% 2.66/1.54 ( ( uSubst23177304_Loopo @ ( some_game @ Alpha ) )
% 2.66/1.54 = ( some_game @ ( loop @ Alpha ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_348_Choiceo_Osimps_I1_J,axiom,
% 2.66/1.54 ! [Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst1484167963hoiceo @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 2.66/1.54 = ( some_game @ ( choice @ Alpha @ Beta ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_349_Composeo_Osimps_I1_J,axiom,
% 2.66/1.54 ! [Alpha: game,Beta: game] :
% 2.66/1.54 ( ( uSubst532817840mposeo @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 2.66/1.54 = ( some_game @ ( compose @ Alpha @ Beta ) ) ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_350_Composeo_Osimps_I3_J,axiom,
% 2.66/1.54 ! [V3: game] :
% 2.66/1.54 ( ( uSubst532817840mposeo @ none_game @ ( some_game @ V3 ) )
% 2.66/1.54 = none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_351_Choiceo_Osimps_I3_J,axiom,
% 2.66/1.54 ! [V3: game] :
% 2.66/1.54 ( ( uSubst1484167963hoiceo @ none_game @ ( some_game @ V3 ) )
% 2.66/1.54 = none_game ) ).
% 2.66/1.54
% 2.66/1.54 thf(fact_352_Composeo_Oelims,axiom,
% 2.66/1.54 ! [X: option_game,Xa: option_game,Y: option_game] :
% 2.66/1.54 ( ( ( uSubst532817840mposeo @ X @ Xa )
% 2.66/1.54 = Y )
% 2.66/1.54 => ( ! [Alpha2: game] :
% 2.66/1.54 ( ( X
% 2.66/1.54 = ( some_game @ Alpha2 ) )
% 2.66/1.54 => ! [Beta2: game] :
% 2.66/1.54 ( ( Xa
% 2.66/1.54 = ( some_game @ Beta2 ) )
% 2.66/1.54 => ( Y
% 2.66/1.54 != ( some_game @ ( compose @ Alpha2 @ Beta2 ) ) ) ) )
% 2.66/1.54 => ( ( ( Xa = none_game )
% 2.66/1.55 => ( Y != none_game ) )
% 2.66/1.55 => ~ ( ( X = none_game )
% 2.66/1.55 => ( ? [V2: game] :
% 2.66/1.55 ( Xa
% 2.66/1.55 = ( some_game @ V2 ) )
% 2.66/1.55 => ( Y != none_game ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_353_Choiceo_Oelims,axiom,
% 2.66/1.55 ! [X: option_game,Xa: option_game,Y: option_game] :
% 2.66/1.55 ( ( ( uSubst1484167963hoiceo @ X @ Xa )
% 2.66/1.55 = Y )
% 2.66/1.55 => ( ! [Alpha2: game] :
% 2.66/1.55 ( ( X
% 2.66/1.55 = ( some_game @ Alpha2 ) )
% 2.66/1.55 => ! [Beta2: game] :
% 2.66/1.55 ( ( Xa
% 2.66/1.55 = ( some_game @ Beta2 ) )
% 2.66/1.55 => ( Y
% 2.66/1.55 != ( some_game @ ( choice @ Alpha2 @ Beta2 ) ) ) ) )
% 2.66/1.55 => ( ( ( Xa = none_game )
% 2.66/1.55 => ( Y != none_game ) )
% 2.66/1.55 => ~ ( ( X = none_game )
% 2.66/1.55 => ( ? [V2: game] :
% 2.66/1.55 ( Xa
% 2.66/1.55 = ( some_game @ V2 ) )
% 2.66/1.55 => ( Y != none_game ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(conj_0,conjecture,
% 2.66/1.55 ord_le282106107riable @ ( sup_sup_set_variable @ ua @ ( static_BVG @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ ( compose @ alpha @ beta ) ) ) ) ) ) @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ( produc893821739n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) @ beta ) ) ).
% 2.66/1.55 ------------------------
% 2.66/1.58 % (20031)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/2Mi)
% 2.66/1.58 % (20030)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_19725 for (2999ds/27Mi)
% 2.66/1.58 % (20032)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_19725 for (2999ds/2Mi)
% 2.66/1.58 % (20031)Instruction limit reached!
% 2.66/1.58 % (20031)------------------------------
% 2.66/1.58 % (20031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.58 % (20031)Termination reason: Unknown
% 2.66/1.58 % (20031)Termination phase: shuffling
% 2.66/1.58
% 2.66/1.58 % (20031)Memory used [KB]: 1407
% 2.66/1.58 % (20031)Time elapsed: 0.003 s
% 2.66/1.58 % (20031)Instructions burned: 4 (million)
% 2.66/1.58 % (20031)------------------------------
% 2.66/1.58 % (20031)------------------------------
% 2.66/1.58 % (20032)Instruction limit reached!
% 2.66/1.58 % (20032)------------------------------
% 2.66/1.58 % (20032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.58 % (20032)Termination reason: Unknown
% 2.66/1.58 % (20032)Termination phase: shuffling
% 2.66/1.58
% 2.66/1.58 % (20032)Memory used [KB]: 1407
% 2.66/1.58 % (20032)Time elapsed: 0.002 s
% 2.66/1.58 % (20032)Instructions burned: 2 (million)
% 2.66/1.58 % (20032)------------------------------
% 2.66/1.58 % (20032)------------------------------
% 2.66/1.58 % (20029)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_19725 for (2999ds/4Mi)
% 2.66/1.58 % (20028)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/183Mi)
% 2.66/1.59 % (20033)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_19725 for (2999ds/275Mi)
% 2.66/1.59 % (20034)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/18Mi)
% 2.66/1.59 % (20030)Instruction limit reached!
% 2.66/1.59 % (20030)------------------------------
% 2.66/1.59 % (20030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (20030)Termination reason: Unknown
% 2.66/1.59 % (20030)Termination phase: Property scanning
% 2.66/1.59
% 2.66/1.59 % (20030)Memory used [KB]: 1791
% 2.66/1.59 % (20030)Time elapsed: 0.010 s
% 2.66/1.59 % (20030)Instructions burned: 27 (million)
% 2.66/1.59 % (20030)------------------------------
% 2.66/1.59 % (20030)------------------------------
% 2.66/1.59 % (20029)Instruction limit reached!
% 2.66/1.59 % (20029)------------------------------
% 2.66/1.59 % (20029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (20029)Termination reason: Unknown
% 2.66/1.59 % (20029)Termination phase: shuffling
% 2.66/1.59
% 2.66/1.59 % (20029)Memory used [KB]: 1407
% 2.66/1.59 % (20029)Time elapsed: 0.005 s
% 2.66/1.59 % (20029)Instructions burned: 5 (million)
% 2.66/1.59 % (20029)------------------------------
% 2.66/1.59 % (20029)------------------------------
% 2.66/1.59 % (20035)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/3Mi)
% 2.66/1.59 % (20037)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_19725 for (2999ds/37Mi)
% 2.66/1.59 % (20035)Instruction limit reached!
% 2.66/1.59 % (20035)------------------------------
% 2.66/1.59 % (20035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (20035)Termination reason: Unknown
% 2.66/1.59 % (20035)Termination phase: shuffling
% 2.66/1.59
% 2.66/1.59 % (20035)Memory used [KB]: 1407
% 2.66/1.59 % (20035)Time elapsed: 0.003 s
% 2.66/1.59 % (20035)Instructions burned: 6 (million)
% 2.66/1.59 % (20035)------------------------------
% 2.66/1.59 % (20035)------------------------------
% 2.66/1.60 % (20038)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_19725 for (2999ds/15Mi)
% 2.70/1.60 % (20034)Instruction limit reached!
% 2.70/1.60 % (20034)------------------------------
% 2.70/1.60 % (20034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (20034)Termination reason: Unknown
% 2.70/1.60 % (20034)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (20034)Memory used [KB]: 1791
% 2.70/1.60 % (20034)Time elapsed: 0.014 s
% 2.70/1.60 % (20034)Instructions burned: 19 (million)
% 2.70/1.60 % (20034)------------------------------
% 2.70/1.60 % (20034)------------------------------
% 2.70/1.60 % (20040)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_19725 for (2999ds/1041Mi)
% 2.70/1.60 % (20037)Instruction limit reached!
% 2.70/1.60 % (20037)------------------------------
% 2.70/1.60 % (20037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (20037)Termination reason: Unknown
% 2.70/1.60 % (20037)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (20037)Memory used [KB]: 2174
% 2.70/1.60 % (20037)Time elapsed: 0.012 s
% 2.70/1.60 % (20037)Instructions burned: 37 (million)
% 2.70/1.60 % (20037)------------------------------
% 2.70/1.60 % (20037)------------------------------
% 2.70/1.60 % (20038)Instruction limit reached!
% 2.70/1.60 % (20038)------------------------------
% 2.70/1.60 % (20038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (20038)Termination reason: Unknown
% 2.70/1.60 % (20038)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (20038)Memory used [KB]: 1791
% 2.70/1.60 % (20038)Time elapsed: 0.007 s
% 2.70/1.60 % (20038)Instructions burned: 17 (million)
% 2.70/1.60 % (20038)------------------------------
% 2.70/1.60 % (20038)------------------------------
% 2.70/1.60 % (20039)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_19725 for (2999ds/3Mi)
% 2.70/1.60 % (20039)Instruction limit reached!
% 2.70/1.60 % (20039)------------------------------
% 2.70/1.60 % (20039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (20039)Termination reason: Unknown
% 2.70/1.60 % (20039)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (20039)Memory used [KB]: 1407
% 2.70/1.60 % (20039)Time elapsed: 0.003 s
% 2.70/1.60 % (20039)Instructions burned: 5 (million)
% 2.70/1.60 % (20039)------------------------------
% 2.70/1.60 % (20039)------------------------------
% 2.70/1.61 % (20042)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/16Mi)
% 2.70/1.61 % (20043)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_19725 for (2999ds/3Mi)
% 2.70/1.61 % (20043)Instruction limit reached!
% 2.70/1.61 % (20043)------------------------------
% 2.70/1.61 % (20043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.61 % (20043)Termination reason: Unknown
% 2.70/1.61 % (20043)Termination phase: shuffling
% 2.70/1.61
% 2.70/1.61 % (20043)Memory used [KB]: 1407
% 2.70/1.61 % (20043)Time elapsed: 0.003 s
% 2.70/1.61 % (20043)Instructions burned: 5 (million)
% 2.70/1.61 % (20043)------------------------------
% 2.70/1.61 % (20043)------------------------------
% 2.70/1.61 % (20044)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_19725 for (2999ds/3Mi)
% 2.70/1.61 % (20044)Instruction limit reached!
% 2.70/1.61 % (20044)------------------------------
% 2.70/1.61 % (20044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.61 % (20044)Termination reason: Unknown
% 2.70/1.61 % (20044)Termination phase: shuffling
% 2.70/1.61
% 2.70/1.61 % (20044)Memory used [KB]: 1407
% 2.70/1.61 % (20044)Time elapsed: 0.003 s
% 2.70/1.61 % (20044)Instructions burned: 3 (million)
% 2.70/1.61 % (20044)------------------------------
% 2.70/1.61 % (20044)------------------------------
% 2.70/1.61 % (20041)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/7Mi)
% 2.70/1.62 % (20042)Instruction limit reached!
% 2.70/1.62 % (20042)------------------------------
% 2.70/1.62 % (20042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (20042)Termination reason: Unknown
% 2.70/1.62 % (20042)Termination phase: shuffling
% 2.70/1.62
% 2.70/1.62 % (20042)Memory used [KB]: 1791
% 2.70/1.62 % (20042)Time elapsed: 0.008 s
% 2.70/1.62 % (20042)Instructions burned: 18 (million)
% 2.70/1.62 % (20042)------------------------------
% 2.70/1.62 % (20042)------------------------------
% 2.70/1.62 % (20041)Instruction limit reached!
% 2.70/1.62 % (20041)------------------------------
% 2.70/1.62 % (20041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (20041)Termination reason: Unknown
% 2.70/1.62 % (20041)Termination phase: shuffling
% 2.70/1.62
% 2.70/1.62 % (20041)Memory used [KB]: 1535
% 2.70/1.62 % (20041)Time elapsed: 0.006 s
% 2.70/1.62 % (20041)Instructions burned: 7 (million)
% 2.70/1.62 % (20041)------------------------------
% 2.70/1.62 % (20041)------------------------------
% 2.70/1.62 % (20045)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/7Mi)
% 2.70/1.62 % (20046)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/3Mi)
% 2.70/1.62 % (20045)Instruction limit reached!
% 2.70/1.62 % (20045)------------------------------
% 2.70/1.62 % (20045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (20045)Termination reason: Unknown
% 2.70/1.62 % (20045)Termination phase: shuffling
% 2.70/1.62
% 2.70/1.62 % (20045)Memory used [KB]: 1535
% 2.70/1.62 % (20045)Time elapsed: 0.004 s
% 2.70/1.62 % (20045)Instructions burned: 9 (million)
% 2.70/1.62 % (20045)------------------------------
% 2.70/1.62 % (20045)------------------------------
% 2.70/1.63 % (20046)Instruction limit reached!
% 2.70/1.63 % (20046)------------------------------
% 2.70/1.63 % (20046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.63 % (20046)Termination reason: Unknown
% 2.70/1.63 % (20046)Termination phase: shuffling
% 2.70/1.63
% 2.70/1.63 % (20046)Memory used [KB]: 1407
% 2.70/1.63 % (20046)Time elapsed: 0.003 s
% 2.70/1.63 % (20046)Instructions burned: 4 (million)
% 2.70/1.63 % (20046)------------------------------
% 2.70/1.63 % (20046)------------------------------
% 2.70/1.63 % (20047)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/4Mi)
% 2.70/1.63 % (20047)Instruction limit reached!
% 2.70/1.63 % (20047)------------------------------
% 2.70/1.63 % (20047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.63 % (20047)Termination reason: Unknown
% 2.70/1.63 % (20047)Termination phase: shuffling
% 2.70/1.63
% 2.70/1.63 % (20047)Memory used [KB]: 1407
% 2.70/1.63 % (20047)Time elapsed: 0.003 s
% 2.70/1.63 % (20047)Instructions burned: 4 (million)
% 2.70/1.63 % (20047)------------------------------
% 2.70/1.63 % (20047)------------------------------
% 2.70/1.63 % (20049)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/710Mi)
% 2.70/1.64 % (20050)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/6Mi)
% 2.70/1.64 % (20048)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/18Mi)
% 2.70/1.64 % (20050)Instruction limit reached!
% 2.70/1.64 % (20050)------------------------------
% 2.70/1.64 % (20050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.64 % (20050)Termination reason: Unknown
% 2.70/1.64 % (20050)Termination phase: shuffling
% 2.70/1.64
% 2.70/1.64 % (20050)Memory used [KB]: 1535
% 2.70/1.64 % (20050)Time elapsed: 0.004 s
% 2.70/1.64 % (20050)Instructions burned: 6 (million)
% 2.70/1.64 % (20050)------------------------------
% 2.70/1.64 % (20050)------------------------------
% 2.70/1.64 % (20051)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_19725 for (2999ds/902Mi)
% 2.70/1.65 % (20048)Instruction limit reached!
% 2.70/1.65 % (20048)------------------------------
% 2.70/1.65 % (20048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.65 % (20048)Termination reason: Unknown
% 2.70/1.65 % (20048)Termination phase: shuffling
% 2.70/1.65
% 2.70/1.65 % (20048)Memory used [KB]: 1791
% 2.70/1.65 % (20048)Time elapsed: 0.013 s
% 2.70/1.65 % (20048)Instructions burned: 18 (million)
% 2.70/1.65 % (20048)------------------------------
% 2.70/1.65 % (20048)------------------------------
% 2.70/1.65 % (20052)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_19725 for (2999ds/21Mi)
% 2.70/1.66 % (20052)Instruction limit reached!
% 2.70/1.66 % (20052)------------------------------
% 2.70/1.66 % (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.66 % (20052)Termination reason: Unknown
% 2.70/1.66 % (20052)Termination phase: shuffling
% 2.70/1.66
% 2.70/1.66 % (20052)Memory used [KB]: 1791
% 2.70/1.66 % (20052)Time elapsed: 0.009 s
% 2.70/1.66 % (20052)Instructions burned: 21 (million)
% 2.70/1.66 % (20052)------------------------------
% 2.70/1.66 % (20052)------------------------------
% 2.70/1.66 % (20053)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19725 for (2999ds/5Mi)
% 2.70/1.66 % (20053)Instruction limit reached!
% 2.70/1.66 % (20053)------------------------------
% 2.70/1.66 % (20053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.66 % (20053)Termination reason: Unknown
% 2.70/1.66 % (20053)Termination phase: shuffling
% 2.70/1.66
% 2.70/1.66 % (20053)Memory used [KB]: 1407
% 2.70/1.66 % (20053)Time elapsed: 0.004 s
% 2.70/1.66 % (20053)Instructions burned: 5 (million)
% 2.70/1.66 % (20053)------------------------------
% 2.70/1.66 % (20053)------------------------------
% 2.70/1.67 % (20054)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_19725 for (2999ds/6Mi)
% 2.70/1.67 % (20054)Instruction limit reached!
% 2.70/1.67 % (20054)------------------------------
% 2.70/1.67 % (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.67 % (20054)Termination reason: Unknown
% 2.70/1.67 % (20054)Termination phase: shuffling
% 2.70/1.67
% 2.70/1.67 % (20054)Memory used [KB]: 1535
% 2.70/1.67 % (20054)Time elapsed: 0.004 s
% 2.70/1.67 % (20054)Instructions burned: 7 (million)
% 2.70/1.67 % (20054)------------------------------
% 2.70/1.67 % (20054)------------------------------
% 2.70/1.68 % (20055)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/377Mi)
% 2.70/1.68 % (20056)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_19725 for (2998ds/779Mi)
% 2.70/1.68 % (20028)Instruction limit reached!
% 2.70/1.68 % (20028)------------------------------
% 2.70/1.68 % (20028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.68 % (20028)Termination reason: Unknown
% 2.70/1.68 % (20028)Termination phase: Saturation
% 2.70/1.68
% 2.70/1.68 % (20028)Memory used [KB]: 7291
% 2.70/1.68 % (20028)Time elapsed: 0.096 s
% 2.70/1.68 % (20028)Instructions burned: 184 (million)
% 2.70/1.68 % (20028)------------------------------
% 2.70/1.68 % (20028)------------------------------
% 2.70/1.69 % (20057)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_19725 for (2998ds/19Mi)
% 2.70/1.69 % (20057)Instruction limit reached!
% 2.70/1.69 % (20057)------------------------------
% 2.70/1.69 % (20057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.69 % (20057)Termination reason: Unknown
% 2.70/1.69 % (20057)Termination phase: shuffling
% 2.70/1.69
% 2.70/1.69 % (20057)Memory used [KB]: 1791
% 2.70/1.70 % (20057)Time elapsed: 0.007 s
% 2.70/1.70 % (20057)Instructions burned: 19 (million)
% 2.70/1.70 % (20057)------------------------------
% 2.70/1.70 % (20057)------------------------------
% 2.70/1.70 % (20033)Instruction limit reached!
% 2.70/1.70 % (20033)------------------------------
% 2.70/1.70 % (20033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.70 % (20033)Termination reason: Unknown
% 2.70/1.70 % (20033)Termination phase: Saturation
% 2.70/1.70
% 2.70/1.70 % (20033)Memory used [KB]: 6908
% 2.70/1.70 % (20033)Time elapsed: 0.119 s
% 2.70/1.70 % (20033)Instructions burned: 276 (million)
% 2.70/1.70 % (20033)------------------------------
% 2.70/1.70 % (20033)------------------------------
% 2.70/1.71 % (20058)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/879Mi)
% 2.70/1.71 % (20059)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/17Mi)
% 2.70/1.72 % (20059)Instruction limit reached!
% 2.70/1.72 % (20059)------------------------------
% 2.70/1.72 % (20059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.72 % (20059)Termination reason: Unknown
% 2.70/1.72 % (20059)Termination phase: shuffling
% 2.70/1.72
% 2.70/1.72 % (20059)Memory used [KB]: 1791
% 2.70/1.72 % (20059)Time elapsed: 0.008 s
% 2.70/1.72 % (20059)Instructions burned: 18 (million)
% 2.70/1.72 % (20059)------------------------------
% 2.70/1.72 % (20059)------------------------------
% 2.70/1.73 % (20060)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/3Mi)
% 2.70/1.73 % (20060)Instruction limit reached!
% 2.70/1.73 % (20060)------------------------------
% 2.70/1.73 % (20060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.73 % (20060)Termination reason: Unknown
% 2.70/1.73 % (20060)Termination phase: shuffling
% 2.70/1.73
% 2.70/1.73 % (20060)Memory used [KB]: 1407
% 2.70/1.73 % (20060)Time elapsed: 0.003 s
% 2.70/1.73 % (20060)Instructions burned: 4 (million)
% 2.70/1.73 % (20060)------------------------------
% 2.70/1.73 % (20060)------------------------------
% 2.70/1.74 % (20061)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/30Mi)
% 2.70/1.75 % (20061)Instruction limit reached!
% 2.70/1.75 % (20061)------------------------------
% 2.70/1.75 % (20061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.75 % (20061)Termination reason: Unknown
% 2.70/1.75 % (20061)Termination phase: Property scanning
% 2.70/1.75
% 2.70/1.75 % (20061)Memory used [KB]: 1918
% 2.70/1.75 % (20061)Time elapsed: 0.012 s
% 2.70/1.75 % (20061)Instructions burned: 30 (million)
% 2.70/1.75 % (20061)------------------------------
% 2.70/1.75 % (20061)------------------------------
% 2.70/1.76 % (20062)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19725 for (2998ds/127Mi)
% 2.70/1.79 % (20055)Instruction limit reached!
% 2.70/1.79 % (20055)------------------------------
% 2.70/1.79 % (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.79 % (20055)Termination reason: Unknown
% 2.70/1.79 % (20055)Termination phase: Saturation
% 2.70/1.79
% 2.70/1.79 % (20055)Memory used [KB]: 8187
% 2.70/1.79 % (20055)Time elapsed: 0.118 s
% 2.70/1.79 % (20055)Instructions burned: 378 (million)
% 2.70/1.79 % (20055)------------------------------
% 2.70/1.79 % (20055)------------------------------
% 2.70/1.80 % (20062)Instruction limit reached!
% 2.70/1.80 % (20062)------------------------------
% 2.70/1.80 % (20062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.80 % (20062)Termination reason: Unknown
% 2.70/1.80 % (20062)Termination phase: Saturation
% 2.70/1.80
% 2.70/1.80 % (20062)Memory used [KB]: 6908
% 2.70/1.80 % (20062)Time elapsed: 0.040 s
% 2.70/1.80 % (20062)Instructions burned: 128 (million)
% 2.70/1.80 % (20062)------------------------------
% 2.70/1.80 % (20062)------------------------------
% 2.70/1.80 % (20063)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19725 for (2997ds/100Mi)
% 2.70/1.81 % (20064)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_19725 for (2997ds/3Mi)
% 2.70/1.81 % (20064)Instruction limit reached!
% 2.70/1.81 % (20064)------------------------------
% 2.70/1.81 % (20064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.81 % (20064)Termination reason: Unknown
% 2.70/1.81 % (20064)Termination phase: shuffling
% 2.70/1.81
% 2.70/1.81 % (20064)Memory used [KB]: 1407
% 2.70/1.81 % (20064)Time elapsed: 0.003 s
% 2.70/1.81 % (20064)Instructions burned: 4 (million)
% 2.70/1.81 % (20064)------------------------------
% 2.70/1.81 % (20064)------------------------------
% 2.70/1.82 % (20065)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_19725 for (2997ds/20Mi)
% 2.70/1.83 % (20065)Instruction limit reached!
% 2.70/1.83 % (20065)------------------------------
% 2.70/1.83 % (20065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.83 % (20065)Termination reason: Unknown
% 2.70/1.83 % (20065)Termination phase: Property scanning
% 2.70/1.83
% 2.70/1.83 % (20065)Memory used [KB]: 1791
% 2.70/1.83 % (20065)Time elapsed: 0.009 s
% 2.70/1.83 % (20065)Instructions burned: 21 (million)
% 2.70/1.83 % (20065)------------------------------
% 2.70/1.83 % (20065)------------------------------
% 2.70/1.83 % (20063)Instruction limit reached!
% 2.70/1.83 % (20063)------------------------------
% 2.70/1.83 % (20063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.83 % (20063)Termination reason: Unknown
% 2.70/1.83 % (20063)Termination phase: Property scanning
% 2.70/1.83
% 2.70/1.83 % (20063)Memory used [KB]: 2302
% 2.70/1.83 % (20063)Time elapsed: 0.030 s
% 2.70/1.83 % (20063)Instructions burned: 102 (million)
% 2.70/1.83 % (20063)------------------------------
% 2.70/1.83 % (20063)------------------------------
% 2.70/1.84 % (20066)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_19725 for (2997ds/86Mi)
% 2.70/1.84 % (20067)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_19725 for (2997ds/107Mi)
% 2.70/1.85 % (20049)Instruction limit reached!
% 2.70/1.85 % (20049)------------------------------
% 2.70/1.85 % (20049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.85 % (20049)Termination reason: Unknown
% 2.70/1.85 % (20049)Termination phase: Saturation
% 2.70/1.85
% 2.70/1.85 % (20049)Memory used [KB]: 7547
% 2.70/1.85 % (20049)Time elapsed: 0.221 s
% 2.70/1.85 % (20049)Instructions burned: 712 (million)
% 2.70/1.85 % (20049)------------------------------
% 2.70/1.85 % (20049)------------------------------
% 2.70/1.86 % (20066)Instruction limit reached!
% 2.70/1.86 % (20066)------------------------------
% 2.70/1.86 % (20066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.86 % (20066)Termination reason: Unknown
% 2.70/1.86 % (20066)Termination phase: Property scanning
% 2.70/1.86
% 2.70/1.86 % (20066)Memory used [KB]: 2174
% 2.70/1.86 % (20066)Time elapsed: 0.027 s
% 2.70/1.86 % (20066)Instructions burned: 87 (million)
% 2.70/1.86 % (20066)------------------------------
% 2.70/1.86 % (20066)------------------------------
% 2.70/1.86 % (20068)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_19725 for (2997ds/39Mi)
% 2.70/1.87 % (20069)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_19725 for (2997ds/448Mi)
% 2.70/1.87 % (20067)Instruction limit reached!
% 2.70/1.87 % (20067)------------------------------
% 2.70/1.87 % (20067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.87 % (20067)Termination reason: Unknown
% 2.70/1.87 % (20067)Termination phase: Saturation
% 2.70/1.87
% 2.70/1.87 % (20067)Memory used [KB]: 6652
% 2.70/1.87 % (20067)Time elapsed: 0.033 s
% 2.70/1.87 % (20067)Instructions burned: 108 (million)
% 2.70/1.87 % (20067)------------------------------
% 2.70/1.87 % (20067)------------------------------
% 2.70/1.87 % (20068)Instruction limit reached!
% 2.70/1.87 % (20068)------------------------------
% 2.70/1.87 % (20068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.87 % (20068)Termination reason: Unknown
% 2.70/1.87 % (20068)Termination phase: shuffling
% 2.70/1.87
% 2.70/1.87 % (20068)Memory used [KB]: 2174
% 2.70/1.87 % (20068)Time elapsed: 0.012 s
% 2.70/1.87 % (20068)Instructions burned: 40 (million)
% 2.70/1.87 % (20068)------------------------------
% 2.70/1.87 % (20068)------------------------------
% 2.70/1.88 % (20070)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/46Mi)
% 2.70/1.88 % (20071)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/98Mi)
% 2.70/1.89 % (20051)Instruction limit reached!
% 2.70/1.89 % (20051)------------------------------
% 2.70/1.89 % (20051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.89 % (20051)Termination reason: Unknown
% 2.70/1.89 % (20051)Termination phase: Saturation
% 2.70/1.89
% 2.70/1.89 % (20051)Memory used [KB]: 8187
% 2.70/1.89 % (20051)Time elapsed: 0.258 s
% 2.70/1.89 % (20051)Instructions burned: 904 (million)
% 2.70/1.89 % (20051)------------------------------
% 2.70/1.89 % (20051)------------------------------
% 2.70/1.90 % (20070)Instruction limit reached!
% 2.70/1.90 % (20070)------------------------------
% 2.70/1.90 % (20070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.90 % (20070)Termination reason: Unknown
% 2.70/1.90 % (20070)Termination phase: Preprocessing 1
% 2.70/1.90
% 2.70/1.90 % (20070)Memory used [KB]: 1791
% 2.70/1.90 % (20070)Time elapsed: 0.015 s
% 2.70/1.90 % (20070)Instructions burned: 46 (million)
% 2.70/1.90 % (20070)------------------------------
% 2.70/1.90 % (20070)------------------------------
% 2.70/1.90 % (20072)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/507Mi)
% 2.70/1.91 % (20073)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/149Mi)
% 2.70/1.91 % (20071)Instruction limit reached!
% 2.70/1.91 % (20071)------------------------------
% 2.70/1.91 % (20071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.91 % (20071)Termination reason: Unknown
% 2.70/1.91 % (20071)Termination phase: Property scanning
% 2.70/1.91
% 2.70/1.91 % (20071)Memory used [KB]: 2302
% 2.70/1.91 % (20071)Time elapsed: 0.026 s
% 2.70/1.91 % (20071)Instructions burned: 99 (million)
% 2.70/1.91 % (20071)------------------------------
% 2.70/1.91 % (20071)------------------------------
% 2.70/1.92 % (20074)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/39Mi)
% 2.70/1.92 % (20040)Instruction limit reached!
% 2.70/1.92 % (20040)------------------------------
% 2.70/1.92 % (20040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.92 % (20040)Termination reason: Unknown
% 2.70/1.92 % (20040)Termination phase: Saturation
% 2.70/1.92
% 2.70/1.92 % (20040)Memory used [KB]: 9722
% 2.70/1.92 % (20040)Time elapsed: 0.321 s
% 2.70/1.92 % (20040)Instructions burned: 1041 (million)
% 2.70/1.92 % (20040)------------------------------
% 2.70/1.92 % (20040)------------------------------
% 2.70/1.92 % (20056)Instruction limit reached!
% 2.70/1.92 % (20056)------------------------------
% 2.70/1.92 % (20056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.92 % (20056)Termination reason: Unknown
% 2.70/1.92 % (20056)Termination phase: Saturation
% 2.70/1.92
% 2.70/1.92 % (20056)Memory used [KB]: 9466
% 2.70/1.92 % (20056)Time elapsed: 0.246 s
% 2.70/1.92 % (20056)Instructions burned: 780 (million)
% 2.70/1.92 % (20056)------------------------------
% 2.70/1.92 % (20056)------------------------------
% 2.70/1.93 % (20075)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/6Mi)
% 2.70/1.93 % (20074)Instruction limit reached!
% 2.70/1.93 % (20074)------------------------------
% 2.70/1.93 % (20074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.93 % (20074)Termination reason: Unknown
% 2.70/1.93 % (20074)Termination phase: Naming
% 2.70/1.93
% 2.70/1.93 % (20074)Memory used [KB]: 1918
% 2.70/1.93 % (20074)Time elapsed: 0.013 s
% 2.70/1.93 % (20074)Instructions burned: 40 (million)
% 2.70/1.93 % (20074)------------------------------
% 2.70/1.93 % (20074)------------------------------
% 2.70/1.93 % (20075)Instruction limit reached!
% 2.70/1.93 % (20075)------------------------------
% 2.70/1.93 % (20075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.93 % (20075)Termination reason: Unknown
% 2.70/1.93 % (20075)Termination phase: shuffling
% 2.70/1.93
% 2.70/1.93 % (20075)Memory used [KB]: 1535
% 2.70/1.93 % (20075)Time elapsed: 0.003 s
% 2.70/1.93 % (20075)Instructions burned: 7 (million)
% 2.70/1.93 % (20075)------------------------------
% 2.70/1.93 % (20075)------------------------------
% 2.70/1.93 % (20076)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/1087Mi)
% 2.70/1.94 % (20077)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/47Mi)
% 2.70/1.94 % (20078)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_19725 for (2996ds/44Mi)
% 2.70/1.95 % (20073)Instruction limit reached!
% 2.70/1.95 % (20073)------------------------------
% 2.70/1.95 % (20073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (20073)Termination reason: Unknown
% 2.70/1.95 % (20073)Termination phase: Saturation
% 2.70/1.95
% 2.70/1.95 % (20073)Memory used [KB]: 7164
% 2.70/1.95 % (20073)Time elapsed: 0.046 s
% 2.70/1.95 % (20073)Instructions burned: 152 (million)
% 2.70/1.95 % (20073)------------------------------
% 2.70/1.95 % (20073)------------------------------
% 2.70/1.95 % (20078)Instruction limit reached!
% 2.70/1.95 % (20078)------------------------------
% 2.70/1.95 % (20078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (20078)Termination reason: Unknown
% 2.70/1.95 % (20078)Termination phase: shuffling
% 2.70/1.95
% 2.70/1.95 % (20078)Memory used [KB]: 2302
% 2.70/1.95 % (20078)Time elapsed: 0.013 s
% 2.70/1.95 % (20078)Instructions burned: 44 (million)
% 2.70/1.95 % (20078)------------------------------
% 2.70/1.95 % (20078)------------------------------
% 2.70/1.95 % (20077)Instruction limit reached!
% 2.70/1.95 % (20077)------------------------------
% 2.70/1.95 % (20077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (20077)Termination reason: Unknown
% 2.70/1.95 % (20077)Termination phase: Property scanning
% 2.70/1.95
% 2.70/1.95 % (20077)Memory used [KB]: 2174
% 2.70/1.95 % (20077)Time elapsed: 0.015 s
% 2.70/1.95 % (20077)Instructions burned: 47 (million)
% 2.70/1.95 % (20077)------------------------------
% 2.70/1.95 % (20077)------------------------------
% 2.70/1.96 % (20080)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/62Mi)
% 2.70/1.96 % (20079)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/432Mi)
% 2.70/1.96 % (20081)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/31Mi)
% 2.70/1.97 % (20081)Instruction limit reached!
% 2.70/1.97 % (20081)------------------------------
% 2.70/1.97 % (20081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.97 % (20081)Termination reason: Unknown
% 2.70/1.97 % (20081)Termination phase: Property scanning
% 2.70/1.97
% 2.70/1.97 % (20081)Memory used [KB]: 1791
% 2.70/1.97 % (20081)Time elapsed: 0.010 s
% 2.70/1.97 % (20081)Instructions burned: 31 (million)
% 2.70/1.97 % (20081)------------------------------
% 2.70/1.97 % (20081)------------------------------
% 2.70/1.98 % (20080)Instruction limit reached!
% 2.70/1.98 % (20080)------------------------------
% 2.70/1.98 % (20080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.98 % (20080)Termination reason: Unknown
% 2.70/1.98 % (20080)Termination phase: Property scanning
% 2.70/1.98
% 2.70/1.98 % (20080)Memory used [KB]: 2302
% 2.70/1.98 % (20080)Time elapsed: 0.018 s
% 2.70/1.98 % (20080)Instructions burned: 65 (million)
% 2.70/1.98 % (20080)------------------------------
% 2.70/1.98 % (20080)------------------------------
% 2.70/1.98 % (20082)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/96Mi)
% 2.70/1.99 % (20083)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/453Mi)
% 2.70/2.00 % (20058)Refutation not found, non-redundant clauses discarded% (20058)------------------------------
% 2.70/2.00 % (20058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (20058)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.70/2.00
% 2.70/2.00 % (20058)Memory used [KB]: 7675
% 2.70/2.00 % (20058)Time elapsed: 0.292 s
% 2.70/2.00 % (20058)Instructions burned: 858 (million)
% 2.70/2.00 % (20058)------------------------------
% 2.70/2.00 % (20058)------------------------------
% 2.70/2.00 % (20069)Instruction limit reached!
% 2.70/2.00 % (20069)------------------------------
% 2.70/2.00 % (20069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (20069)Termination reason: Unknown
% 2.70/2.00 % (20069)Termination phase: Saturation
% 2.70/2.00
% 2.70/2.00 % (20069)Memory used [KB]: 8699
% 2.70/2.00 % (20069)Time elapsed: 0.134 s
% 2.70/2.00 % (20069)Instructions burned: 450 (million)
% 2.70/2.00 % (20069)------------------------------
% 2.70/2.00 % (20069)------------------------------
% 2.70/2.01 % (20082)Instruction limit reached!
% 2.70/2.01 % (20082)------------------------------
% 2.70/2.01 % (20082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.01 % (20082)Termination reason: Unknown
% 2.70/2.01 % (20082)Termination phase: Property scanning
% 2.70/2.01
% 2.70/2.01 % (20082)Memory used [KB]: 2174
% 2.70/2.01 % (20082)Time elapsed: 0.027 s
% 2.70/2.01 % (20082)Instructions burned: 96 (million)
% 2.70/2.01 % (20082)------------------------------
% 2.70/2.01 % (20082)------------------------------
% 5.77/2.01 % (20084)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/71Mi)
% 5.77/2.02 % (20085)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/83Mi)
% 5.77/2.02 % (20086)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/11Mi)
% 5.77/2.02 % (20086)Instruction limit reached!
% 5.77/2.02 % (20086)------------------------------
% 5.77/2.02 % (20086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.02 % (20086)Termination reason: Unknown
% 5.77/2.02 % (20086)Termination phase: shuffling
% 5.77/2.02
% 5.77/2.02 % (20086)Memory used [KB]: 1663
% 5.77/2.02 % (20086)Time elapsed: 0.004 s
% 5.77/2.02 % (20086)Instructions burned: 11 (million)
% 5.77/2.02 % (20086)------------------------------
% 5.77/2.02 % (20086)------------------------------
% 5.77/2.03 % (20087)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/41Mi)
% 5.77/2.04 % (20085)Instruction limit reached!
% 5.77/2.04 % (20085)------------------------------
% 5.77/2.04 % (20085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.04 % (20085)Termination reason: Unknown
% 5.77/2.04 % (20085)Termination phase: Saturation
% 5.77/2.04
% 5.77/2.04 % (20085)Memory used [KB]: 6524
% 5.77/2.04 % (20085)Time elapsed: 0.027 s
% 5.77/2.04 % (20085)Instructions burned: 83 (million)
% 5.77/2.04 % (20085)------------------------------
% 5.77/2.04 % (20085)------------------------------
% 5.77/2.04 % (20087)Instruction limit reached!
% 5.77/2.04 % (20087)------------------------------
% 5.77/2.04 % (20087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.04 % (20087)Termination reason: Unknown
% 5.77/2.04 % (20087)Termination phase: shuffling
% 5.77/2.04
% 5.77/2.04 % (20087)Memory used [KB]: 2174
% 5.77/2.04 % (20087)Time elapsed: 0.013 s
% 5.77/2.04 % (20087)Instructions burned: 42 (million)
% 5.77/2.04 % (20087)------------------------------
% 5.77/2.04 % (20087)------------------------------
% 5.77/2.05 % (20072)Instruction limit reached!
% 5.77/2.05 % (20072)------------------------------
% 5.77/2.05 % (20072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.05 % (20072)Termination reason: Unknown
% 5.77/2.05 % (20072)Termination phase: Saturation
% 5.77/2.05
% 5.77/2.05 % (20072)Memory used [KB]: 8059
% 5.77/2.05 % (20072)Time elapsed: 0.166 s
% 5.77/2.05 % (20072)Instructions burned: 508 (million)
% 5.77/2.05 % (20072)------------------------------
% 5.77/2.05 % (20072)------------------------------
% 5.77/2.05 % (20089)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/150Mi)
% 5.77/2.05 % (20088)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/6Mi)
% 5.77/2.05 % (20084)Instruction limit reached!
% 5.77/2.05 % (20084)------------------------------
% 5.77/2.05 % (20084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.05 % (20084)Termination reason: Unknown
% 5.77/2.05 % (20084)Termination phase: Function definition elimination
% 5.77/2.05
% 5.77/2.05 % (20084)Memory used [KB]: 2174
% 5.77/2.05 % (20084)Time elapsed: 0.041 s
% 5.77/2.05 % (20084)Instructions burned: 71 (million)
% 5.77/2.05 % (20084)------------------------------
% 5.77/2.05 % (20084)------------------------------
% 5.77/2.05 % (20088)Instruction limit reached!
% 5.77/2.05 % (20088)------------------------------
% 5.77/2.05 % (20088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.05 % (20088)Termination reason: Unknown
% 5.77/2.05 % (20088)Termination phase: shuffling
% 5.77/2.05
% 5.77/2.05 % (20088)Memory used [KB]: 1535
% 5.77/2.05 % (20088)Time elapsed: 0.004 s
% 5.77/2.05 % (20088)Instructions burned: 6 (million)
% 5.77/2.05 % (20088)------------------------------
% 5.77/2.05 % (20088)------------------------------
% 5.77/2.06 % (20090)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19725 for (2995ds/343Mi)
% 5.77/2.06 % (20091)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/109Mi)
% 5.77/2.07 % (20092)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/253Mi)
% 5.77/2.09 % (20079)Instruction limit reached!
% 5.77/2.09 % (20079)------------------------------
% 5.77/2.09 % (20079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.09 % (20079)Termination reason: Unknown
% 5.77/2.09 % (20079)Termination phase: Saturation
% 5.77/2.09
% 5.77/2.09 % (20079)Memory used [KB]: 3582
% 5.77/2.09 % (20079)Time elapsed: 0.130 s
% 5.77/2.09 % (20079)Instructions burned: 433 (million)
% 5.77/2.09 % (20079)------------------------------
% 5.77/2.09 % (20079)------------------------------
% 5.77/2.09 % (20089)Instruction limit reached!
% 5.77/2.09 % (20089)------------------------------
% 5.77/2.09 % (20089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.09 % (20089)Termination reason: Unknown
% 5.77/2.09 % (20089)Termination phase: Saturation
% 5.77/2.09
% 5.77/2.09 % (20089)Memory used [KB]: 7036
% 5.77/2.09 % (20089)Time elapsed: 0.042 s
% 5.77/2.09 % (20089)Instructions burned: 151 (million)
% 5.77/2.09 % (20089)------------------------------
% 5.77/2.09 % (20089)------------------------------
% 5.77/2.09 % (20091)Instruction limit reached!
% 5.77/2.09 % (20091)------------------------------
% 5.77/2.09 % (20091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.09 % (20091)Termination reason: Unknown
% 5.77/2.09 % (20091)Termination phase: Property scanning
% 5.77/2.09
% 5.77/2.09 % (20091)Memory used [KB]: 2174
% 5.77/2.09 % (20091)Time elapsed: 0.032 s
% 5.77/2.09 % (20091)Instructions burned: 111 (million)
% 5.77/2.09 % (20091)------------------------------
% 5.77/2.09 % (20091)------------------------------
% 5.77/2.10 % (20093)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/140Mi)
% 5.77/2.10 % (20094)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/614Mi)
% 5.77/2.10 % (20095)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/202Mi)
% 5.77/2.11 % (20083)Instruction limit reached!
% 5.77/2.11 % (20083)------------------------------
% 5.77/2.11 % (20083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.11 % (20083)Termination reason: Unknown
% 5.77/2.11 % (20083)Termination phase: Saturation
% 5.77/2.11
% 5.77/2.11 % (20083)Memory used [KB]: 8059
% 5.77/2.11 % (20083)Time elapsed: 0.124 s
% 5.77/2.11 % (20083)Instructions burned: 455 (million)
% 5.77/2.11 % (20083)------------------------------
% 5.77/2.11 % (20083)------------------------------
% 6.34/2.12 % (20096)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/339Mi)
% 6.34/2.14 % (20093)Instruction limit reached!
% 6.34/2.14 % (20093)------------------------------
% 6.34/2.14 % (20093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.14 % (20093)Termination reason: Unknown
% 6.34/2.14 % (20093)Termination phase: Saturation
% 6.34/2.14
% 6.34/2.14 % (20093)Memory used [KB]: 7036
% 6.34/2.14 % (20093)Time elapsed: 0.044 s
% 6.34/2.14 % (20093)Instructions burned: 141 (million)
% 6.34/2.14 % (20093)------------------------------
% 6.34/2.14 % (20093)------------------------------
% 6.34/2.15 % (20090)Instruction limit reached!
% 6.34/2.15 % (20090)------------------------------
% 6.34/2.15 % (20090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.15 % (20090)Termination reason: Unknown
% 6.34/2.15 % (20090)Termination phase: Saturation
% 6.34/2.15
% 6.34/2.15 % (20090)Memory used [KB]: 7931
% 6.34/2.15 % (20090)Time elapsed: 0.099 s
% 6.34/2.15 % (20090)Instructions burned: 343 (million)
% 6.34/2.15 % (20090)------------------------------
% 6.34/2.15 % (20090)------------------------------
% 6.34/2.15 % (20097)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/283Mi)
% 6.34/2.16 % (20095)Instruction limit reached!
% 6.34/2.16 % (20095)------------------------------
% 6.34/2.16 % (20095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.16 % (20095)Termination reason: Unknown
% 6.34/2.16 % (20095)Termination phase: Saturation
% 6.34/2.16
% 6.34/2.16 % (20095)Memory used [KB]: 7036
% 6.34/2.16 % (20095)Time elapsed: 0.061 s
% 6.34/2.16 % (20095)Instructions burned: 204 (million)
% 6.34/2.16 % (20095)------------------------------
% 6.34/2.16 % (20095)------------------------------
% 6.34/2.16 % (20098)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19725 for (2994ds/134Mi)
% 6.34/2.17 % (20099)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/298Mi)
% 6.34/2.18 % (20092)Instruction limit reached!
% 6.34/2.18 % (20092)------------------------------
% 6.34/2.18 % (20092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.18 % (20092)Termination reason: Unknown
% 6.34/2.18 % (20092)Termination phase: Saturation
% 6.34/2.18
% 6.34/2.18 % (20092)Memory used [KB]: 7036
% 6.34/2.18 % (20092)Time elapsed: 0.109 s
% 6.34/2.18 % (20092)Instructions burned: 253 (million)
% 6.34/2.18 % (20092)------------------------------
% 6.34/2.18 % (20092)------------------------------
% 6.34/2.19 % (20100)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/192Mi)
% 6.77/2.20 % (20098)Instruction limit reached!
% 6.77/2.20 % (20098)------------------------------
% 6.77/2.20 % (20098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.20 % (20098)Termination reason: Unknown
% 6.77/2.20 % (20098)Termination phase: Saturation
% 6.77/2.20
% 6.77/2.20 % (20098)Memory used [KB]: 7036
% 6.77/2.20 % (20098)Time elapsed: 0.038 s
% 6.77/2.20 % (20098)Instructions burned: 137 (million)
% 6.77/2.20 % (20098)------------------------------
% 6.77/2.20 % (20098)------------------------------
% 6.77/2.21 % (20101)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/258Mi)
% 6.77/2.22 % (20096)Instruction limit reached!
% 6.77/2.22 % (20096)------------------------------
% 6.77/2.22 % (20096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.22 % (20096)Termination reason: Unknown
% 6.77/2.22 % (20096)Termination phase: Saturation
% 6.77/2.22
% 6.77/2.22 % (20096)Memory used [KB]: 7931
% 6.77/2.22 % (20096)Time elapsed: 0.098 s
% 6.77/2.22 % (20096)Instructions burned: 342 (million)
% 6.77/2.22 % (20096)------------------------------
% 6.77/2.22 % (20096)------------------------------
% 6.77/2.23 % (20102)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/90Mi)
% 6.77/2.23 % (20097)Instruction limit reached!
% 6.77/2.23 % (20097)------------------------------
% 6.77/2.23 % (20097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.23 % (20097)Termination reason: Unknown
% 6.77/2.23 % (20097)Termination phase: Saturation
% 6.77/2.23
% 6.77/2.23 % (20097)Memory used [KB]: 7547
% 6.77/2.23 % (20097)Time elapsed: 0.078 s
% 6.77/2.23 % (20097)Instructions burned: 283 (million)
% 6.77/2.23 % (20097)------------------------------
% 6.77/2.23 % (20097)------------------------------
% 6.77/2.24 % (20103)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/231Mi)
% 6.77/2.25 % (20100)Instruction limit reached!
% 6.77/2.25 % (20100)------------------------------
% 6.77/2.25 % (20100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.25 % (20100)Termination reason: Unknown
% 6.77/2.25 % (20100)Termination phase: Saturation
% 6.77/2.25
% 6.77/2.25 % (20100)Memory used [KB]: 3198
% 6.77/2.25 % (20100)Time elapsed: 0.060 s
% 6.77/2.25 % (20100)Instructions burned: 192 (million)
% 6.77/2.25 % (20100)------------------------------
% 6.77/2.25 % (20100)------------------------------
% 6.77/2.25 % (20099)Instruction limit reached!
% 6.77/2.25 % (20099)------------------------------
% 6.77/2.25 % (20099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.25 % (20099)Termination reason: Unknown
% 6.77/2.25 % (20099)Termination phase: Saturation
% 6.77/2.25
% 6.77/2.25 % (20099)Memory used [KB]: 7675
% 6.77/2.25 % (20099)Time elapsed: 0.080 s
% 6.77/2.25 % (20099)Instructions burned: 299 (million)
% 6.77/2.25 % (20099)------------------------------
% 6.77/2.25 % (20099)------------------------------
% 6.77/2.25 % (20102)Instruction limit reached!
% 6.77/2.25 % (20102)------------------------------
% 6.77/2.25 % (20102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.25 % (20102)Termination reason: Unknown
% 6.77/2.25 % (20102)Termination phase: Property scanning
% 6.77/2.25
% 6.77/2.25 % (20102)Memory used [KB]: 2174
% 6.77/2.25 % (20102)Time elapsed: 0.026 s
% 6.77/2.25 % (20102)Instructions burned: 91 (million)
% 6.77/2.25 % (20102)------------------------------
% 6.77/2.25 % (20102)------------------------------
% 6.77/2.26 % (20104)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/458Mi)
% 6.77/2.26 % (20105)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/31Mi)
% 6.77/2.26 % (20106)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_19725 for (2993ds/297Mi)
% 6.77/2.27 % (20105)Instruction limit reached!
% 6.77/2.27 % (20105)------------------------------
% 6.77/2.27 % (20105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.27 % (20105)Termination reason: Unknown
% 6.77/2.27 % (20105)Termination phase: Property scanning
% 6.77/2.27
% 6.77/2.27 % (20105)Memory used [KB]: 1791
% 6.77/2.27 % (20105)Time elapsed: 0.010 s
% 6.77/2.27 % (20105)Instructions burned: 31 (million)
% 6.77/2.27 % (20105)------------------------------
% 6.77/2.27 % (20105)------------------------------
% 6.77/2.28 % (20076)Instruction limit reached!
% 6.77/2.28 % (20076)------------------------------
% 6.77/2.28 % (20076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.28 % (20076)Termination reason: Unknown
% 6.77/2.28 % (20076)Termination phase: Saturation
% 6.77/2.28
% 6.77/2.28 % (20076)Memory used [KB]: 7931
% 6.77/2.28 % (20076)Time elapsed: 0.345 s
% 6.77/2.28 % (20076)Instructions burned: 1087 (million)
% 6.77/2.28 % (20076)------------------------------
% 6.77/2.28 % (20076)------------------------------
% 6.77/2.28 % (20107)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/987Mi)
% 6.77/2.28 % (20094)Instruction limit reached!
% 6.77/2.28 % (20094)------------------------------
% 6.77/2.28 % (20094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.28 % (20094)Termination reason: Unknown
% 6.77/2.28 % (20094)Termination phase: Saturation
% 6.77/2.28
% 6.77/2.28 % (20094)Memory used [KB]: 9083
% 6.77/2.28 % (20094)Time elapsed: 0.184 s
% 6.77/2.28 % (20094)Instructions burned: 616 (million)
% 6.77/2.28 % (20094)------------------------------
% 6.77/2.28 % (20094)------------------------------
% 6.77/2.29 % (20101)Instruction limit reached!
% 6.77/2.29 % (20101)------------------------------
% 6.77/2.29 % (20101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.29 % (20101)Termination reason: Unknown
% 6.77/2.29 % (20101)Termination phase: Saturation
% 6.77/2.29
% 6.77/2.29 % (20101)Memory used [KB]: 7291
% 6.77/2.29 % (20101)Time elapsed: 0.077 s
% 6.77/2.29 % (20101)Instructions burned: 260 (million)
% 6.77/2.29 % (20101)------------------------------
% 6.77/2.29 % (20101)------------------------------
% 6.77/2.29 % (20108)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/182Mi)
% 6.77/2.29 % (20109)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/182Mi)
% 6.77/2.30 % (20110)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/154Mi)
% 7.59/2.30 % (20103)Instruction limit reached!
% 7.59/2.30 % (20103)------------------------------
% 7.59/2.30 % (20103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.30 % (20103)Termination reason: Unknown
% 7.59/2.30 % (20103)Termination phase: Saturation
% 7.59/2.30
% 7.59/2.30 % (20103)Memory used [KB]: 7419
% 7.59/2.30 % (20103)Time elapsed: 0.060 s
% 7.59/2.30 % (20103)Instructions burned: 234 (million)
% 7.59/2.30 % (20103)------------------------------
% 7.59/2.30 % (20103)------------------------------
% 7.59/2.31 % (20111)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/79Mi)
% 7.59/2.33 % (20111)Instruction limit reached!
% 7.59/2.33 % (20111)------------------------------
% 7.59/2.33 % (20111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.33 % (20111)Termination reason: Unknown
% 7.59/2.33 % (20111)Termination phase: Property scanning
% 7.59/2.33
% 7.59/2.33 % (20111)Memory used [KB]: 2174
% 7.59/2.33 % (20111)Time elapsed: 0.024 s
% 7.59/2.33 % (20111)Instructions burned: 79 (million)
% 7.59/2.33 % (20111)------------------------------
% 7.59/2.33 % (20111)------------------------------
% 7.59/2.33 % (20110)Instruction limit reached!
% 7.59/2.33 % (20110)------------------------------
% 7.59/2.33 % (20110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.33 % (20110)Termination reason: Unknown
% 7.59/2.33 % (20110)Termination phase: Property scanning
% 7.59/2.33
% 7.59/2.34 % (20110)Memory used [KB]: 2686
% 7.59/2.34 % (20110)Time elapsed: 0.041 s
% 7.59/2.34 % (20110)Instructions burned: 154 (million)
% 7.59/2.34 % (20110)------------------------------
% 7.59/2.34 % (20110)------------------------------
% 7.59/2.34 % (20108)Instruction limit reached!
% 7.59/2.34 % (20108)------------------------------
% 7.59/2.34 % (20108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.34 % (20108)Termination reason: Unknown
% 7.59/2.34 % (20108)Termination phase: Saturation
% 7.59/2.34
% 7.59/2.34 % (20108)Memory used [KB]: 7164
% 7.59/2.34 % (20108)Time elapsed: 0.052 s
% 7.59/2.34 % (20108)Instructions burned: 185 (million)
% 7.59/2.34 % (20108)------------------------------
% 7.59/2.34 % (20108)------------------------------
% 7.59/2.34 % (20112)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/216Mi)
% 7.59/2.34 % (20113)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/114Mi)
% 7.59/2.35 % (20114)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/922Mi)
% 7.59/2.35 % (20106)Instruction limit reached!
% 7.59/2.35 % (20106)------------------------------
% 7.59/2.35 % (20106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (20106)Termination reason: Unknown
% 7.59/2.35 % (20106)Termination phase: Saturation
% 7.59/2.35
% 7.59/2.35 % (20106)Memory used [KB]: 7675
% 7.59/2.35 % (20106)Time elapsed: 0.087 s
% 7.59/2.35 % (20106)Instructions burned: 300 (million)
% 7.59/2.35 % (20106)------------------------------
% 7.59/2.35 % (20106)------------------------------
% 7.59/2.35 % (20109)Instruction limit reached!
% 7.59/2.35 % (20109)------------------------------
% 7.59/2.35 % (20109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (20109)Termination reason: Unknown
% 7.59/2.35 % (20109)Termination phase: Saturation
% 7.59/2.35
% 7.59/2.35 % (20109)Memory used [KB]: 7036
% 7.59/2.35 % (20109)Time elapsed: 0.057 s
% 7.59/2.35 % (20109)Instructions burned: 184 (million)
% 7.59/2.35 % (20109)------------------------------
% 7.59/2.35 % (20109)------------------------------
% 7.59/2.36 % (20115)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/182Mi)
% 7.59/2.36 % (20116)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_19725 for (2992ds/164Mi)
% 7.59/2.38 % (20113)Instruction limit reached!
% 7.59/2.38 % (20113)------------------------------
% 7.59/2.38 % (20113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.38 % (20113)Termination reason: Unknown
% 7.59/2.38 % (20113)Termination phase: Saturation
% 7.59/2.38
% 7.59/2.38 % (20113)Memory used [KB]: 6908
% 7.59/2.38 % (20113)Time elapsed: 0.032 s
% 7.59/2.38 % (20113)Instructions burned: 116 (million)
% 7.59/2.38 % (20113)------------------------------
% 7.59/2.38 % (20113)------------------------------
% 7.59/2.38 % (20117)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/50Mi)
% 7.59/2.40 % (20112)Instruction limit reached!
% 7.59/2.40 % (20112)------------------------------
% 7.59/2.40 % (20112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.40 % (20112)Termination reason: Unknown
% 7.59/2.40 % (20112)Termination phase: Saturation
% 7.59/2.40
% 7.59/2.40 % (20112)Memory used [KB]: 7291
% 7.59/2.40 % (20112)Time elapsed: 0.056 s
% 7.59/2.40 % (20112)Instructions burned: 217 (million)
% 7.59/2.40 % (20112)------------------------------
% 7.59/2.40 % (20112)------------------------------
% 8.07/2.40 % (20117)Instruction limit reached!
% 8.07/2.40 % (20117)------------------------------
% 8.07/2.40 % (20117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.40 % (20117)Termination reason: Unknown
% 8.07/2.40 % (20117)Termination phase: Property scanning
% 8.07/2.40
% 8.07/2.40 % (20117)Memory used [KB]: 2302
% 8.07/2.40 % (20117)Time elapsed: 0.015 s
% 8.07/2.40 % (20117)Instructions burned: 53 (million)
% 8.07/2.40 % (20117)------------------------------
% 8.07/2.40 % (20117)------------------------------
% 8.07/2.40 % (20104)Instruction limit reached!
% 8.07/2.40 % (20104)------------------------------
% 8.07/2.40 % (20104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.40 % (20104)Termination reason: Unknown
% 8.07/2.40 % (20104)Termination phase: Saturation
% 8.07/2.40
% 8.07/2.40 % (20104)Memory used [KB]: 8443
% 8.07/2.40 % (20104)Time elapsed: 0.145 s
% 8.07/2.40 % (20104)Instructions burned: 458 (million)
% 8.07/2.40 % (20104)------------------------------
% 8.07/2.40 % (20104)------------------------------
% 8.07/2.40 % (20116)Instruction limit reached!
% 8.07/2.40 % (20116)------------------------------
% 8.07/2.40 % (20116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.40 % (20116)Termination reason: Unknown
% 8.07/2.40 % (20116)Termination phase: Saturation
% 8.07/2.40
% 8.07/2.40 % (20116)Memory used [KB]: 2814
% 8.07/2.40 % (20116)Time elapsed: 0.045 s
% 8.07/2.40 % (20116)Instructions burned: 164 (million)
% 8.07/2.40 % (20116)------------------------------
% 8.07/2.40 % (20116)------------------------------
% 8.07/2.40 % (20115)Instruction limit reached!
% 8.07/2.40 % (20115)------------------------------
% 8.07/2.40 % (20115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.40 % (20115)Termination reason: Unknown
% 8.07/2.40 % (20115)Termination phase: Property scanning
% 8.07/2.40
% 8.07/2.40 % (20115)Memory used [KB]: 2686
% 8.07/2.40 % (20115)Time elapsed: 0.047 s
% 8.07/2.40 % (20115)Instructions burned: 184 (million)
% 8.07/2.40 % (20115)------------------------------
% 8.07/2.40 % (20115)------------------------------
% 8.07/2.41 % (20118)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/368Mi)
% 8.07/2.41 % (20119)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/1021Mi)
% 8.07/2.41 % (20120)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/267Mi)
% 8.07/2.41 % (20122)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/26Mi)
% 8.07/2.42 % (20122)Instruction limit reached!
% 8.07/2.42 % (20122)------------------------------
% 8.07/2.42 % (20122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.42 % (20122)Termination reason: Unknown
% 8.07/2.42 % (20122)Termination phase: shuffling
% 8.07/2.42
% 8.07/2.42 % (20122)Memory used [KB]: 1918
% 8.07/2.42 % (20122)Time elapsed: 0.008 s
% 8.07/2.42 % (20122)Instructions burned: 26 (million)
% 8.07/2.42 % (20122)------------------------------
% 8.07/2.42 % (20122)------------------------------
% 8.07/2.42 % (20121)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/204Mi)
% 8.07/2.43 % (20123)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/53Mi)
% 8.07/2.44 % (20123)Instruction limit reached!
% 8.07/2.44 % (20123)------------------------------
% 8.07/2.44 % (20123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.44 % (20123)Termination reason: Unknown
% 8.07/2.44 % (20123)Termination phase: Property scanning
% 8.07/2.44
% 8.07/2.44 % (20123)Memory used [KB]: 2302
% 8.07/2.44 % (20123)Time elapsed: 0.016 s
% 8.07/2.44 % (20123)Instructions burned: 53 (million)
% 8.07/2.44 % (20123)------------------------------
% 8.07/2.44 % (20123)------------------------------
% 8.07/2.45 % (20124)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_19725 for (2991ds/4436Mi)
% 8.07/2.49 % (20120)Instruction limit reached!
% 8.07/2.49 % (20120)------------------------------
% 8.07/2.49 % (20120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.49 % (20120)Termination reason: Unknown
% 8.07/2.49 % (20120)Termination phase: Saturation
% 8.07/2.49
% 8.07/2.49 % (20120)Memory used [KB]: 7547
% 8.07/2.49 % (20120)Time elapsed: 0.104 s
% 8.07/2.49 % (20120)Instructions burned: 267 (million)
% 8.07/2.49 % (20120)------------------------------
% 8.07/2.49 % (20120)------------------------------
% 8.49/2.50 % (20125)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_19725 for (2990ds/1539Mi)
% 8.49/2.51 % (20121)Instruction limit reached!
% 8.49/2.51 % (20121)------------------------------
% 8.49/2.51 % (20121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.51 % (20121)Termination reason: Unknown
% 8.49/2.51 % (20121)Termination phase: Saturation
% 8.49/2.51
% 8.49/2.51 % (20121)Memory used [KB]: 7291
% 8.49/2.51 % (20121)Time elapsed: 0.095 s
% 8.49/2.51 % (20121)Instructions burned: 204 (million)
% 8.49/2.51 % (20121)------------------------------
% 8.49/2.51 % (20121)------------------------------
% 8.49/2.52 % (20118)Instruction limit reached!
% 8.49/2.52 % (20118)------------------------------
% 8.49/2.52 % (20118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.52 % (20118)Termination reason: Unknown
% 8.49/2.52 % (20118)Termination phase: Saturation
% 8.49/2.52
% 8.49/2.52 % (20118)Memory used [KB]: 7803
% 8.49/2.52 % (20118)Time elapsed: 0.135 s
% 8.49/2.52 % (20118)Instructions burned: 368 (million)
% 8.49/2.52 % (20118)------------------------------
% 8.49/2.52 % (20118)------------------------------
% 8.49/2.52 % (20126)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_19725 for (2990ds/408Mi)
% 8.49/2.52 % (20127)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_19725 for (2990ds/5205Mi)
% 8.49/2.58 % (20107)Instruction limit reached!
% 8.49/2.58 % (20107)------------------------------
% 8.49/2.58 % (20107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.58 % (20107)Termination reason: Unknown
% 8.49/2.58 % (20107)Termination phase: Saturation
% 8.49/2.58
% 8.49/2.58 % (20107)Memory used [KB]: 9722
% 8.49/2.58 % (20107)Time elapsed: 0.299 s
% 8.49/2.58 % (20107)Instructions burned: 989 (million)
% 8.49/2.58 % (20107)------------------------------
% 8.49/2.58 % (20107)------------------------------
% 8.49/2.59 % (20128)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_19725 for (2989ds/1913Mi)
% 9.03/2.63 % (20114)Instruction limit reached!
% 9.03/2.63 % (20114)------------------------------
% 9.03/2.63 % (20114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.63 % (20114)Termination reason: Unknown
% 9.03/2.63 % (20114)Termination phase: Saturation
% 9.03/2.63
% 9.03/2.63 % (20114)Memory used [KB]: 7803
% 9.03/2.63 % (20114)Time elapsed: 0.310 s
% 9.03/2.63 % (20114)Instructions burned: 924 (million)
% 9.03/2.63 % (20114)------------------------------
% 9.03/2.63 % (20114)------------------------------
% 9.03/2.64 % (20129)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_19725 for (2989ds/4350Mi)
% 9.03/2.65 % (20126)Instruction limit reached!
% 9.03/2.65 % (20126)------------------------------
% 9.03/2.65 % (20126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.65 % (20126)Termination reason: Unknown
% 9.03/2.65 % (20126)Termination phase: Saturation
% 9.03/2.65
% 9.03/2.65 % (20126)Memory used [KB]: 7931
% 9.03/2.65 % (20126)Time elapsed: 0.131 s
% 9.03/2.65 % (20126)Instructions burned: 408 (million)
% 9.03/2.65 % (20126)------------------------------
% 9.03/2.65 % (20126)------------------------------
% 9.03/2.66 % (20130)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_19725 for (2988ds/68Mi)
% 9.03/2.68 % (20130)Instruction limit reached!
% 9.03/2.68 % (20130)------------------------------
% 9.03/2.68 % (20130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.68 % (20130)Termination reason: Unknown
% 9.03/2.68 % (20130)Termination phase: Property scanning
% 9.03/2.68
% 9.03/2.68 % (20130)Memory used [KB]: 2046
% 9.03/2.68 % (20130)Time elapsed: 0.021 s
% 9.03/2.68 % (20130)Instructions burned: 71 (million)
% 9.03/2.68 % (20130)------------------------------
% 9.03/2.68 % (20130)------------------------------
% 9.03/2.69 % (20131)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_19725 for (2988ds/358Mi)
% 9.50/2.70 % (20119)Instruction limit reached!
% 9.50/2.70 % (20119)------------------------------
% 9.50/2.70 % (20119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.70 % (20119)Termination reason: Unknown
% 9.50/2.70 % (20119)Termination phase: Saturation
% 9.50/2.70
% 9.50/2.70 % (20119)Memory used [KB]: 8187
% 9.50/2.70 % (20119)Time elapsed: 0.315 s
% 9.50/2.70 % (20119)Instructions burned: 1023 (million)
% 9.50/2.70 % (20119)------------------------------
% 9.50/2.70 % (20119)------------------------------
% 9.50/2.71 % (20132)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19725 for (2988ds/31Mi)
% 9.50/2.72 % (20132)Instruction limit reached!
% 9.50/2.72 % (20132)------------------------------
% 9.50/2.72 % (20132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.72 % (20132)Termination reason: Unknown
% 9.50/2.72 % (20132)Termination phase: Property scanning
% 9.50/2.72
% 9.50/2.72 % (20132)Memory used [KB]: 1791
% 9.50/2.72 % (20132)Time elapsed: 0.010 s
% 9.50/2.72 % (20132)Instructions burned: 31 (million)
% 9.50/2.72 % (20132)------------------------------
% 9.50/2.72 % (20132)------------------------------
% 9.50/2.73 % (20133)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19725 for (2988ds/279Mi)
% 9.50/2.77 % (20133)Refutation not found, incomplete strategy
% 9.50/2.77 % (20133)------------------------------
% 9.50/2.77 % (20133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.77 % (20133)Termination reason: Refutation not found, incomplete strategy
% 9.50/2.77
% 9.50/2.77
% 9.50/2.77 % (20133)Memory used [KB]: 7164
% 9.50/2.77 % (20133)Time elapsed: 0.040 s
% 9.50/2.77 % (20133)Instructions burned: 139 (million)
% 9.50/2.77 % (20133)------------------------------
% 9.50/2.77 % (20133)------------------------------
% 9.50/2.78 % (20134)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19725 for (2987ds/258Mi)
% 9.87/2.80 % (20131)Instruction limit reached!
% 9.87/2.80 % (20131)------------------------------
% 9.87/2.80 % (20131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.80 % (20131)Termination reason: Unknown
% 9.87/2.80 % (20131)Termination phase: Saturation
% 9.87/2.80
% 9.87/2.80 % (20131)Memory used [KB]: 7803
% 9.87/2.80 % (20131)Time elapsed: 0.110 s
% 9.87/2.80 % (20131)Instructions burned: 360 (million)
% 9.87/2.80 % (20131)------------------------------
% 9.87/2.80 % (20131)------------------------------
% 9.87/2.81 % (20135)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19725 for (2987ds/26Mi)
% 9.87/2.82 % (20135)Instruction limit reached!
% 9.87/2.82 % (20135)------------------------------
% 9.87/2.82 % (20135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.82 % (20135)Termination reason: Unknown
% 9.87/2.82 % (20135)Termination phase: shuffling
% 9.87/2.82
% 9.87/2.82 % (20135)Memory used [KB]: 1918
% 9.87/2.82 % (20135)Time elapsed: 0.008 s
% 9.87/2.82 % (20135)Instructions burned: 26 (million)
% 9.87/2.82 % (20135)------------------------------
% 9.87/2.82 % (20135)------------------------------
% 9.87/2.83 % (20136)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_19725 for (2987ds/995Mi)
% 9.87/2.86 % (20134)Instruction limit reached!
% 9.87/2.86 % (20134)------------------------------
% 9.87/2.86 % (20134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.86 % (20134)Termination reason: Unknown
% 9.87/2.86 % (20134)Termination phase: Saturation
% 9.87/2.86
% 9.87/2.86 % (20134)Memory used [KB]: 7547
% 9.87/2.86 % (20134)Time elapsed: 0.079 s
% 9.87/2.86 % (20134)Instructions burned: 260 (million)
% 9.87/2.86 % (20134)------------------------------
% 9.87/2.86 % (20134)------------------------------
% 9.87/2.86 % (20137)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_19725 for (2986ds/373Mi)
% 10.09/2.96 % (20125)Instruction limit reached!
% 10.09/2.96 % (20125)------------------------------
% 10.09/2.96 % (20125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.96 % (20125)Termination reason: Unknown
% 10.09/2.96 % (20125)Termination phase: Saturation
% 10.09/2.96
% 10.09/2.96 % (20125)Memory used [KB]: 9083
% 10.09/2.96 % (20125)Time elapsed: 0.461 s
% 10.09/2.96 % (20125)Instructions burned: 1539 (million)
% 10.09/2.96 % (20125)------------------------------
% 10.09/2.96 % (20125)------------------------------
% 10.09/2.97 % (20138)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_19725 for (2985ds/253Mi)
% 10.09/2.97 % (20137)Instruction limit reached!
% 10.09/2.97 % (20137)------------------------------
% 10.09/2.97 % (20137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.97 % (20137)Termination reason: Unknown
% 10.09/2.97 % (20137)Termination phase: Saturation
% 10.09/2.97
% 10.09/2.97 % (20137)Memory used [KB]: 7931
% 10.09/2.97 % (20137)Time elapsed: 0.107 s
% 10.09/2.97 % (20137)Instructions burned: 375 (million)
% 10.09/2.97 % (20137)------------------------------
% 10.09/2.97 % (20137)------------------------------
% 10.09/2.98 % (20139)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_19725 for (2985ds/832Mi)
% 10.09/2.99 % (20128)Instruction limit reached!
% 10.09/2.99 % (20128)------------------------------
% 10.09/2.99 % (20128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.99 % (20128)Termination reason: Unknown
% 10.09/2.99 % (20128)Termination phase: Saturation
% 10.09/2.99
% 10.09/2.99 % (20128)Memory used [KB]: 3070
% 10.09/2.99 % (20128)Time elapsed: 0.409 s
% 10.09/2.99 % (20128)Instructions burned: 1913 (million)
% 10.09/2.99 % (20128)------------------------------
% 10.09/2.99 % (20128)------------------------------
% 10.09/3.00 % (20140)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_19725 for (2985ds/668Mi)
% 12.79/3.03 % (20138)Instruction limit reached!
% 12.79/3.03 % (20138)------------------------------
% 12.79/3.03 % (20138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.03 % (20138)Termination reason: Unknown
% 12.79/3.03 % (20138)Termination phase: Saturation
% 12.79/3.03
% 12.79/3.03 % (20138)Memory used [KB]: 7547
% 12.79/3.03 % (20138)Time elapsed: 0.067 s
% 12.79/3.03 % (20138)Instructions burned: 254 (million)
% 12.79/3.03 % (20138)------------------------------
% 12.79/3.03 % (20138)------------------------------
% 12.79/3.04 % (20141)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=40:si=on:rtra=on_0 on DTF2THF_19725 for (2985ds/40Mi)
% 12.79/3.05 % (20141)Instruction limit reached!
% 12.79/3.05 % (20141)------------------------------
% 12.79/3.05 % (20141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.05 % (20141)Termination reason: Unknown
% 12.79/3.05 % (20141)Termination phase: shuffling
% 12.79/3.05
% 12.79/3.05 % (20141)Memory used [KB]: 2174
% 12.79/3.05 % (20141)Time elapsed: 0.013 s
% 12.79/3.05 % (20141)Instructions burned: 42 (million)
% 12.79/3.05 % (20141)------------------------------
% 12.79/3.05 % (20141)------------------------------
% 12.79/3.06 % (20142)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_19725 for (2985ds/294Mi)
% 12.79/3.10 % (20142)Refutation not found, incomplete strategy
% 12.79/3.10 % (20142)------------------------------
% 12.79/3.10 % (20142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.10 % (20142)Termination reason: Refutation not found, incomplete strategy
% 12.79/3.10
% 12.79/3.10
% 12.79/3.10 % (20142)Memory used [KB]: 7036
% 12.79/3.10 % (20142)Time elapsed: 0.035 s
% 12.79/3.10 % (20142)Instructions burned: 130 (million)
% 12.79/3.10 % (20142)------------------------------
% 12.79/3.10 % (20142)------------------------------
% 12.79/3.11 % (20143)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_19725 for (2984ds/187Mi)
% 13.48/3.13 % (20136)Instruction limit reached!
% 13.48/3.13 % (20136)------------------------------
% 13.48/3.13 % (20136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.13 % (20136)Termination reason: Unknown
% 13.48/3.13 % (20136)Termination phase: Saturation
% 13.48/3.13
% 13.48/3.13 % (20136)Memory used [KB]: 9850
% 13.48/3.13 % (20136)Time elapsed: 0.286 s
% 13.48/3.13 % (20136)Instructions burned: 998 (million)
% 13.48/3.13 % (20136)------------------------------
% 13.48/3.13 % (20136)------------------------------
% 13.48/3.14 % (20144)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_19725 for (2984ds/371Mi)
% 13.48/3.16 % (20143)Instruction limit reached!
% 13.48/3.16 % (20143)------------------------------
% 13.48/3.16 % (20143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.16 % (20143)Termination reason: Unknown
% 13.48/3.16 % (20143)Termination phase: Saturation
% 13.48/3.16
% 13.48/3.16 % (20143)Memory used [KB]: 7164
% 13.48/3.16 % (20143)Time elapsed: 0.052 s
% 13.48/3.16 % (20143)Instructions burned: 189 (million)
% 13.48/3.16 % (20143)------------------------------
% 13.48/3.16 % (20143)------------------------------
% 13.48/3.17 % (20145)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_19725 for (2983ds/1827Mi)
% 13.48/3.19 % (20140)Instruction limit reached!
% 13.48/3.19 % (20140)------------------------------
% 13.48/3.19 % (20140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.19 % (20140)Termination reason: Unknown
% 13.48/3.19 % (20140)Termination phase: Saturation
% 13.48/3.19
% 13.48/3.19 % (20140)Memory used [KB]: 14200
% 13.48/3.19 % (20140)Time elapsed: 0.189 s
% 13.48/3.19 % (20140)Instructions burned: 669 (million)
% 13.48/3.19 % (20140)------------------------------
% 13.48/3.19 % (20140)------------------------------
% 13.97/3.20 % (20146)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_19725 for (2983ds/70Mi)
% 13.97/3.22 % (20146)Instruction limit reached!
% 13.97/3.22 % (20146)------------------------------
% 13.97/3.22 % (20146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.22 % (20146)Termination reason: Unknown
% 13.97/3.22 % (20146)Termination phase: Property scanning
% 13.97/3.22
% 13.97/3.22 % (20146)Memory used [KB]: 2302
% 13.97/3.22 % (20146)Time elapsed: 0.021 s
% 13.97/3.22 % (20146)Instructions burned: 73 (million)
% 13.97/3.22 % (20146)------------------------------
% 13.97/3.22 % (20146)------------------------------
% 13.97/3.22 % (20139)Instruction limit reached!
% 13.97/3.22 % (20139)------------------------------
% 13.97/3.22 % (20139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.22 % (20139)Termination reason: Unknown
% 13.97/3.22 % (20139)Termination phase: Saturation
% 13.97/3.22
% 13.97/3.22 % (20139)Memory used [KB]: 7931
% 13.97/3.22 % (20139)Time elapsed: 0.244 s
% 13.97/3.22 % (20139)Instructions burned: 833 (million)
% 13.97/3.22 % (20139)------------------------------
% 13.97/3.22 % (20139)------------------------------
% 13.97/3.23 % (20147)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_19725 for (2983ds/316Mi)
% 13.97/3.23 % (20148)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_19725 for (2983ds/932Mi)
% 13.97/3.25 % (20144)Instruction limit reached!
% 13.97/3.25 % (20144)------------------------------
% 13.97/3.25 % (20144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.25 % (20144)Termination reason: Unknown
% 13.97/3.25 % (20144)Termination phase: Saturation
% 13.97/3.25
% 13.97/3.25 % (20144)Memory used [KB]: 7419
% 13.97/3.25 % (20144)Time elapsed: 0.113 s
% 13.97/3.25 % (20144)Instructions burned: 371 (million)
% 13.97/3.25 % (20144)------------------------------
% 13.97/3.25 % (20144)------------------------------
% 13.97/3.26 % (20149)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_19725 for (2983ds/4714Mi)
% 14.46/3.30 % (20147)Refutation not found, incomplete strategy
% 14.46/3.30 % (20147)------------------------------
% 14.46/3.30 % (20147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.30 % (20147)Termination reason: Refutation not found, incomplete strategy
% 14.46/3.30
% 14.46/3.30
% 14.46/3.30 % (20147)Memory used [KB]: 7675
% 14.46/3.30 % (20147)Time elapsed: 0.070 s
% 14.46/3.30 % (20147)Instructions burned: 262 (million)
% 14.46/3.30 % (20147)------------------------------
% 14.46/3.30 % (20147)------------------------------
% 14.46/3.31 % (20150)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_19725 for (2982ds/8250Mi)
% 14.46/3.34 % (20149)Refutation not found, incomplete strategy
% 14.46/3.34 % (20149)------------------------------
% 14.46/3.34 % (20149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.34 % (20149)Termination reason: Refutation not found, incomplete strategy
% 14.46/3.34
% 14.46/3.34
% 14.46/3.34 % (20149)Memory used [KB]: 7803
% 14.46/3.34 % (20149)Time elapsed: 0.080 s
% 14.46/3.34 % (20149)Instructions burned: 296 (million)
% 14.46/3.34 % (20149)------------------------------
% 14.46/3.34 % (20149)------------------------------
% 14.46/3.35 % (20151)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_19725 for (2982ds/770Mi)
% 15.23/3.51 % (20148)Instruction limit reached!
% 15.23/3.51 % (20148)------------------------------
% 15.23/3.51 % (20148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.51 % (20148)Termination reason: Unknown
% 15.23/3.51 % (20148)Termination phase: Saturation
% 15.23/3.51
% 15.23/3.51 % (20148)Memory used [KB]: 10234
% 15.23/3.51 % (20148)Time elapsed: 0.277 s
% 15.23/3.51 % (20148)Instructions burned: 933 (million)
% 15.23/3.51 % (20148)------------------------------
% 15.23/3.51 % (20148)------------------------------
% 15.23/3.52 % (20152)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_19725 for (2980ds/794Mi)
% 15.23/3.58 % (20151)Instruction limit reached!
% 15.23/3.58 % (20151)------------------------------
% 15.23/3.58 % (20151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.58 % (20151)Termination reason: Unknown
% 15.23/3.58 % (20151)Termination phase: Saturation
% 15.23/3.58
% 15.23/3.58 % (20151)Memory used [KB]: 7675
% 15.23/3.58 % (20151)Time elapsed: 0.233 s
% 15.23/3.58 % (20151)Instructions burned: 770 (million)
% 15.23/3.58 % (20151)------------------------------
% 15.23/3.58 % (20151)------------------------------
% 15.23/3.59 % (20153)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_19725 for (2979ds/464Mi)
% 16.36/3.72 % (20153)Instruction limit reached!
% 16.36/3.72 % (20153)------------------------------
% 16.36/3.72 % (20153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.36/3.72 % (20153)Termination reason: Unknown
% 16.36/3.72 % (20153)Termination phase: Saturation
% 16.36/3.72
% 16.36/3.72 % (20153)Memory used [KB]: 8059
% 16.36/3.72 % (20153)Time elapsed: 0.137 s
% 16.36/3.72 % (20153)Instructions burned: 466 (million)
% 16.36/3.72 % (20153)------------------------------
% 16.36/3.72 % (20153)------------------------------
% 16.36/3.73 % (20154)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_19725 for (2978ds/1376Mi)
% 16.36/3.74 % (20145)Instruction limit reached!
% 16.36/3.74 % (20145)------------------------------
% 16.36/3.74 % (20145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.36/3.74 % (20145)Termination reason: Unknown
% 16.36/3.74 % (20145)Termination phase: Saturation
% 16.36/3.74
% 16.36/3.74 % (20145)Memory used [KB]: 9083
% 16.36/3.74 % (20145)Time elapsed: 0.569 s
% 16.36/3.74 % (20145)Instructions burned: 1829 (million)
% 16.36/3.74 % (20145)------------------------------
% 16.36/3.74 % (20145)------------------------------
% 16.36/3.75 % (20155)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_19725 for (2978ds/906Mi)
% 16.36/3.75 % (20152)Instruction limit reached!
% 16.36/3.75 % (20152)------------------------------
% 16.36/3.75 % (20152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.36/3.75 % (20152)Termination reason: Unknown
% 16.36/3.75 % (20152)Termination phase: Saturation
% 16.36/3.75
% 16.36/3.75 % (20152)Memory used [KB]: 5117
% 16.36/3.75 % (20152)Time elapsed: 0.229 s
% 16.36/3.75 % (20152)Instructions burned: 797 (million)
% 16.36/3.75 % (20152)------------------------------
% 16.36/3.75 % (20152)------------------------------
% 16.36/3.76 % (20156)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_19725 for (2978ds/434Mi)
% 17.62/3.86 % (20124)Instruction limit reached!
% 17.62/3.86 % (20124)------------------------------
% 17.62/3.86 % (20124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.62/3.86 % (20124)Termination reason: Unknown
% 17.62/3.86 % (20124)Termination phase: Saturation
% 17.62/3.86
% 17.62/3.86 % (20124)Memory used [KB]: 10874
% 17.62/3.86 % (20124)Time elapsed: 1.404 s
% 17.62/3.86 % (20124)Instructions burned: 4437 (million)
% 17.62/3.86 % (20124)------------------------------
% 17.62/3.86 % (20124)------------------------------
% 17.62/3.87 % (20157)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_19725 for (2977ds/865Mi)
% 17.62/3.88 % (20156)Instruction limit reached!
% 17.62/3.88 % (20156)------------------------------
% 17.62/3.88 % (20156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.62/3.88 % (20156)Termination reason: Unknown
% 17.62/3.88 % (20156)Termination phase: Saturation
% 17.62/3.88
% 17.62/3.88 % (20156)Memory used [KB]: 7164
% 17.62/3.88 % (20156)Time elapsed: 0.149 s
% 17.62/3.88 % (20156)Instructions burned: 434 (million)
% 17.62/3.88 % (20156)------------------------------
% 17.62/3.88 % (20156)------------------------------
% 17.62/3.89 % (20158)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_19725 for (2976ds/593Mi)
% 18.04/3.91 % (20129)Instruction limit reached!
% 18.04/3.91 % (20129)------------------------------
% 18.04/3.91 % (20129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.04/3.91 % (20129)Termination reason: Unknown
% 18.04/3.91 % (20129)Termination phase: Saturation
% 18.04/3.91
% 18.04/3.91 % (20129)Memory used [KB]: 9978
% 18.04/3.91 % (20129)Time elapsed: 1.264 s
% 18.04/3.91 % (20129)Instructions burned: 4350 (million)
% 18.04/3.91 % (20129)------------------------------
% 18.04/3.91 % (20129)------------------------------
% 18.04/3.92 % (20159)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_19725 for (2976ds/443Mi)
% 19.76/4.04 % (20155)Instruction limit reached!
% 19.76/4.04 % (20155)------------------------------
% 19.76/4.04 % (20155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.76/4.04 % (20155)Termination reason: Unknown
% 19.76/4.04 % (20155)Termination phase: Saturation
% 19.76/4.04
% 19.76/4.04 % (20155)Memory used [KB]: 10746
% 19.76/4.04 % (20155)Time elapsed: 0.317 s
% 19.76/4.04 % (20155)Instructions burned: 907 (million)
% 19.76/4.04 % (20155)------------------------------
% 19.76/4.04 % (20155)------------------------------
% 19.76/4.05 % (20160)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_19725 for (2975ds/594Mi)
% 19.76/4.05 % (20159)Instruction limit reached!
% 19.76/4.05 % (20159)------------------------------
% 19.76/4.05 % (20159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.76/4.05 % (20159)Termination reason: Unknown
% 19.76/4.05 % (20159)Termination phase: Saturation
% 19.76/4.05
% 19.76/4.05 % (20159)Memory used [KB]: 7803
% 19.76/4.05 % (20159)Time elapsed: 0.160 s
% 19.76/4.05 % (20159)Instructions burned: 445 (million)
% 19.76/4.05 % (20159)------------------------------
% 19.76/4.05 % (20159)------------------------------
% 19.76/4.06 % (20161)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_19725 for (2974ds/327Mi)
% 19.76/4.06 % (20158)Instruction limit reached!
% 19.76/4.06 % (20158)------------------------------
% 19.76/4.06 % (20158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.76/4.06 % (20158)Termination reason: Unknown
% 19.76/4.06 % (20158)Termination phase: Saturation
% 19.76/4.06
% 19.76/4.06 % (20158)Memory used [KB]: 9466
% 19.76/4.06 % (20158)Time elapsed: 0.193 s
% 19.76/4.06 % (20158)Instructions burned: 594 (million)
% 19.76/4.06 % (20158)------------------------------
% 19.76/4.06 % (20158)------------------------------
% 19.76/4.07 % (20162)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_19725 for (2974ds/5411Mi)
% 20.32/4.12 % (20127)Instruction limit reached!
% 20.32/4.12 % (20127)------------------------------
% 20.32/4.12 % (20127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.12 % (20127)Termination reason: Unknown
% 20.32/4.12 % (20127)Termination phase: Saturation
% 20.32/4.12
% 20.32/4.12 % (20127)Memory used [KB]: 13432
% 20.32/4.12 % (20127)Time elapsed: 1.601 s
% 20.32/4.12 % (20127)Instructions burned: 5207 (million)
% 20.32/4.12 % (20127)------------------------------
% 20.32/4.12 % (20127)------------------------------
% 20.32/4.13 % (20157)Instruction limit reached!
% 20.32/4.13 % (20157)------------------------------
% 20.32/4.13 % (20157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.13 % (20157)Termination reason: Unknown
% 20.32/4.13 % (20157)Termination phase: Saturation
% 20.32/4.13
% 20.32/4.13 % (20157)Memory used [KB]: 8699
% 20.32/4.13 % (20157)Time elapsed: 0.287 s
% 20.32/4.13 % (20157)Instructions burned: 867 (million)
% 20.32/4.13 % (20157)------------------------------
% 20.32/4.13 % (20157)------------------------------
% 20.32/4.14 % (20163)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_19725 for (2974ds/1762Mi)
% 20.32/4.14 % (20164)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_19725 for (2974ds/96Mi)
% 20.32/4.16 % (20161)Instruction limit reached!
% 20.32/4.16 % (20161)------------------------------
% 20.32/4.16 % (20161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.16 % (20161)Termination reason: Unknown
% 20.32/4.16 % (20161)Termination phase: Saturation
% 20.32/4.16
% 20.32/4.16 % (20161)Memory used [KB]: 7547
% 20.32/4.16 % (20161)Time elapsed: 0.101 s
% 20.32/4.16 % (20161)Instructions burned: 328 (million)
% 20.32/4.16 % (20161)------------------------------
% 20.32/4.16 % (20161)------------------------------
% 20.32/4.17 % (20164)Instruction limit reached!
% 20.32/4.17 % (20164)------------------------------
% 20.32/4.17 % (20164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.17 % (20164)Termination reason: Unknown
% 20.32/4.17 % (20164)Termination phase: Property scanning
% 20.32/4.17
% 20.32/4.17 % (20164)Memory used [KB]: 2302
% 20.32/4.17 % (20164)Time elapsed: 0.027 s
% 20.32/4.17 % (20164)Instructions burned: 96 (million)
% 20.32/4.17 % (20164)------------------------------
% 20.32/4.17 % (20164)------------------------------
% 20.32/4.17 % (20165)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/503Mi)
% 20.32/4.18 % (20166)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/90Mi)
% 20.69/4.20 % (20166)Instruction limit reached!
% 20.69/4.20 % (20166)------------------------------
% 20.69/4.20 % (20166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.20 % (20166)Termination reason: Unknown
% 20.69/4.20 % (20166)Termination phase: Property scanning
% 20.69/4.20
% 20.69/4.20 % (20166)Memory used [KB]: 2174
% 20.69/4.20 % (20166)Time elapsed: 0.025 s
% 20.69/4.20 % (20166)Instructions burned: 90 (million)
% 20.69/4.20 % (20166)------------------------------
% 20.69/4.20 % (20166)------------------------------
% 20.69/4.21 % (20165)Refutation not found, incomplete strategy
% 20.69/4.21 % (20165)------------------------------
% 20.69/4.21 % (20165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.21 % (20165)Termination reason: Refutation not found, incomplete strategy
% 20.69/4.21
% 20.69/4.21
% 20.69/4.21 % (20165)Memory used [KB]: 7164
% 20.69/4.21 % (20165)Time elapsed: 0.036 s
% 20.69/4.21 % (20165)Instructions burned: 118 (million)
% 20.69/4.21 % (20165)------------------------------
% 20.69/4.21 % (20165)------------------------------
% 20.69/4.21 % (20167)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/593Mi)
% 20.69/4.22 % (20154)Instruction limit reached!
% 20.69/4.22 % (20154)------------------------------
% 20.69/4.22 % (20154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.22 % (20154)Termination reason: Unknown
% 20.69/4.22 % (20154)Termination phase: Saturation
% 20.69/4.22
% 20.69/4.22 % (20154)Memory used [KB]: 11513
% 20.69/4.22 % (20154)Time elapsed: 0.483 s
% 20.69/4.22 % (20154)Instructions burned: 1376 (million)
% 20.69/4.22 % (20154)------------------------------
% 20.69/4.22 % (20154)------------------------------
% 20.69/4.22 % (20168)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/1512Mi)
% 20.69/4.23 % (20169)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/569Mi)
% 20.69/4.23 % (20160)Instruction limit reached!
% 20.69/4.23 % (20160)------------------------------
% 20.69/4.23 % (20160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.23 % (20160)Termination reason: Unknown
% 20.69/4.23 % (20160)Termination phase: Saturation
% 20.69/4.23
% 20.69/4.23 % (20160)Memory used [KB]: 7803
% 20.69/4.23 % (20160)Time elapsed: 0.183 s
% 20.69/4.23 % (20160)Instructions burned: 595 (million)
% 20.69/4.23 % (20160)------------------------------
% 20.69/4.23 % (20160)------------------------------
% 20.69/4.24 % (20170)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_19725 for (2973ds/501Mi)
% 21.10/4.32 % (20170)Refutation not found, incomplete strategy
% 21.10/4.32 % (20170)------------------------------
% 21.10/4.32 % (20170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.10/4.32 % (20170)Termination reason: Refutation not found, incomplete strategy
% 21.10/4.32
% 21.10/4.32
% 21.10/4.32 % (20170)Memory used [KB]: 7931
% 21.10/4.32 % (20170)Time elapsed: 0.074 s
% 21.10/4.32 % (20170)Instructions burned: 265 (million)
% 21.10/4.32 % (20170)------------------------------
% 21.10/4.32 % (20170)------------------------------
% 21.10/4.33 % (20171)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_19725 for (2972ds/562Mi)
% 21.10/4.38 % (20167)Instruction limit reached!
% 21.10/4.38 % (20167)------------------------------
% 21.10/4.38 % (20167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.10/4.38 % (20167)Termination reason: Unknown
% 21.10/4.38 % (20167)Termination phase: Saturation
% 21.10/4.38
% 21.10/4.38 % (20167)Memory used [KB]: 8443
% 21.10/4.38 % (20167)Time elapsed: 0.176 s
% 21.10/4.38 % (20167)Instructions burned: 594 (million)
% 21.10/4.38 % (20167)------------------------------
% 21.10/4.38 % (20167)------------------------------
% 21.10/4.39 % (20172)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_19725 for (2971ds/406Mi)
% 21.46/4.40 % (20169)Instruction limit reached!
% 21.46/4.40 % (20169)------------------------------
% 21.46/4.40 % (20169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.40 % (20169)Termination reason: Unknown
% 21.46/4.40 % (20169)Termination phase: Saturation
% 21.46/4.40
% 21.46/4.40 % (20169)Memory used [KB]: 8955
% 21.46/4.40 % (20169)Time elapsed: 0.173 s
% 21.46/4.40 % (20169)Instructions burned: 569 (million)
% 21.46/4.40 % (20169)------------------------------
% 21.46/4.40 % (20169)------------------------------
% 21.46/4.41 % (20173)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_19725 for (2971ds/582Mi)
% 21.46/4.48 % (20171)Instruction limit reached!
% 21.46/4.48 % (20171)------------------------------
% 21.46/4.48 % (20171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.48 % (20171)Termination reason: Unknown
% 21.46/4.48 % (20171)Termination phase: Saturation
% 21.46/4.48
% 21.46/4.48 % (20171)Memory used [KB]: 8699
% 21.46/4.48 % (20171)Time elapsed: 0.158 s
% 21.46/4.48 % (20171)Instructions burned: 564 (million)
% 21.46/4.48 % (20171)------------------------------
% 21.46/4.48 % (20171)------------------------------
% 21.46/4.49 % (20174)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_19725 for (2970ds/456Mi)
% 21.92/4.52 % (20172)Instruction limit reached!
% 21.92/4.52 % (20172)------------------------------
% 21.92/4.52 % (20172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.52 % (20172)Termination reason: Unknown
% 21.92/4.52 % (20172)Termination phase: Saturation
% 21.92/4.52
% 21.92/4.52 % (20172)Memory used [KB]: 7931
% 21.92/4.52 % (20172)Time elapsed: 0.131 s
% 21.92/4.52 % (20172)Instructions burned: 406 (million)
% 21.92/4.52 % (20172)------------------------------
% 21.92/4.52 % (20172)------------------------------
% 21.92/4.53 % (20175)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_19725 for (2970ds/393Mi)
% 21.92/4.59 % (20173)Instruction limit reached!
% 21.92/4.59 % (20173)------------------------------
% 21.92/4.59 % (20173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.59 % (20173)Termination reason: Unknown
% 21.92/4.59 % (20173)Termination phase: Saturation
% 21.92/4.59
% 21.92/4.59 % (20173)Memory used [KB]: 7675
% 21.92/4.59 % (20173)Time elapsed: 0.186 s
% 21.92/4.59 % (20173)Instructions burned: 582 (million)
% 21.92/4.59 % (20173)------------------------------
% 21.92/4.59 % (20173)------------------------------
% 22.34/4.60 % (20176)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_19725 for (2969ds/1335Mi)
% 22.34/4.63 % (20174)Instruction limit reached!
% 22.34/4.63 % (20174)------------------------------
% 22.34/4.63 % (20174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.34/4.63 % (20174)Termination reason: Unknown
% 22.34/4.63 % (20174)Termination phase: Saturation
% 22.34/4.63
% 22.34/4.63 % (20174)Memory used [KB]: 7547
% 22.34/4.63 % (20174)Time elapsed: 0.136 s
% 22.34/4.63 % (20174)Instructions burned: 458 (million)
% 22.34/4.63 % (20174)------------------------------
% 22.34/4.63 % (20174)------------------------------
% 22.34/4.64 % (20177)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_19725 for (2969ds/3373Mi)
% 22.34/4.64 % (20175)Instruction limit reached!
% 22.34/4.64 % (20175)------------------------------
% 22.34/4.64 % (20175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.34/4.64 % (20175)Termination reason: Unknown
% 22.34/4.64 % (20175)Termination phase: Saturation
% 22.34/4.64
% 22.34/4.64 % (20175)Memory used [KB]: 8315
% 22.34/4.64 % (20175)Time elapsed: 0.108 s
% 22.34/4.64 % (20175)Instructions burned: 393 (million)
% 22.34/4.64 % (20175)------------------------------
% 22.34/4.64 % (20175)------------------------------
% 22.34/4.65 % (20178)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_19725 for (2969ds/474Mi)
% 22.34/4.65 % (20163)Instruction limit reached!
% 22.34/4.65 % (20163)------------------------------
% 22.34/4.65 % (20163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.34/4.65 % (20163)Termination reason: Unknown
% 22.34/4.65 % (20163)Termination phase: Saturation
% 22.34/4.65
% 22.34/4.65 % (20163)Memory used [KB]: 9594
% 22.34/4.65 % (20163)Time elapsed: 0.516 s
% 22.34/4.65 % (20163)Instructions burned: 1765 (million)
% 22.34/4.65 % (20163)------------------------------
% 22.34/4.65 % (20163)------------------------------
% 22.34/4.66 % (20179)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_19725 for (2969ds/157Mi)
% 22.34/4.66 % (20168)Instruction limit reached!
% 22.34/4.66 % (20168)------------------------------
% 22.34/4.66 % (20168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.34/4.66 % (20168)Termination reason: Unknown
% 22.34/4.66 % (20168)Termination phase: Saturation
% 22.34/4.66
% 22.34/4.66 % (20168)Memory used [KB]: 8315
% 22.34/4.66 % (20168)Time elapsed: 0.448 s
% 22.34/4.66 % (20168)Instructions burned: 1515 (million)
% 22.34/4.66 % (20168)------------------------------
% 22.34/4.66 % (20168)------------------------------
% 22.34/4.67 % (20180)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_19725 for (2968ds/590Mi)
% 23.69/4.70 % (20179)Instruction limit reached!
% 23.69/4.70 % (20179)------------------------------
% 23.69/4.70 % (20179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.69/4.70 % (20179)Termination reason: Unknown
% 23.69/4.70 % (20179)Termination phase: Property scanning
% 23.69/4.70
% 23.69/4.70 % (20179)Memory used [KB]: 2814
% 23.69/4.70 % (20179)Time elapsed: 0.042 s
% 23.69/4.70 % (20179)Instructions burned: 160 (million)
% 23.69/4.70 % (20179)------------------------------
% 23.69/4.70 % (20179)------------------------------
% 23.69/4.71 % (20181)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_19725 for (2968ds/104Mi)
% 23.69/4.74 % (20181)Instruction limit reached!
% 23.69/4.74 % (20181)------------------------------
% 23.69/4.74 % (20181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.69/4.74 % (20181)Termination reason: Unknown
% 23.69/4.74 % (20181)Termination phase: Property scanning
% 23.69/4.74
% 23.69/4.74 % (20181)Memory used [KB]: 2174
% 23.69/4.74 % (20181)Time elapsed: 0.030 s
% 23.69/4.74 % (20181)Instructions burned: 104 (million)
% 23.69/4.74 % (20181)------------------------------
% 23.69/4.74 % (20181)------------------------------
% 23.69/4.75 % (20182)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_19725 for (2968ds/414Mi)
% 23.69/4.79 % (20178)Instruction limit reached!
% 23.69/4.79 % (20178)------------------------------
% 23.69/4.79 % (20178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.69/4.79 % (20178)Termination reason: Unknown
% 23.69/4.79 % (20178)Termination phase: Saturation
% 23.69/4.79
% 23.69/4.79 % (20178)Memory used [KB]: 8059
% 23.69/4.79 % (20178)Time elapsed: 0.137 s
% 23.69/4.79 % (20178)Instructions burned: 477 (million)
% 23.69/4.79 % (20178)------------------------------
% 23.69/4.79 % (20178)------------------------------
% 23.69/4.80 % (20183)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_19725 for (2967ds/715Mi)
% 24.03/4.84 % (20180)Instruction limit reached!
% 24.03/4.84 % (20180)------------------------------
% 24.03/4.84 % (20180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.03/4.84 % (20180)Termination reason: Unknown
% 24.03/4.84 % (20180)Termination phase: Saturation
% 24.03/4.84
% 24.03/4.84 % (20180)Memory used [KB]: 9083
% 24.03/4.84 % (20180)Time elapsed: 0.170 s
% 24.03/4.84 % (20180)Instructions burned: 590 (million)
% 24.03/4.84 % (20180)------------------------------
% 24.03/4.84 % (20180)------------------------------
% 24.03/4.85 % (20184)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_19725 for (2967ds/961Mi)
% 24.03/4.86 % (20182)Instruction limit reached!
% 24.03/4.86 % (20182)------------------------------
% 24.03/4.86 % (20182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.03/4.86 % (20182)Termination reason: Unknown
% 24.03/4.86 % (20182)Termination phase: Saturation
% 24.03/4.86
% 24.03/4.86 % (20182)Memory used [KB]: 7931
% 24.03/4.86 % (20182)Time elapsed: 0.114 s
% 24.03/4.86 % (20182)Instructions burned: 416 (million)
% 24.03/4.86 % (20182)------------------------------
% 24.03/4.86 % (20182)------------------------------
% 24.03/4.87 % (20185)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_19725 for (2966ds/1213Mi)
% 24.44/5.00 % (20176)Instruction limit reached!
% 24.44/5.00 % (20176)------------------------------
% 24.44/5.00 % (20176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.44/5.00 % (20176)Termination reason: Unknown
% 24.44/5.00 % (20176)Termination phase: Saturation
% 24.44/5.00
% 24.44/5.00 % (20176)Memory used [KB]: 9850
% 24.44/5.00 % (20176)Time elapsed: 0.394 s
% 24.44/5.00 % (20176)Instructions burned: 1335 (million)
% 24.44/5.00 % (20176)------------------------------
% 24.44/5.00 % (20176)------------------------------
% 24.44/5.01 % (20186)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_19725 for (2965ds/1979Mi)
% 24.44/5.02 % (20183)Instruction limit reached!
% 24.44/5.02 % (20183)------------------------------
% 24.44/5.02 % (20183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.44/5.02 % (20183)Termination reason: Unknown
% 24.44/5.02 % (20183)Termination phase: Saturation
% 24.44/5.02
% 24.44/5.02 % (20183)Memory used [KB]: 3837
% 24.44/5.02 % (20183)Time elapsed: 0.224 s
% 24.44/5.02 % (20183)Instructions burned: 716 (million)
% 24.44/5.02 % (20183)------------------------------
% 24.44/5.02 % (20183)------------------------------
% 26.88/5.03 % (20187)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_19725 for (2965ds/481Mi)
% 26.88/5.12 % (20184)Instruction limit reached!
% 26.88/5.12 % (20184)------------------------------
% 26.88/5.12 % (20184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.88/5.12 % (20184)Termination reason: Unknown
% 26.88/5.12 % (20184)Termination phase: Saturation
% 26.88/5.12
% 26.88/5.12 % (20184)Memory used [KB]: 8187
% 26.88/5.12 % (20184)Time elapsed: 0.270 s
% 26.88/5.12 % (20184)Instructions burned: 961 (million)
% 26.88/5.12 % (20184)------------------------------
% 26.88/5.12 % (20184)------------------------------
% 27.51/5.13 % (20188)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_19725 for (2964ds/783Mi)
% 27.51/5.17 % (20187)Instruction limit reached!
% 27.51/5.17 % (20187)------------------------------
% 27.51/5.17 % (20187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.51/5.17 % (20187)Termination reason: Unknown
% 27.51/5.17 % (20187)Termination phase: Saturation
% 27.51/5.17
% 27.51/5.17 % (20187)Memory used [KB]: 8059
% 27.51/5.17 % (20187)Time elapsed: 0.143 s
% 27.51/5.17 % (20187)Instructions burned: 482 (million)
% 27.51/5.17 % (20187)------------------------------
% 27.51/5.17 % (20187)------------------------------
% 27.51/5.18 % (20189)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_19725 for (2963ds/432Mi)
% 28.04/5.26 % (20185)Instruction limit reached!
% 28.04/5.26 % (20185)------------------------------
% 28.04/5.26 % (20185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.04/5.26 % (20185)Termination reason: Unknown
% 28.04/5.26 % (20185)Termination phase: Saturation
% 28.04/5.26
% 28.04/5.26 % (20185)Memory used [KB]: 8315
% 28.04/5.26 % (20185)Time elapsed: 0.385 s
% 28.04/5.26 % (20185)Instructions burned: 1216 (million)
% 28.04/5.26 % (20185)------------------------------
% 28.04/5.26 % (20185)------------------------------
% 28.04/5.27 % (20190)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_19725 for (2963ds/1670Mi)
% 28.50/5.31 % (20189)Instruction limit reached!
% 28.50/5.31 % (20189)------------------------------
% 28.50/5.31 % (20189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.50/5.31 % (20189)Termination reason: Unknown
% 28.50/5.31 % (20189)Termination phase: Saturation
% 28.50/5.31
% 28.50/5.31 % (20189)Memory used [KB]: 7547
% 28.50/5.31 % (20189)Time elapsed: 0.134 s
% 28.50/5.31 % (20189)Instructions burned: 433 (million)
% 28.50/5.31 % (20189)------------------------------
% 28.50/5.31 % (20189)------------------------------
% 28.50/5.32 % (20191)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_19725 for (2962ds/90Mi)
% 28.50/5.35 % (20191)Instruction limit reached!
% 28.50/5.35 % (20191)------------------------------
% 28.50/5.35 % (20191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.50/5.35 % (20191)Termination reason: Unknown
% 28.50/5.35 % (20191)Termination phase: Property scanning
% 28.50/5.35
% 28.50/5.35 % (20191)Memory used [KB]: 2174
% 28.50/5.35 % (20191)Time elapsed: 0.026 s
% 28.50/5.35 % (20191)Instructions burned: 93 (million)
% 28.50/5.35 % (20191)------------------------------
% 28.50/5.35 % (20191)------------------------------
% 28.50/5.36 % (20192)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_19725 for (2962ds/346Mi)
% 28.50/5.37 % (20188)Instruction limit reached!
% 28.50/5.37 % (20188)------------------------------
% 28.50/5.37 % (20188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.50/5.37 % (20188)Termination reason: Unknown
% 28.50/5.37 % (20188)Termination phase: Saturation
% 28.50/5.37
% 28.50/5.37 % (20188)Memory used [KB]: 7931
% 28.50/5.37 % (20188)Time elapsed: 0.238 s
% 28.50/5.37 % (20188)Instructions burned: 784 (million)
% 28.50/5.37 % (20188)------------------------------
% 28.50/5.37 % (20188)------------------------------
% 28.50/5.38 % (20193)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_19725 for (2961ds/401Mi)
% 29.33/5.45 % (20192)Instruction limit reached!
% 29.33/5.45 % (20192)------------------------------
% 29.33/5.45 % (20192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.45 % (20192)Termination reason: Unknown
% 29.33/5.45 % (20192)Termination phase: Saturation
% 29.33/5.45
% 29.33/5.45 % (20192)Memory used [KB]: 7803
% 29.33/5.45 % (20192)Time elapsed: 0.095 s
% 29.33/5.45 % (20192)Instructions burned: 348 (million)
% 29.33/5.45 % (20192)------------------------------
% 29.33/5.45 % (20192)------------------------------
% 29.33/5.46 % (20194)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_19725 for (2961ds/6454Mi)
% 29.33/5.46 % (20162)First to succeed.
% 29.33/5.47 % (20162)Refutation found. Thanks to Tanya!
% 29.33/5.47 % SZS status Theorem for DTF2THF_19725
% 29.33/5.47 % SZS output start Proof for DTF2THF_19725
% 29.33/5.47 thf(type_def_5, type, set_Pr1625152599n_game: $tType).
% 29.33/5.47 thf(type_def_6, type, option_game: $tType).
% 29.33/5.47 thf(type_def_7, type, set_variable: $tType).
% 29.33/5.47 thf(type_def_9, type, produc1078154247n_game: $tType).
% 29.33/5.47 thf(type_def_10, type, produc1016592119n_game: $tType).
% 29.33/5.47 thf(type_def_11, type, variable: $tType).
% 29.33/5.47 thf(type_def_12, type, set_Pr166476775n_game: $tType).
% 29.33/5.47 thf(type_def_13, type, game: $tType).
% 29.33/5.47 thf(type_def_14, type, produc735959047riable: $tType).
% 29.33/5.47 thf(type_def_15, type, produc1418842292n_game: $tType).
% 29.33/5.47 thf(func_def_0, type, produc1418842292n_game: $tType).
% 29.33/5.47 thf(func_def_1, type, set_Pr1625152599n_game: $tType).
% 29.33/5.47 thf(func_def_2, type, set_Pr166476775n_game: $tType).
% 29.33/5.47 thf(func_def_3, type, produc1016592119n_game: $tType).
% 29.33/5.47 thf(func_def_4, type, produc1078154247n_game: $tType).
% 29.33/5.47 thf(func_def_5, type, produc735959047riable: $tType).
% 29.33/5.47 thf(func_def_6, type, option_game: $tType).
% 29.33/5.47 thf(func_def_7, type, set_variable: $tType).
% 29.33/5.47 thf(func_def_8, type, variable: $tType).
% 29.33/5.47 thf(func_def_9, type, game: $tType).
% 29.33/5.47 thf(func_def_10, type, bNF_Ca1986151756riable: set_Pr1625152599n_game > (option_game > set_variable) > $o).
% 29.33/5.47 thf(func_def_11, type, bNF_fs984229733n_game: (set_variable > option_game > $o) > (option_game > option_game > $o) > produc1078154247n_game > produc1078154247n_game).
% 29.33/5.47 thf(func_def_12, type, bNF_pi856525207n_game: (set_variable > option_game > $o) > (option_game > option_game > $o) > set_variable > option_game > option_game).
% 29.33/5.47 thf(func_def_13, type, bNF_pi1813424679n_game: (set_variable > set_variable > $o) > (set_variable > option_game > $o) > set_variable > option_game > set_variable).
% 29.33/5.47 thf(func_def_14, type, bNF_sn1374695591n_game: (set_variable > option_game > $o) > (option_game > option_game > $o) > produc1078154247n_game > produc1016592119n_game).
% 29.33/5.47 thf(func_def_15, type, bNF_sn582998327n_game: (set_variable > set_variable > $o) > (set_variable > option_game > $o) > produc1078154247n_game > produc1078154247n_game).
% 29.33/5.47 thf(func_def_16, type, sup_su169929796game_o: (option_game > option_game > $o) > (option_game > option_game > $o) > option_game > option_game > $o).
% 29.33/5.47 thf(func_def_17, type, sup_su1229228248game_o: (option_game > $o) > (option_game > $o) > option_game > $o).
% 29.33/5.47 thf(func_def_18, type, sup_su1227468340game_o: (set_variable > option_game > $o) > (set_variable > option_game > $o) > set_variable > option_game > $o).
% 29.33/5.47 thf(func_def_19, type, sup_sup_variable_o: (variable > $o) > (variable > $o) > variable > $o).
% 29.33/5.47 thf(func_def_20, type, sup_sup_o: $o > $o > $o).
% 29.33/5.47 thf(func_def_21, type, sup_su423136299n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > set_Pr1625152599n_game).
% 29.33/5.47 thf(func_def_22, type, sup_su796825019n_game: set_Pr166476775n_game > set_Pr166476775n_game > set_Pr166476775n_game).
% 29.33/5.47 thf(func_def_23, type, sup_sup_set_variable: set_variable > set_variable > set_variable).
% 29.33/5.47 thf(func_def_24, type, none_game: option_game).
% 29.33/5.47 thf(func_def_25, type, some_game: game > option_game).
% 29.33/5.47 thf(func_def_26, type, the_game: option_game > game).
% 29.33/5.47 thf(func_def_27, type, ord_le707292176game_o: (option_game > option_game > $o) > (option_game > option_game > $o) > $o).
% 29.33/5.47 thf(func_def_28, type, ord_le2134856704game_o: (set_variable > option_game > $o) > (set_variable > option_game > $o) > $o).
% 29.33/5.47 thf(func_def_29, type, ord_le1407353162able_o: (variable > $o) > (variable > $o) > $o).
% 29.33/5.47 thf(func_def_30, type, ord_le1780499447n_game: set_Pr1625152599n_game > set_Pr1625152599n_game > $o).
% 29.33/5.47 thf(func_def_31, type, ord_le17855367n_game: set_Pr166476775n_game > set_Pr166476775n_game > $o).
% 29.33/5.47 thf(func_def_32, type, ord_le282106107riable: set_variable > set_variable > $o).
% 29.33/5.47 thf(func_def_33, type, order_272405634riable: (set_variable > $o) > set_variable).
% 29.33/5.47 thf(func_def_34, type, produc1111617711n_game: option_game > option_game > produc1016592119n_game).
% 29.33/5.47 thf(func_def_35, type, produc1140431679riable: option_game > set_variable > produc735959047riable).
% 29.33/5.47 thf(func_def_36, type, produc1149443391n_game: set_variable > option_game > produc1078154247n_game).
% 29.33/5.47 thf(func_def_37, type, produc1942569115n_game: produc1016592119n_game > option_game).
% 29.33/5.47 thf(func_def_38, type, produc884810027riable: produc735959047riable > option_game).
% 29.33/5.47 thf(func_def_39, type, produc893821739n_game: produc1078154247n_game > set_variable).
% 29.33/5.47 thf(func_def_40, type, produc279011037n_game: produc1016592119n_game > option_game).
% 29.33/5.47 thf(func_def_41, type, produc284475501riable: produc735959047riable > set_variable).
% 29.33/5.47 thf(func_def_42, type, produc293487213n_game: produc1078154247n_game > option_game).
% 29.33/5.47 thf(func_def_43, type, produc1696194127n_game: produc1016592119n_game > produc1016592119n_game).
% 29.33/5.47 thf(func_def_44, type, produc345397471riable: produc735959047riable > produc1078154247n_game).
% 29.33/5.47 thf(func_def_45, type, produc354409183n_game: produc1078154247n_game > produc735959047riable).
% 29.33/5.47 thf(func_def_46, type, collec884051426n_game: (produc1016592119n_game > $o) > set_Pr1625152599n_game).
% 29.33/5.47 thf(func_def_47, type, collec1702522994n_game: (produc1078154247n_game > $o) > set_Pr166476775n_game).
% 29.33/5.47 thf(func_def_48, type, collect_variable: (variable > $o) > set_variable).
% 29.33/5.47 thf(func_def_49, type, static_BVG: game > set_variable).
% 29.33/5.47 thf(func_def_50, type, choice: game > game > game).
% 29.33/5.47 thf(func_def_51, type, compose: game > game > game).
% 29.33/5.47 thf(func_def_52, type, loop: game > game).
% 29.33/5.47 thf(func_def_53, type, uSubst1484167963hoiceo: option_game > option_game > option_game).
% 29.33/5.47 thf(func_def_54, type, uSubst532817840mposeo: option_game > option_game > option_game).
% 29.33/5.47 thf(func_def_55, type, uSubst23177304_Loopo: option_game > option_game).
% 29.33/5.47 thf(func_def_56, type, uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game).
% 29.33/5.47 thf(func_def_57, type, member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o).
% 29.33/5.47 thf(func_def_58, type, member171223600n_game: produc1078154247n_game > set_Pr166476775n_game > $o).
% 29.33/5.47 thf(func_def_59, type, member_variable: variable > set_variable > $o).
% 29.33/5.47 thf(func_def_60, type, ua: set_variable).
% 29.33/5.47 thf(func_def_61, type, alpha: game).
% 29.33/5.47 thf(func_def_62, type, beta: game).
% 29.33/5.47 thf(func_def_63, type, sigma: produc1418842292n_game).
% 29.33/5.47 thf(func_def_78, type, sP0: (option_game > option_game > $o) > option_game > option_game > $o).
% 29.33/5.47 thf(func_def_79, type, sK1: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_80, type, sK2: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_81, type, sK3: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_82, type, sK4: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_83, type, sK5: option_game > game).
% 29.33/5.47 thf(func_def_84, type, sK6: (option_game > $o) > game).
% 29.33/5.47 thf(func_def_85, type, sK7: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_86, type, sK8: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_87, type, sK9: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_88, type, sK10: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_89, type, sK11: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_90, type, sK12: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_91, type, sK13: (set_variable > set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_92, type, sK14: set_variable > set_variable > set_variable > set_variable).
% 29.33/5.47 thf(func_def_93, type, sK15: set_variable > set_variable > set_variable > set_variable).
% 29.33/5.47 thf(func_def_94, type, sK16: option_game > game).
% 29.33/5.47 thf(func_def_95, type, sK17: (produc1078154247n_game > $o) > option_game).
% 29.33/5.47 thf(func_def_96, type, sK18: (produc1078154247n_game > $o) > set_variable).
% 29.33/5.47 thf(func_def_97, type, sK19: option_game > game).
% 29.33/5.47 thf(func_def_98, type, sK20: (option_game > option_game > $o) > option_game > option_game > game).
% 29.33/5.47 thf(func_def_99, type, sK21: (option_game > option_game > $o) > option_game > option_game > game).
% 29.33/5.47 thf(func_def_100, type, sK22: option_game > game).
% 29.33/5.47 thf(func_def_101, type, sK23: produc1078154247n_game > option_game).
% 29.33/5.47 thf(func_def_102, type, sK24: produc1078154247n_game > set_variable).
% 29.33/5.47 thf(func_def_103, type, sK25: produc1078154247n_game > set_variable > option_game).
% 29.33/5.47 thf(func_def_104, type, sK26: (produc1078154247n_game > $o) > set_variable).
% 29.33/5.47 thf(func_def_105, type, sK27: (produc1078154247n_game > $o) > option_game).
% 29.33/5.47 thf(func_def_106, type, sK28: option_game > game).
% 29.33/5.47 thf(func_def_107, type, sK29: produc1016592119n_game > option_game).
% 29.33/5.47 thf(func_def_108, type, sK30: produc1016592119n_game > game).
% 29.33/5.47 thf(func_def_109, type, sK31: produc1016592119n_game > game).
% 29.33/5.47 thf(func_def_110, type, sK32: produc1016592119n_game > game).
% 29.33/5.47 thf(func_def_111, type, sK33: produc1078154247n_game > option_game > set_variable).
% 29.33/5.47 thf(func_def_112, type, sK34: (option_game > option_game > $o) > option_game).
% 29.33/5.47 thf(func_def_113, type, sK35: (option_game > option_game > $o) > game).
% 29.33/5.47 thf(func_def_114, type, sK36: (option_game > option_game > $o) > game).
% 29.33/5.47 thf(func_def_115, type, sK37: (option_game > option_game > $o) > game).
% 29.33/5.47 thf(func_def_116, type, sK38: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_117, type, sK39: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_118, type, sK40: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_119, type, sK41: (set_variable > set_variable) > set_variable).
% 29.33/5.47 thf(func_def_120, type, sK42: produc1078154247n_game > option_game).
% 29.33/5.47 thf(func_def_121, type, sK43: produc1078154247n_game > set_variable).
% 29.33/5.47 thf(func_def_122, type, sK44: (option_game > $o) > game).
% 29.33/5.47 thf(func_def_123, type, sK45: (option_game > set_variable > $o) > set_variable).
% 29.33/5.47 thf(func_def_124, type, sK46: (option_game > set_variable > $o) > option_game).
% 29.33/5.47 thf(func_def_126, type, ph48: !>[X0: $tType]:(X0)).
% 29.33/5.47 thf(f10714,plain,(
% 29.33/5.47 $false),
% 29.33/5.47 inference(avatar_sat_refutation,[status(thm)],[f1328,f1397,f10713])).
% 29.33/5.47 thf(f10713,plain,(
% 29.33/5.47 spl47_1),
% 29.33/5.47 inference(avatar_contradiction_clause,[status(thm)],[f10712])).
% 29.33/5.47 thf(f10712,plain,(
% 29.33/5.47 $false | spl47_1),
% 29.33/5.47 inference(subsumption_resolution,[status(thm)],[f10643,f1206])).
% 29.33/5.47 thf(f1206,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) = $true)),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f543])).
% 29.33/5.47 thf(f543,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) = $true)),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f542])).
% 29.33/5.47 thf(f542,plain,(
% 29.33/5.47 (ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))))),
% 29.33/5.47 inference(rectify,[status(thm)],[f2])).
% 29.33/5.47 thf(f2,axiom,(
% 29.33/5.47 (ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_1_fact)).
% 29.33/5.47 thf(f10643,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_1),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f10634])).
% 29.33/5.47 thf(f10634,plain,(
% 29.33/5.47 ($true != $true) | ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_1),
% 29.33/5.47 inference(superposition,[status(thm)],[f2521,f1176])).
% 29.33/5.47 thf(f1176,plain,(
% 29.33/5.47 ( ! [X2 : set_variable,X0 : set_variable,X1 : set_variable] : (((ord_le282106107riable @ X2 @ (sup_sup_set_variable @ X1 @ X0)) = $true) | ($true != (ord_le282106107riable @ X2 @ X0))) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f915])).
% 29.33/5.47 thf(f915,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ X2 @ (sup_sup_set_variable @ X1 @ X0)) = $true) | ($true != (ord_le282106107riable @ X2 @ X0)))),
% 29.33/5.47 inference(ennf_transformation,[status(thm)],[f687])).
% 29.33/5.47 thf(f687,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (($true = (ord_le282106107riable @ X2 @ X0)) => ((ord_le282106107riable @ X2 @ (sup_sup_set_variable @ X1 @ X0)) = $true))),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f686])).
% 29.33/5.47 thf(f686,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((ord_le282106107riable @ X2 @ X0) => (ord_le282106107riable @ X2 @ (sup_sup_set_variable @ X1 @ X0)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f164])).
% 29.33/5.47 thf(f164,axiom,(
% 29.33/5.47 ! [X10 : set_variable,X12 : set_variable,X11 : set_variable] : ((ord_le282106107riable @ X11 @ X10) => (ord_le282106107riable @ X11 @ (sup_sup_set_variable @ X12 @ X10)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_163_sup_OcoboundedI2)).
% 29.33/5.47 thf(f2521,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ ua @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))))) != $true) | spl47_1),
% 29.33/5.47 inference(forward_demodulation,[status(thm)],[f2513,f1062])).
% 29.33/5.47 thf(f1062,plain,(
% 29.33/5.47 ( ! [X2 : set_variable,X0 : set_variable,X1 : set_variable] : (((sup_sup_set_variable @ X0 @ (sup_sup_set_variable @ X1 @ X2)) = (sup_sup_set_variable @ (sup_sup_set_variable @ X0 @ X1) @ X2))) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f807])).
% 29.33/5.47 thf(f807,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((sup_sup_set_variable @ X0 @ (sup_sup_set_variable @ X1 @ X2)) = (sup_sup_set_variable @ (sup_sup_set_variable @ X0 @ X1) @ X2))),
% 29.33/5.47 inference(rectify,[status(thm)],[f149])).
% 29.33/5.47 thf(f149,axiom,(
% 29.33/5.47 ! [X7 : set_variable,X8 : set_variable,X9 : set_variable] : ((sup_sup_set_variable @ X7 @ (sup_sup_set_variable @ X8 @ X9)) = (sup_sup_set_variable @ (sup_sup_set_variable @ X7 @ X8) @ X9))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_148_inf__sup__aci_I6_J)).
% 29.33/5.47 thf(f2513,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_1),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f2466])).
% 29.33/5.47 thf(f2466,plain,(
% 29.33/5.47 ($true != $true) | ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_1),
% 29.33/5.47 inference(superposition,[status(thm)],[f1490,f1175])).
% 29.33/5.47 thf(f1175,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f573])).
% 29.33/5.47 thf(f573,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f572])).
% 29.33/5.47 thf(f572,plain,(
% 29.33/5.47 (ord_le282106107riable @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f1])).
% 29.33/5.47 thf(f1,axiom,(
% 29.33/5.47 (ord_le282106107riable @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_0__092_060open_062U_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_A_092_060union_062_ABVG_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_J_J_A_092_060subseteq_062_Afst_A_Iusubstappp_A_092_060sigma_062_A_Ifst_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_A_092_060beta_062_J_092_060close_062)).
% 29.33/5.47 thf(f1490,plain,(
% 29.33/5.47 ( ! [X0 : set_variable] : (((ord_le282106107riable @ X0 @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ X0) != $true)) ) | spl47_1),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f1482])).
% 29.33/5.47 thf(f1482,plain,(
% 29.33/5.47 ( ! [X0 : set_variable] : (((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ X0) != $true) | ($true != $true) | ((ord_le282106107riable @ X0 @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true)) ) | spl47_1),
% 29.33/5.47 inference(superposition,[status(thm)],[f1300,f1078])).
% 29.33/5.47 thf(f1078,plain,(
% 29.33/5.47 ( ! [X2 : set_variable,X0 : set_variable,X1 : set_variable] : (((ord_le282106107riable @ X0 @ X1) = $true) | ((ord_le282106107riable @ X2 @ X1) != $true) | ((ord_le282106107riable @ X0 @ X2) != $true)) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f956])).
% 29.33/5.47 thf(f956,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ X0 @ X1) = $true) | ((ord_le282106107riable @ X0 @ X2) != $true) | ((ord_le282106107riable @ X2 @ X1) != $true))),
% 29.33/5.47 inference(flattening,[status(thm)],[f955])).
% 29.33/5.47 thf(f955,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((((ord_le282106107riable @ X0 @ X1) = $true) | ((ord_le282106107riable @ X0 @ X2) != $true)) | ((ord_le282106107riable @ X2 @ X1) != $true))),
% 29.33/5.47 inference(ennf_transformation,[status(thm)],[f657])).
% 29.33/5.47 thf(f657,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ X2 @ X1) = $true) => (((ord_le282106107riable @ X0 @ X2) = $true) => ((ord_le282106107riable @ X0 @ X1) = $true)))),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f656])).
% 29.33/5.47 thf(f656,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((ord_le282106107riable @ X2 @ X1) => ((ord_le282106107riable @ X0 @ X2) => (ord_le282106107riable @ X0 @ X1)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f230])).
% 29.33/5.47 thf(f230,axiom,(
% 29.33/5.47 ! [X11 : set_variable,X12 : set_variable,X10 : set_variable] : ((ord_le282106107riable @ X10 @ X12) => ((ord_le282106107riable @ X11 @ X10) => (ord_le282106107riable @ X11 @ X12)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_229_dual__order_Otrans)).
% 29.33/5.47 thf(f1300,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | spl47_1),
% 29.33/5.47 inference(avatar_component_clause,[status(thm)],[f1298])).
% 29.33/5.47 thf(f1298,definition,(
% 29.33/5.47 spl47_1 <=> ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 29.33/5.47 introduced(definition,[new_symbols(naming,[spl47_1])],[avatar_definition])).
% 29.33/5.47 thf(f1397,plain,(
% 29.33/5.47 spl47_2),
% 29.33/5.47 inference(avatar_contradiction_clause,[status(thm)],[f1396])).
% 29.33/5.47 thf(f1396,plain,(
% 29.33/5.47 $false | spl47_2),
% 29.33/5.47 inference(subsumption_resolution,[status(thm)],[f1395,f1099])).
% 29.33/5.47 thf(f1099,plain,(
% 29.33/5.47 ( ! [X0 : set_variable,X1 : set_variable] : (((ord_le282106107riable @ X0 @ (sup_sup_set_variable @ X0 @ X1)) = $true)) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f735])).
% 29.33/5.47 thf(f735,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable] : ((ord_le282106107riable @ X0 @ (sup_sup_set_variable @ X0 @ X1)) = $true)),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f734])).
% 29.33/5.47 thf(f734,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable] : (ord_le282106107riable @ X0 @ (sup_sup_set_variable @ X0 @ X1))),
% 29.33/5.47 inference(rectify,[status(thm)],[f197])).
% 29.33/5.47 thf(f197,axiom,(
% 29.33/5.47 ! [X4 : set_variable,X5 : set_variable] : (ord_le282106107riable @ X4 @ (sup_sup_set_variable @ X4 @ X5))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_196_Un__upper1)).
% 29.33/5.47 thf(f1395,plain,(
% 29.33/5.47 ((ord_le282106107riable @ ua @ (sup_sup_set_variable @ ua @ (sup_sup_set_variable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))))) != $true) | spl47_2),
% 29.33/5.47 inference(forward_demodulation,[status(thm)],[f1375,f1062])).
% 29.33/5.47 thf(f1375,plain,(
% 29.33/5.47 ((ord_le282106107riable @ ua @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_2),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f1340])).
% 29.33/5.47 thf(f1340,plain,(
% 29.33/5.47 ($true != $true) | ((ord_le282106107riable @ ua @ (sup_sup_set_variable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha))))) @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))))) != $true) | spl47_2),
% 29.33/5.47 inference(superposition,[status(thm)],[f1338,f1175])).
% 29.33/5.47 thf(f1338,plain,(
% 29.33/5.47 ( ! [X0 : set_variable] : (((ord_le282106107riable @ X0 @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ((ord_le282106107riable @ ua @ X0) != $true)) ) | spl47_2),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f1329])).
% 29.33/5.47 thf(f1329,plain,(
% 29.33/5.47 ( ! [X0 : set_variable] : (((ord_le282106107riable @ ua @ X0) != $true) | ($true != $true) | ((ord_le282106107riable @ X0 @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true)) ) | spl47_2),
% 29.33/5.47 inference(superposition,[status(thm)],[f1304,f1053])).
% 29.33/5.47 thf(f1053,plain,(
% 29.33/5.47 ( ! [X2 : set_variable,X0 : set_variable,X1 : set_variable] : (((ord_le282106107riable @ X0 @ X2) = $true) | ($true != (ord_le282106107riable @ X1 @ X2)) | ((ord_le282106107riable @ X0 @ X1) != $true)) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f856])).
% 29.33/5.47 thf(f856,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ X0 @ X1) != $true) | ((ord_le282106107riable @ X0 @ X2) = $true) | ($true != (ord_le282106107riable @ X1 @ X2)))),
% 29.33/5.47 inference(flattening,[status(thm)],[f855])).
% 29.33/5.47 thf(f855,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((((ord_le282106107riable @ X0 @ X2) = $true) | ($true != (ord_le282106107riable @ X1 @ X2))) | ((ord_le282106107riable @ X0 @ X1) != $true))),
% 29.33/5.47 inference(ennf_transformation,[status(thm)],[f369])).
% 29.33/5.47 thf(f369,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ X0 @ X1) = $true) => (($true = (ord_le282106107riable @ X1 @ X2)) => ((ord_le282106107riable @ X0 @ X2) = $true)))),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f368])).
% 29.33/5.47 thf(f368,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((ord_le282106107riable @ X0 @ X1) => ((ord_le282106107riable @ X1 @ X2) => (ord_le282106107riable @ X0 @ X2)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f81])).
% 29.33/5.47 thf(f81,axiom,(
% 29.33/5.47 ! [X4 : set_variable,X5 : set_variable,X6 : set_variable] : ((ord_le282106107riable @ X4 @ X5) => ((ord_le282106107riable @ X5 @ X6) => (ord_le282106107riable @ X4 @ X6)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_80_subset__trans)).
% 29.33/5.47 thf(f1304,plain,(
% 29.33/5.47 ($true != (ord_le282106107riable @ ua @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))) | spl47_2),
% 29.33/5.47 inference(avatar_component_clause,[status(thm)],[f1302])).
% 29.33/5.47 thf(f1302,definition,(
% 29.33/5.47 spl47_2 <=> ($true = (ord_le282106107riable @ ua @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))),
% 29.33/5.47 introduced(definition,[new_symbols(naming,[spl47_2])],[avatar_definition])).
% 29.33/5.47 thf(f1328,plain,(
% 29.33/5.47 ~spl47_2 | ~spl47_1),
% 29.33/5.47 inference(avatar_split_clause,[status(thm)],[f1285,f1298,f1302])).
% 29.33/5.47 thf(f1285,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ($true != (ord_le282106107riable @ ua @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))))),
% 29.33/5.47 inference(trivial_inequality_removal,[status(thm)],[f1280])).
% 29.33/5.47 thf(f1280,plain,(
% 29.33/5.47 ($true != (ord_le282106107riable @ ua @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))) | ((ord_le282106107riable @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true) | ($true != $true)),
% 29.33/5.47 inference(superposition,[status(thm)],[f1073,f1098])).
% 29.33/5.47 thf(f1098,plain,(
% 29.33/5.47 ( ! [X2 : set_variable,X0 : set_variable,X1 : set_variable] : (((ord_le282106107riable @ (sup_sup_set_variable @ X2 @ X1) @ X0) = $true) | ($true != (ord_le282106107riable @ X1 @ X0)) | ($true != (ord_le282106107riable @ X2 @ X0))) )),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f923])).
% 29.33/5.47 thf(f923,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (((ord_le282106107riable @ (sup_sup_set_variable @ X2 @ X1) @ X0) = $true) | ($true != (ord_le282106107riable @ X1 @ X0)) | ($true != (ord_le282106107riable @ X2 @ X0)))),
% 29.33/5.47 inference(flattening,[status(thm)],[f922])).
% 29.33/5.47 thf(f922,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((((ord_le282106107riable @ (sup_sup_set_variable @ X2 @ X1) @ X0) = $true) | ($true != (ord_le282106107riable @ X1 @ X0))) | ($true != (ord_le282106107riable @ X2 @ X0)))),
% 29.33/5.47 inference(ennf_transformation,[status(thm)],[f467])).
% 29.33/5.47 thf(f467,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : (($true = (ord_le282106107riable @ X2 @ X0)) => (($true = (ord_le282106107riable @ X1 @ X0)) => ((ord_le282106107riable @ (sup_sup_set_variable @ X2 @ X1) @ X0) = $true)))),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f466])).
% 29.33/5.47 thf(f466,plain,(
% 29.33/5.47 ! [X0 : set_variable,X1 : set_variable,X2 : set_variable] : ((ord_le282106107riable @ X2 @ X0) => ((ord_le282106107riable @ X1 @ X0) => (ord_le282106107riable @ (sup_sup_set_variable @ X2 @ X1) @ X0)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f181])).
% 29.33/5.47 thf(f181,axiom,(
% 29.33/5.47 ! [X7 : set_variable,X9 : set_variable,X8 : set_variable] : ((ord_le282106107riable @ X8 @ X7) => ((ord_le282106107riable @ X9 @ X7) => (ord_le282106107riable @ (sup_sup_set_variable @ X8 @ X9) @ X7)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',fact_180_sup__least)).
% 29.33/5.47 thf(f1073,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true)),
% 29.33/5.47 inference(cnf_transformation,[status(thm)],[f802])).
% 29.33/5.47 thf(f802,plain,(
% 29.33/5.47 ((ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) != $true)),
% 29.33/5.47 inference(flattening,[status(thm)],[f707])).
% 29.33/5.47 thf(f707,plain,(
% 29.33/5.47 ~((ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta))) = $true)),
% 29.33/5.47 inference(fool_elimination,[status(thm)],[f706])).
% 29.33/5.47 thf(f706,plain,(
% 29.33/5.47 ~(ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))),
% 29.33/5.47 inference(rectify,[status(thm)],[f356])).
% 29.33/5.47 thf(f356,negated_conjecture,(
% 29.33/5.47 ~(ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))),
% 29.33/5.47 inference(negated_conjecture,[status(cth)],[f355])).
% 29.33/5.47 thf(f355,conjecture,(
% 29.33/5.47 (ord_le282106107riable @ (sup_sup_set_variable @ ua @ (static_BVG @ (the_game @ (produc293487213n_game @ (uSubst516392814stappp @ sigma @ ua @ (compose @ alpha @ beta)))))) @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ (produc893821739n_game @ (uSubst516392814stappp @ sigma @ ua @ alpha)) @ beta)))),
% 29.33/5.47 file('/export/starexec/sandbox/tmp/tmp.zBOvDNTbqR/DTF2THF_19725.p',conj_0)).
% 29.33/5.47 % SZS output end Proof for DTF2THF_19725
% 29.33/5.47 % (20162)------------------------------
% 29.33/5.47 % (20162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.47 % (20162)Termination reason: Refutation
% 29.33/5.47
% 29.33/5.47 % (20162)Memory used [KB]: 8955
% 29.33/5.47 % (20162)Time elapsed: 1.394 s
% 29.33/5.47 % (20162)Instructions burned: 4734 (million)
% 29.33/5.47 % (20162)------------------------------
% 29.33/5.47 % (20162)------------------------------
% 29.33/5.47 % (20027)Success in time 3.907 s
%------------------------------------------------------------------------------