%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP204^1 : 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 : n015.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 3.18s 1.82s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 87 ( 76 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1057 ( 33 ~; 17 |; 6 &; 987 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 520 ( 520 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 76 usr; 12 con; 0-3 aty)
% Number of variables : 488 ( 488 ^; 0 !; 0 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
option_fml: $tType ).
thf(type_def_7,type,
option_trm: $tType ).
thf(type_def_8,type,
variable: $tType ).
thf(type_def_9,type,
set_variable: $tType ).
thf(type_def_10,type,
option_game: $tType ).
thf(type_def_11,type,
fml: $tType ).
thf(type_def_12,type,
game: $tType ).
thf(type_def_13,type,
trm: $tType ).
thf(type_def_14,type,
produc1739631244on_fml: $tType ).
thf(type_def_15,type,
char: $tType ).
thf(type_def_16,type,
produc799602994n_game: $tType ).
thf(type_def_17,type,
produc62062515n_game: $tType ).
thf(type_def_18,type,
produc1418842292n_game: $tType ).
thf(func_def_0,type,
produc1418842292n_game: $tType ).
thf(func_def_1,type,
produc62062515n_game: $tType ).
thf(func_def_2,type,
produc799602994n_game: $tType ).
thf(func_def_3,type,
produc1739631244on_fml: $tType ).
thf(func_def_4,type,
option_game: $tType ).
thf(func_def_5,type,
option_trm: $tType ).
thf(func_def_6,type,
option_fml: $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,
char: $tType ).
thf(func_def_11,type,
trm: $tType ).
thf(func_def_12,type,
fml: $tType ).
thf(func_def_13,type,
if_option_fml: $o > option_fml > option_fml > option_fml ).
thf(func_def_14,type,
if_option_trm: $o > option_trm > option_trm > option_trm ).
thf(func_def_15,type,
inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
thf(func_def_16,type,
inf_inf_o: $o > $o > $o ).
thf(func_def_17,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_18,type,
none_fml: option_fml ).
thf(func_def_19,type,
none_game: option_game ).
thf(func_def_20,type,
none_trm: option_trm ).
thf(func_def_21,type,
some_fml: fml > option_fml ).
thf(func_def_22,type,
some_game: game > option_game ).
thf(func_def_23,type,
some_trm: trm > option_trm ).
thf(func_def_24,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_25,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_26,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_27,type,
case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
thf(func_def_28,type,
case_o325794063ml_trm: option_fml > ( trm > option_fml ) > option_trm > option_fml ).
thf(func_def_29,type,
case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
thf(func_def_30,type,
the_fml: option_fml > fml ).
thf(func_def_31,type,
the_game: option_game > game ).
thf(func_def_32,type,
the_trm: option_trm > trm ).
thf(func_def_33,type,
bot_bot_variable_o: variable > $o ).
thf(func_def_34,type,
bot_bot_set_variable: set_variable ).
thf(func_def_35,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_36,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_37,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_38,type,
produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_39,type,
produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_40,type,
produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
thf(func_def_41,type,
produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
thf(func_def_42,type,
produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_43,type,
produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_44,type,
produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
thf(func_def_45,type,
produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
thf(func_def_46,type,
produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_47,type,
produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
thf(func_def_48,type,
produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_49,type,
produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_50,type,
produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
thf(func_def_51,type,
produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
thf(func_def_52,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_53,type,
produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_54,type,
produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
thf(func_def_55,type,
produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
thf(func_def_56,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_57,type,
produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
thf(func_def_58,type,
produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
thf(func_def_59,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_60,type,
is_empty_variable: set_variable > $o ).
thf(func_def_61,type,
static_FVF: fml > set_variable ).
thf(func_def_62,type,
static_FVT: trm > set_variable ).
thf(func_def_63,type,
geq: trm > trm > fml ).
thf(func_def_64,type,
pred: char > trm > fml ).
thf(func_def_65,type,
const: char > trm ).
thf(func_def_66,type,
func: char > trm > trm ).
thf(func_def_67,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_68,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(func_def_69,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_70,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_71,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_72,type,
member_variable: variable > set_variable > $o ).
thf(func_def_73,type,
ua: set_variable ).
thf(func_def_74,type,
va: set_variable ).
thf(func_def_75,type,
sigma: produc1418842292n_game ).
thf(func_def_76,type,
theta: trm ).
thf(func_def_77,type,
p: char ).
thf(func_def_78,type,
vv: set_variable > set_variable > variable ).
thf(func_def_79,type,
vva: set_variable > set_variable > variable ).
thf(func_def_96,type,
sK0: char > set_variable > produc1418842292n_game > fml ).
thf(func_def_97,type,
sK1: char > produc1418842292n_game > set_variable > trm ).
thf(func_def_98,type,
sK2: char > set_variable > produc1418842292n_game > trm ).
thf(func_def_99,type,
sK3: ( char > option_trm > $o ) > trm ).
thf(func_def_100,type,
sK4: ( char > option_trm > $o ) > char ).
thf(func_def_101,type,
sK5: ( char > option_trm > $o ) > char ).
thf(func_def_102,type,
sK6: set_variable > produc1418842292n_game > char > trm ).
thf(f1158,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1136,f1153,f1157]) ).
thf(f1157,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f1156]) ).
thf(f1156,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f1155,f1154]) ).
thf(f1154,plain,
( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1061,f971]) ).
thf(f971,plain,
( ( uSubst516392818stappt @ sigma @ va @ theta )
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,axiom,
( ( uSubst516392818stappt @ sigma @ va @ theta )
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_8_f7) ).
thf(f1061,plain,
( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va )
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ),
inference(definition_unfolding,[status(thm)],[f942,f937,f1009,f953,f981,f944]) ).
thf(f944,plain,
( produc1420172399on_fml
= ( ^ [Y0: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y1: produc799602994n_game,Y2: char] :
( produc347802313on_fml
@ ^ [Y3: char > option_fml,Y4: char > option_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
thf(f394,plain,
( produc1420172399on_fml
= ( ^ [Y0: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y1: produc799602994n_game,Y2: char] :
( produc347802313on_fml
@ ^ [Y3: char > option_fml,Y4: char > option_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f393]) ).
thf(f393,plain,
( produc1420172399on_fml
= ( ^ [X0: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X1: produc799602994n_game,X2: char] :
( produc347802313on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : ( X0 @ X3 @ X4 @ X2 )
@ X1 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( produc1420172399on_fml
= ( ^ [X16: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X17: produc799602994n_game,X18: char] :
( produc347802313on_fml
@ ^ [X19: char > option_fml,X20: char > option_game] : ( X16 @ X19 @ X20 @ X18 )
@ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_13_case__prod__app) ).
thf(f981,plain,
( produc1615133358on_fml
= ( ^ [Y0: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y1: produc62062515n_game,Y2: char] :
( produc154833544on_fml
@ ^ [Y3: char > option_trm,Y4: produc799602994n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f700]) ).
thf(f700,plain,
( produc1615133358on_fml
= ( ^ [Y0: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y1: produc62062515n_game,Y2: char] :
( produc154833544on_fml
@ ^ [Y3: char > option_trm,Y4: produc799602994n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f699]) ).
thf(f699,plain,
( produc1615133358on_fml
= ( ^ [X0: ( char > option_trm ) > produc799602994n_game > char > option_fml,X1: produc62062515n_game,X2: char] :
( produc154833544on_fml
@ ^ [X3: char > option_trm,X4: produc799602994n_game] : ( X0 @ X3 @ X4 @ X2 )
@ X1 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( produc1615133358on_fml
= ( ^ [X16: ( char > option_trm ) > produc799602994n_game > char > option_fml,X17: produc62062515n_game,X18: char] :
( produc154833544on_fml
@ ^ [X19: char > option_trm,X20: produc799602994n_game] : ( X16 @ X19 @ X20 @ X18 )
@ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_11_case__prod__app) ).
thf(f953,plain,
( produc1250175341on_fml
= ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f610]) ).
thf(f610,plain,
( produc1250175341on_fml
= ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f609]) ).
thf(f609,plain,
( produc1250175341on_fml
= ( ^ [X0: ( char > option_trm ) > produc62062515n_game > char > option_fml,X1: produc1418842292n_game,X2: char] :
( produc1499310791on_fml
@ ^ [X3: char > option_trm,X4: produc62062515n_game] : ( X0 @ X3 @ X4 @ X2 )
@ X1 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( produc1250175341on_fml
= ( ^ [X16: ( char > option_trm ) > produc62062515n_game > char > option_fml,X17: produc1418842292n_game,X18: char] :
( produc1499310791on_fml
@ ^ [X19: char > option_trm,X20: produc62062515n_game] : ( X16 @ X19 @ X20 @ X18 )
@ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_9_case__prod__app) ).
thf(f1009,plain,
( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ),
inference(definition_unfolding,[status(thm)],[f943,f953,f981,f944]) ).
thf(f943,plain,
( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ),
inference(cnf_transformation,[status(thm)],[f903]) ).
thf(f903,plain,
( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
& ( none_fml
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f364]) ).
thf(f364,plain,
~ ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( none_fml
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f363]) ).
thf(f363,plain,
~ ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X0: char > option_trm] :
( produc1615133358on_fml
@ ^ [X1: char > option_trm] :
( produc1420172399on_fml
@ ^ [X2: char > option_fml,X3: char > option_game] : X2 ) )
@ sigma
@ p ) ) )
@ va )
= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
~ ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) )
@ va )
= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062) ).
thf(f937,plain,
( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ),
inference(cnf_transformation,[status(thm)],[f897]) ).
thf(f897,plain,
( ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
& ( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(ennf_transformation,[status(thm)],[f478]) ).
thf(f478,plain,
~ ( ( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(fool_elimination,[status(thm)],[f477]) ).
thf(f477,plain,
~ ( ( none_fml
= ( produc1250175341on_fml
@ ^ [X0: char > option_trm] :
( produc1615133358on_fml
@ ^ [X1: char > option_trm] :
( produc1420172399on_fml
@ ^ [X2: char > option_fml,X3: char > option_game] : X2 ) )
@ sigma
@ p ) )
| ( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
inference(rectify,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
~ ( ( none_fml
= ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) )
| ( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
( ( none_fml
= ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) )
| ( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',conj_0) ).
thf(f942,plain,
( none_fml
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ),
inference(cnf_transformation,[status(thm)],[f903]) ).
thf(f1155,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) )
| ~ spl7_2 ),
inference(forward_demodulation,[status(thm)],[f1135,f971]) ).
thf(f1135,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f1133]) ).
thf(f1133,definition,
( spl7_2
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f1153,plain,
~ spl7_1,
inference(avatar_split_clause,[status(thm)],[f1088,f1129]) ).
thf(f1129,definition,
( spl7_1
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f1088,plain,
( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ),
inference(beta_eta_normalization,[status(thm)],[f1016]) ).
thf(f1016,plain,
( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ),
inference(definition_unfolding,[status(thm)],[f936,f937,f953,f981,f944]) ).
thf(f936,plain,
( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ),
inference(cnf_transformation,[status(thm)],[f897]) ).
thf(f1136,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f1122,f1133,f1129]) ).
thf(f1122,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) )
@ va )
@ ( the_fml
@ ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ) )
| ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( produc1499310791on_fml
@ ^ [Y0: char > option_trm] :
( produc154833544on_fml
@ ^ [Y1: char > option_trm] :
( produc347802313on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : ( Y2 @ p ) ) )
@ sigma ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1121]) ).
thf(f1121,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va )
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) )
| ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) )
| ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) )
@ ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va )
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) )
| ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va )
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( ^ [Y0: ( char > option_trm ) > produc62062515n_game > char > option_fml,Y1: produc1418842292n_game,Y2: char] :
( produc1499310791on_fml
@ ^ [Y3: char > option_trm,Y4: produc62062515n_game] : ( Y0 @ Y3 @ Y4 @ Y2 )
@ Y1 )
@ ^ [Y0: char > option_trm] :
( ^ [Y1: ( char > option_trm ) > produc799602994n_game > char > option_fml,Y2: produc62062515n_game,Y3: char] :
( produc154833544on_fml
@ ^ [Y4: char > option_trm,Y5: produc799602994n_game] : ( Y1 @ Y4 @ Y5 @ Y3 )
@ Y2 )
@ ^ [Y1: char > option_trm] :
( ^ [Y2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Y3: produc799602994n_game,Y4: char] :
( produc347802313on_fml
@ ^ [Y5: char > option_fml,Y6: char > option_game] : ( Y2 @ Y5 @ Y6 @ Y4 )
@ Y3 )
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ) ),
inference(definition_unfolding,[status(thm)],[f989,f1009,f953,f981,f944,f1009,f953,f981,f944,f937,f953,f981,f944]) ).
thf(f989,plain,
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(cnf_transformation,[status(thm)],[f894]) ).
thf(f894,plain,
( ( ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ) )
& ( ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(ennf_transformation,[status(thm)],[f412]) ).
thf(f412,plain,
( ~ ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ) )
& ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
inference(fool_elimination,[status(thm)],[f411]) ).
thf(f411,plain,
( ~ ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X0: char > option_trm] :
( produc1615133358on_fml
@ ^ [X1: char > option_trm] :
( produc1420172399on_fml
@ ^ [X2: char > option_fml,X3: char > option_game] : X2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ sigma
@ p ) ) )
@ va )
!= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> ( none_fml
= ( produc1250175341on_fml
@ ^ [X12: char > option_trm] :
( produc1615133358on_fml
@ ^ [X13: char > option_trm] :
( produc1420172399on_fml
@ ^ [X14: char > option_fml,X15: char > option_game] : X14 ) )
@ sigma
@ p ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ~ ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) )
@ va )
!= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> ( none_fml
= ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP204^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n015.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 08:30:02 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : ITP204^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.47 % Domain : Interactive Theorem Proving
% 0.20/0.47 % Problem : Sledgehammer USubst problem prob_793__6341386_1
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Des21]
% 0.20/0.47 % Names : USubst/prob_793__6341386_1 [Des21]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.20/0.47 % Syntax : Number of formulae : 438 ( 222 unt; 80 typ; 0 def)
% 0.20/0.47 % Number of atoms : 895 ( 538 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 9 ( 2 avg)
% 0.20/0.47 % Number of connectives : 2963 ( 148 ~; 31 |; 71 &;2383 @)
% 0.20/0.47 % ( 0 <=>; 330 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 19 ( 5 avg)
% 0.20/0.47 % Number of types : 14 ( 13 usr)
% 0.20/0.47 % Number of type conns : 693 ( 693 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 70 ( 67 usr; 11 con; 0-3 aty)
% 0.20/0.47 % Number of variables : 1209 ( 339 ^; 849 !; 21 ?;1209 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:38.645
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % Could-be-implicit typings (13)
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.20/0.47 produc1418842292n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 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__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J,type,
% 0.20/0.47 produc62062515n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__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,type,
% 0.20/0.47 produc799602994n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1739631244on_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.20/0.47 option_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 option_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 option_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.20/0.47 set_variable: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ovariable,type,
% 0.20/0.47 variable: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ogame,type,
% 0.20/0.47 game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__String__Ochar,type,
% 0.20/0.47 char: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Otrm,type,
% 0.20/0.47 trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ofml,type,
% 0.20/0.47 fml: $tType ).
% 0.20/0.47
% 0.20/0.47 % Explicit typings (67)
% 0.20/0.47 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 if_option_fml: $o > option_fml > option_fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.20/0.47 inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
% 0.20/0.47 inf_inf_o: $o > $o > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.20/0.47 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 0.20/0.47 none_fml: option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.20/0.47 none_game: option_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 0.20/0.47 none_trm: option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 0.20/0.47 some_fml: fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 0.20/0.47 some_game: game > option_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 0.20/0.47 some_trm: trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 0.20/0.47 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 0.20/0.47 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 0.20/0.47 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Ofml,type,
% 0.20/0.47 case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Otrm,type,
% 0.20/0.47 case_o325794063ml_trm: option_fml > ( trm > option_fml ) > option_trm > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Syntax__Otrm,type,
% 0.20/0.47 case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 0.20/0.47 the_fml: option_fml > fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.20/0.47 the_game: option_game > game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 0.20/0.47 the_trm: option_trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.20/0.47 bot_bot_variable_o: variable > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.20/0.47 bot_bot_set_variable: set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.20/0.47 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.20/0.47 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.20/0.47 collect_variable: ( variable > $o ) > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 0.20/0.47 is_empty_variable: set_variable > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Static__Semantics_OFVF,type,
% 0.20/0.47 static_FVF: fml > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Static__Semantics_OFVT,type,
% 0.20/0.47 static_FVT: trm > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.20/0.47 geq: trm > trm > fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Ofml_OPred,type,
% 0.20/0.47 pred: char > trm > fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.20/0.47 const: char > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.20/0.47 func: char > trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 0.20/0.47 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 0.20/0.47 uSubst1408967625substt: trm > produc1418842292n_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 0.20/0.47 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 0.20/0.47 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.20/0.47 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.20/0.47 member_variable: variable > set_variable > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_Ua____,type,
% 0.20/0.47 ua: set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_Va____,type,
% 0.20/0.47 va: set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v__092_060sigma_062,type,
% 0.20/0.47 sigma: produc1418842292n_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v__092_060theta_062____,type,
% 0.20/0.47 theta: trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_p____,type,
% 0.20/0.47 p: char ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_vv____,type,
% 0.20/0.47 vv: set_variable > set_variable > variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_vva____,type,
% 0.20/0.47 vva: set_variable > set_variable > variable ).
% 0.20/0.47
% 0.20/0.47 % Relevant facts (352)
% 0.20/0.47 thf(fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062,axiom,
% 0.20/0.47 ! [X0: set_variable,X1: set_variable] :
% 0.20/0.47 ( ( ? [V2: variable] :
% 0.20/0.47 ( ( member_variable @ V2 @ X1 )
% 0.20/0.47 & ? [V3: variable] :
% 0.20/0.47 ( ( member_variable @ V3 @ X0 )
% 0.20/0.47 & ( V2 = V3 ) ) ) )
% 0.20/0.47 = ( ( member_variable @ ( vv @ X0 @ X1 ) @ X1 )
% 0.20/0.47 & ? [V3: variable] :
% 0.20/0.47 ( ( member_variable @ V3 @ X0 )
% 0.20/0.47 & ( ( vv @ X0 @ X1 )
% 0.20/0.47 = V3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<forall>x0 x1. (\<exists>v2. v2 \<in> x1 \<and> (\<exists>v3. v3 \<in> x0 \<and> v2 = v3)) = (vv x0 x1 \<in> x1 \<and> (\<exists>v3. v3 \<in> x0 \<and> vv x0 x1 = v3))\<close>
% 0.20/0.47 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 0.20/0.47 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 != none_fml ) ).
% 0.20/0.47
% 0.20/0.47 % Pred.prems(2)
% 0.20/0.47 thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
% 0.20/0.47 ~ ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 = none_fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> undeff\<close>
% 0.20/0.47 thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
% 0.20/0.47 ( ~ ( ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 => ( none_fml
% 0.20/0.47 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
% 0.20/0.47 => ( ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p )
% 0.20/0.47 = none_fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> usubstappf \<sigma> V (Pred p \<theta>) \<Longrightarrow> SPreds \<sigma> p = undeff\<close>
% 0.20/0.47 thf(fact_4_usubstappf__det,axiom,
% 0.20/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Phi: fml,V: set_variable] :
% 0.20/0.47 ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.20/0.47 != none_fml )
% 0.20/0.47 => ( ( ( uSubst516392804stappf @ Sigma @ V @ Phi )
% 0.20/0.47 != none_fml )
% 0.20/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.20/0.47 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappf_det
% 0.20/0.47 thf(fact_5_f8,axiom,
% 0.20/0.47 ( ( ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p )
% 0.20/0.47 = none_fml )
% 0.20/0.47 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f8
% 0.20/0.47 thf(fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062,axiom,
% 0.20/0.47 ( ~ ( member_variable
% 0.20/0.47 @ ( vv @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 | ~ ( member_variable
% 0.20/0.47 @ ( vva @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 | ( ( vv @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 != ( vva @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>vv V (FVF (the (SPreds \<sigma> p))) \<notin> FVF (the (SPreds \<sigma> p)) \<or> vva V (FVF (the (SPreds \<sigma> p))) \<notin> V \<or> vv V (FVF (the (SPreds \<sigma> p))) \<noteq> vva V (FVF (the (SPreds \<sigma> p)))\<close>
% 0.20/0.47 thf(fact_7_fml_Oinject_I1_J,axiom,
% 0.20/0.47 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 0.20/0.47 ( ( ( pred @ X11 @ X12 )
% 0.20/0.47 = ( pred @ Y11 @ Y12 ) )
% 0.20/0.47 = ( ( X11 = Y11 )
% 0.20/0.47 & ( X12 = Y12 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fml.inject(1)
% 0.20/0.47 thf(fact_8_f7,axiom,
% 0.20/0.47 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 0.20/0.47 = ( uSubst516392818stappt @ sigma @ va @ theta ) ) ).
% 0.20/0.47
% 0.20/0.47 % f7
% 0.20/0.47 thf(fact_9_case__prod__app,axiom,
% 0.20/0.47 ( produc1250175341on_fml
% 0.20/0.47 = ( ^ [F: ( char > option_trm ) > produc62062515n_game > char > option_fml,X: produc1418842292n_game,Y: char] :
% 0.20/0.47 ( produc1499310791on_fml
% 0.20/0.47 @ ^ [L: char > option_trm,R: produc62062515n_game] : ( F @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_10_case__prod__app,axiom,
% 0.20/0.47 ( produc1231571704on_trm
% 0.20/0.47 = ( ^ [F: ( char > option_trm ) > produc799602994n_game > char > option_trm,X: produc62062515n_game,Y: char] :
% 0.20/0.47 ( produc692578258on_trm
% 0.20/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_11_case__prod__app,axiom,
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 = ( ^ [F: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 0.20/0.47 ( produc154833544on_fml
% 0.20/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_12_case__prod__app,axiom,
% 0.20/0.47 ( produc1036610745on_trm
% 0.20/0.47 = ( ^ [F: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 0.20/0.47 ( produc885547027on_trm
% 0.20/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_13_case__prod__app,axiom,
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 = ( ^ [F: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 0.20/0.47 ( produc347802313on_fml
% 0.20/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_14_f1,axiom,
% 0.20/0.47 ! [V4: variable] :
% 0.20/0.47 ( ~ ( member_variable @ V4 @ va )
% 0.20/0.47 | ( member_variable @ V4 @ ua ) ) ).
% 0.20/0.47
% 0.20/0.47 % f1
% 0.20/0.47 thf(fact_15_f10,axiom,
% 0.20/0.47 ( ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 | ! [V4: variable] :
% 0.20/0.47 ( ~ ( member_variable @ V4
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 | ! [Va: variable] :
% 0.20/0.47 ( ~ ( member_variable @ Va @ va )
% 0.20/0.47 | ( V4 != Va ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 | ( ( member_variable
% 0.20/0.47 @ ( vv @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 & ( member_variable
% 0.20/0.47 @ ( vva @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 & ( ( vv @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) )
% 0.20/0.47 = ( vva @ va
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f10
% 0.20/0.47 thf(fact_16_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_17_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_18_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc885547027on_trm @ F2 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_19_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc885547027on_trm @ F2 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_20_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_trm ) > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1036610745on_trm @ F2 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_21_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_trm ) > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1036610745on_trm @ F2 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_22_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_fml ) > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1420172399on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_23_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_fml ) > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1420172399on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_24_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > char > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc1036610745on_trm
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_25_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > char > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 0.20/0.47 = ( produc1420172399on_fml
% 0.20/0.47 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_26_usubstappf__pred2,axiom,
% 0.20/0.47 ! [Sigma: produc1418842292n_game,P2: char,R2: fml,U: set_variable,Theta: trm] :
% 0.20/0.47 ( ( ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ Sigma
% 0.20/0.47 @ P2 )
% 0.20/0.47 = ( some_fml @ R2 ) )
% 0.20/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.20/0.47 = none_fml ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappf_pred2
% 0.20/0.47 thf(fact_27_f2,axiom,
% 0.20/0.47 ! [Z: option_fml,F3: fml > option_fml,Za: option_fml] :
% 0.20/0.47 ( ( ( Za = none_fml )
% 0.20/0.47 => ( ( case_o209804997ml_fml @ Z @ F3 @ Za )
% 0.20/0.47 = Z ) )
% 0.20/0.47 & ( ( Za != none_fml )
% 0.20/0.47 => ( ( case_o209804997ml_fml @ Z @ F3 @ Za )
% 0.20/0.47 = ( F3 @ ( the_fml @ Za ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f2
% 0.20/0.47 thf(fact_28_Pred_Oprems_I1_J,axiom,
% 0.20/0.47 ord_le282106107riable @ va @ ua ).
% 0.20/0.47
% 0.20/0.47 % Pred.prems(1)
% 0.20/0.47 thf(fact_29_f9,axiom,
% 0.20/0.47 ! [V5: set_variable,Va2: set_variable] :
% 0.20/0.47 ( ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 | ! [V4: variable] :
% 0.20/0.47 ( ~ ( member_variable @ V4 @ V5 )
% 0.20/0.47 | ! [Va: variable] :
% 0.20/0.47 ( ~ ( member_variable @ Va @ Va2 )
% 0.20/0.47 | ( V4 != Va ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 | ( ( member_variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 0.20/0.47 & ( member_variable @ ( vva @ Va2 @ V5 ) @ Va2 )
% 0.20/0.47 & ( ( vv @ Va2 @ V5 )
% 0.20/0.47 = ( vva @ Va2 @ V5 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f9
% 0.20/0.47 thf(fact_30__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.47 ~ ! [Vva: set_variable > set_variable > variable] :
% 0.20/0.47 ~ ! [V5: set_variable,Va2: set_variable] :
% 0.20/0.47 ( ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 | ! [V4: variable] :
% 0.20/0.47 ( ~ ( member_variable @ V4 @ V5 )
% 0.20/0.47 | ! [Va: variable] :
% 0.20/0.47 ( ~ ( member_variable @ Va @ Va2 )
% 0.20/0.47 | ( V4 != Va ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 | ( ( member_variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 0.20/0.47 & ( member_variable @ ( Vva @ Va2 @ V5 ) @ Va2 )
% 0.20/0.47 & ( ( vv @ Va2 @ V5 )
% 0.20/0.47 = ( Vva @ Va2 @ V5 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<And>thesis. (\<And>vva. \<forall>V Va. (V \<inter> Va \<noteq> {} \<or> (\<forall>v. v \<notin> V \<or> (\<forall>va. va \<notin> Va \<or> v \<noteq> va))) \<and> (V \<inter> Va = {} \<or> vv Va V \<in> V \<and> vva Va V \<in> Va \<and> vv Va V = vva Va V) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.47 thf(fact_31_option_Oinject,axiom,
% 0.20/0.47 ! [X22: fml,Y2: fml] :
% 0.20/0.47 ( ( ( some_fml @ X22 )
% 0.20/0.47 = ( some_fml @ Y2 ) )
% 0.20/0.47 = ( X22 = Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inject
% 0.20/0.47 thf(fact_32_option_Oinject,axiom,
% 0.20/0.47 ! [X22: trm,Y2: trm] :
% 0.20/0.47 ( ( ( some_trm @ X22 )
% 0.20/0.47 = ( some_trm @ Y2 ) )
% 0.20/0.47 = ( X22 = Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inject
% 0.20/0.47 thf(fact_33_option_Oinject,axiom,
% 0.20/0.47 ! [X22: game,Y2: game] :
% 0.20/0.47 ( ( ( some_game @ X22 )
% 0.20/0.47 = ( some_game @ Y2 ) )
% 0.20/0.47 = ( X22 = Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inject
% 0.20/0.47 thf(fact_34_f5,axiom,
% 0.20/0.47 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 0.20/0.47 != none_trm ) ).
% 0.20/0.47
% 0.20/0.47 % f5
% 0.20/0.47 thf(fact_35_not__Some__eq,axiom,
% 0.20/0.47 ! [X3: option_fml] :
% 0.20/0.47 ( ( ! [Y: fml] :
% 0.20/0.47 ( X3
% 0.20/0.47 != ( some_fml @ Y ) ) )
% 0.20/0.47 = ( X3 = none_fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_Some_eq
% 0.20/0.47 thf(fact_36_not__Some__eq,axiom,
% 0.20/0.47 ! [X3: option_trm] :
% 0.20/0.47 ( ( ! [Y: trm] :
% 0.20/0.47 ( X3
% 0.20/0.47 != ( some_trm @ Y ) ) )
% 0.20/0.47 = ( X3 = none_trm ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_Some_eq
% 0.20/0.47 thf(fact_37_not__Some__eq,axiom,
% 0.20/0.47 ! [X3: option_game] :
% 0.20/0.47 ( ( ! [Y: game] :
% 0.20/0.47 ( X3
% 0.20/0.47 != ( some_game @ Y ) ) )
% 0.20/0.47 = ( X3 = none_game ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_Some_eq
% 0.20/0.47 thf(fact_38_not__None__eq,axiom,
% 0.20/0.47 ! [X3: option_fml] :
% 0.20/0.47 ( ( X3 != none_fml )
% 0.20/0.47 = ( ? [Y: fml] :
% 0.20/0.47 ( X3
% 0.20/0.47 = ( some_fml @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_None_eq
% 0.20/0.47 thf(fact_39_not__None__eq,axiom,
% 0.20/0.47 ! [X3: option_trm] :
% 0.20/0.47 ( ( X3 != none_trm )
% 0.20/0.47 = ( ? [Y: trm] :
% 0.20/0.47 ( X3
% 0.20/0.47 = ( some_trm @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_None_eq
% 0.20/0.47 thf(fact_40_not__None__eq,axiom,
% 0.20/0.47 ! [X3: option_game] :
% 0.20/0.47 ( ( X3 != none_game )
% 0.20/0.47 = ( ? [Y: game] :
% 0.20/0.47 ( X3
% 0.20/0.47 = ( some_game @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_None_eq
% 0.20/0.47 thf(fact_41_option_Ocollapse,axiom,
% 0.20/0.47 ! [Option: option_fml] :
% 0.20/0.47 ( ( Option != none_fml )
% 0.20/0.47 => ( ( some_fml @ ( the_fml @ Option ) )
% 0.20/0.47 = Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.collapse
% 0.20/0.47 thf(fact_42_option_Ocollapse,axiom,
% 0.20/0.47 ! [Option: option_trm] :
% 0.20/0.47 ( ( Option != none_trm )
% 0.20/0.47 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.20/0.47 = Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.collapse
% 0.20/0.47 thf(fact_43_option_Ocollapse,axiom,
% 0.20/0.47 ! [Option: option_game] :
% 0.20/0.47 ( ( Option != none_game )
% 0.20/0.47 => ( ( some_game @ ( the_game @ Option ) )
% 0.20/0.47 = Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.collapse
% 0.20/0.47 thf(fact_44_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: $o,F22: game > $o,X22: game] :
% 0.20/0.47 ( ( case_option_o_game @ F1 @ F22 @ ( some_game @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_45_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: $o,F22: trm > $o,X22: trm] :
% 0.20/0.47 ( ( case_option_o_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_46_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: $o,F22: fml > $o,X22: fml] :
% 0.20/0.47 ( ( case_option_o_fml @ F1 @ F22 @ ( some_fml @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_47_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: option_fml,F22: fml > option_fml,X22: fml] :
% 0.20/0.47 ( ( case_o209804997ml_fml @ F1 @ F22 @ ( some_fml @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_48_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: option_fml,F22: trm > option_fml,X22: trm] :
% 0.20/0.47 ( ( case_o325794063ml_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_49_option_Osimps_I5_J,axiom,
% 0.20/0.47 ! [F1: option_trm,F22: trm > option_trm,X22: trm] :
% 0.20/0.47 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.simps(5)
% 0.20/0.47 thf(fact_50_option_Osel,axiom,
% 0.20/0.47 ! [X22: fml] :
% 0.20/0.47 ( ( the_fml @ ( some_fml @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % option.sel
% 0.20/0.47 thf(fact_51_option_Osel,axiom,
% 0.20/0.47 ! [X22: trm] :
% 0.20/0.47 ( ( the_trm @ ( some_trm @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % option.sel
% 0.20/0.47 thf(fact_52_option_Osel,axiom,
% 0.20/0.47 ! [X22: game] :
% 0.20/0.47 ( ( the_game @ ( some_game @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % option.sel
% 0.20/0.47 thf(fact_53_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_game )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_game @ ( the_game @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_game @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_54_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_trm )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_55_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_fml )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_56_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.20/0.47 ( ( P3 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_fml )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_57_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_trm )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_58_option_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ( ( Option = none_trm )
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel
% 0.20/0.47 thf(fact_59_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_fml,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.20/0.47 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_o209804997ml_fml @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_60_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_fml,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_o325794063ml_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_61_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_trm,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_o487727941rm_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_62_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_fml,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_o325794063ml_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_63_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_o487727941rm_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_64_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 0.20/0.47 ( ( H @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option_o_game @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: game] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_65_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option_o_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_66_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 0.20/0.47 ( ( H @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option_o_fml @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_67_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.20/0.47 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option_o_fml @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_68_option_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.20/0.47 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( case_option_o_trm @ ( H @ F1 )
% 0.20/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.20/0.47 @ Option ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_distrib
% 0.20/0.47 thf(fact_69_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_game )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_game @ ( the_game @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_game @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_70_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_71_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 0.20/0.47 ( ( P3 @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_fml )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_72_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.20/0.47 ( ( P3 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_fml )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_73_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_74_option_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.20/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.20/0.47 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.split_sel_asm
% 0.20/0.47 thf(fact_75_usubstappt__det,axiom,
% 0.20/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 0.20/0.47 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.47 != none_trm )
% 0.20/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 0.20/0.47 != none_trm )
% 0.20/0.47 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.47 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt_det
% 0.20/0.47 thf(fact_76_usubstappt__antimon,axiom,
% 0.20/0.47 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Theta: trm] :
% 0.20/0.47 ( ( ord_le282106107riable @ V @ U )
% 0.20/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.47 != none_trm )
% 0.20/0.47 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.47 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % usubstappt_antimon
% 0.20/0.47 thf(fact_77_option_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Option: option_fml] :
% 0.20/0.47 ( ( Option != none_fml )
% 0.20/0.47 => ( Option
% 0.20/0.47 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust_sel
% 0.20/0.47 thf(fact_78_option_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Option: option_trm] :
% 0.20/0.47 ( ( Option != none_trm )
% 0.20/0.47 => ( Option
% 0.20/0.47 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust_sel
% 0.20/0.47 thf(fact_79_option_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Option: option_game] :
% 0.20/0.47 ( ( Option != none_game )
% 0.20/0.47 => ( Option
% 0.20/0.47 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust_sel
% 0.20/0.47 thf(fact_80_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_fml,P3: option_fml > option_fml > $o,Y3: option_fml] :
% 0.20/0.47 ( ( ( X3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: fml,B: fml] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_fml @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_fml @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_81_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_fml,P3: option_fml > option_trm > $o,Y3: option_trm] :
% 0.20/0.47 ( ( ( X3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: fml,B: trm] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_fml @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_trm @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_82_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_fml,P3: option_fml > option_game > $o,Y3: option_game] :
% 0.20/0.47 ( ( ( X3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: fml,B: game] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_fml @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_game @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_83_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_trm,P3: option_trm > option_fml > $o,Y3: option_fml] :
% 0.20/0.47 ( ( ( X3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: trm,B: fml] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_trm @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_fml @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_84_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_trm,P3: option_trm > option_trm > $o,Y3: option_trm] :
% 0.20/0.47 ( ( ( X3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: trm,B: trm] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_trm @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_trm @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_85_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_trm,P3: option_trm > option_game > $o,Y3: option_game] :
% 0.20/0.47 ( ( ( X3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: trm,B: game] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_trm @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_game @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_86_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_game,P3: option_game > option_fml > $o,Y3: option_fml] :
% 0.20/0.47 ( ( ( X3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_fml )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: game,B: fml] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_game @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_fml @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_87_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_game,P3: option_game > option_trm > $o,Y3: option_trm] :
% 0.20/0.47 ( ( ( X3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_trm )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: game,B: trm] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_game @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_trm @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_88_combine__options__cases,axiom,
% 0.20/0.47 ! [X3: option_game,P3: option_game > option_game > $o,Y3: option_game] :
% 0.20/0.47 ( ( ( X3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ( ( Y3 = none_game )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) )
% 0.20/0.47 => ( ! [A: game,B: game] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( some_game @ A ) )
% 0.20/0.47 => ( ( Y3
% 0.20/0.47 = ( some_game @ B ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) )
% 0.20/0.47 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % combine_options_cases
% 0.20/0.47 thf(fact_89_split__option__all,axiom,
% 0.20/0.47 ( ( ^ [P4: option_fml > $o] :
% 0.20/0.47 ! [X4: option_fml] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_fml > $o] :
% 0.20/0.47 ( ( P @ none_fml )
% 0.20/0.47 & ! [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_all
% 0.20/0.47 thf(fact_90_split__option__all,axiom,
% 0.20/0.47 ( ( ^ [P4: option_trm > $o] :
% 0.20/0.47 ! [X4: option_trm] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_trm > $o] :
% 0.20/0.47 ( ( P @ none_trm )
% 0.20/0.47 & ! [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_all
% 0.20/0.47 thf(fact_91_split__option__all,axiom,
% 0.20/0.47 ( ( ^ [P4: option_game > $o] :
% 0.20/0.47 ! [X4: option_game] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_game > $o] :
% 0.20/0.47 ( ( P @ none_game )
% 0.20/0.47 & ! [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_all
% 0.20/0.47 thf(fact_92_split__option__ex,axiom,
% 0.20/0.47 ( ( ^ [P4: option_fml > $o] :
% 0.20/0.47 ? [X4: option_fml] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_fml > $o] :
% 0.20/0.47 ( ( P @ none_fml )
% 0.20/0.47 | ? [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_ex
% 0.20/0.47 thf(fact_93_split__option__ex,axiom,
% 0.20/0.47 ( ( ^ [P4: option_trm > $o] :
% 0.20/0.47 ? [X4: option_trm] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_trm > $o] :
% 0.20/0.47 ( ( P @ none_trm )
% 0.20/0.47 | ? [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_ex
% 0.20/0.47 thf(fact_94_split__option__ex,axiom,
% 0.20/0.47 ( ( ^ [P4: option_game > $o] :
% 0.20/0.47 ? [X4: option_game] : ( P4 @ X4 ) )
% 0.20/0.47 = ( ^ [P: option_game > $o] :
% 0.20/0.47 ( ( P @ none_game )
% 0.20/0.47 | ? [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_option_ex
% 0.20/0.47 thf(fact_95_option_Oinducts,axiom,
% 0.20/0.47 ! [P3: option_fml > $o,Option: option_fml] :
% 0.20/0.47 ( ( P3 @ none_fml )
% 0.20/0.47 => ( ! [X5: fml] : ( P3 @ ( some_fml @ X5 ) )
% 0.20/0.47 => ( P3 @ Option ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inducts
% 0.20/0.47 thf(fact_96_option_Oinducts,axiom,
% 0.20/0.47 ! [P3: option_trm > $o,Option: option_trm] :
% 0.20/0.47 ( ( P3 @ none_trm )
% 0.20/0.47 => ( ! [X5: trm] : ( P3 @ ( some_trm @ X5 ) )
% 0.20/0.47 => ( P3 @ Option ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inducts
% 0.20/0.47 thf(fact_97_option_Oinducts,axiom,
% 0.20/0.47 ! [P3: option_game > $o,Option: option_game] :
% 0.20/0.47 ( ( P3 @ none_game )
% 0.20/0.47 => ( ! [X5: game] : ( P3 @ ( some_game @ X5 ) )
% 0.20/0.47 => ( P3 @ Option ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.inducts
% 0.20/0.47 thf(fact_98_option_Oexhaust,axiom,
% 0.20/0.47 ! [Y3: option_fml] :
% 0.20/0.47 ( ( Y3 != none_fml )
% 0.20/0.47 => ~ ! [X23: fml] :
% 0.20/0.47 ( Y3
% 0.20/0.47 != ( some_fml @ X23 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust
% 0.20/0.47 thf(fact_99_option_Oexhaust,axiom,
% 0.20/0.47 ! [Y3: option_trm] :
% 0.20/0.47 ( ( Y3 != none_trm )
% 0.20/0.47 => ~ ! [X23: trm] :
% 0.20/0.47 ( Y3
% 0.20/0.47 != ( some_trm @ X23 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust
% 0.20/0.47 thf(fact_100_option_Oexhaust,axiom,
% 0.20/0.47 ! [Y3: option_game] :
% 0.20/0.47 ( ( Y3 != none_game )
% 0.20/0.47 => ~ ! [X23: game] :
% 0.20/0.47 ( Y3
% 0.20/0.47 != ( some_game @ X23 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.exhaust
% 0.20/0.47 thf(fact_101_option_OdiscI,axiom,
% 0.20/0.47 ! [Option: option_fml,X22: fml] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 = ( some_fml @ X22 ) )
% 0.20/0.47 => ( Option != none_fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.discI
% 0.20/0.47 thf(fact_102_option_OdiscI,axiom,
% 0.20/0.47 ! [Option: option_trm,X22: trm] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 = ( some_trm @ X22 ) )
% 0.20/0.47 => ( Option != none_trm ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.discI
% 0.20/0.47 thf(fact_103_option_OdiscI,axiom,
% 0.20/0.47 ! [Option: option_game,X22: game] :
% 0.20/0.47 ( ( Option
% 0.20/0.47 = ( some_game @ X22 ) )
% 0.20/0.47 => ( Option != none_game ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.discI
% 0.20/0.47 thf(fact_104_option_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X22: fml] :
% 0.20/0.47 ( none_fml
% 0.20/0.47 != ( some_fml @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.distinct(1)
% 0.20/0.47 thf(fact_105_option_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X22: trm] :
% 0.20/0.47 ( none_trm
% 0.20/0.47 != ( some_trm @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.distinct(1)
% 0.20/0.47 thf(fact_106_option_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X22: game] :
% 0.20/0.47 ( none_game
% 0.20/0.47 != ( some_game @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.distinct(1)
% 0.20/0.47 thf(fact_107_option_Ocase__eq__if,axiom,
% 0.20/0.47 ( case_option_o_game
% 0.20/0.47 = ( ^ [F12: $o,F23: game > $o,Option2: option_game] :
% 0.20/0.47 ( ( ( Option2 = none_game )
% 0.20/0.47 => F12 )
% 0.20/0.47 & ( ( Option2 != none_game )
% 0.20/0.47 => ( F23 @ ( the_game @ Option2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % option.case_eq_if
% 0.20/0.47 thf(fact_108_option_Ocase__eq__if,axiom,
% 0.20/0.47 ( case_option_o_trm
% 0.20/0.47 = ( ^ [F12: $o,F23: trm > $o,Option2: option_trm] :
% 0.20/0.47 ( ( ( Option2 = none_trm )
% 0.20/0.47 => F12 )
% 0.20/0.47 & ( ( Option2 != none_trm )
% 0.20/0.48 => ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.case_eq_if
% 0.20/0.48 thf(fact_109_option_Ocase__eq__if,axiom,
% 0.20/0.48 ( case_option_o_fml
% 0.20/0.48 = ( ^ [F12: $o,F23: fml > $o,Option2: option_fml] :
% 0.20/0.48 ( ( ( Option2 = none_fml )
% 0.20/0.48 => F12 )
% 0.20/0.48 & ( ( Option2 != none_fml )
% 0.20/0.48 => ( F23 @ ( the_fml @ Option2 ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.case_eq_if
% 0.20/0.48 thf(fact_110_option_Ocase__eq__if,axiom,
% 0.20/0.48 ( case_o209804997ml_fml
% 0.20/0.48 = ( ^ [F12: option_fml,F23: fml > option_fml,Option2: option_fml] : ( if_option_fml @ ( Option2 = none_fml ) @ F12 @ ( F23 @ ( the_fml @ Option2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.case_eq_if
% 0.20/0.48 thf(fact_111_option_Ocase__eq__if,axiom,
% 0.20/0.48 ( case_o325794063ml_trm
% 0.20/0.48 = ( ^ [F12: option_fml,F23: trm > option_fml,Option2: option_trm] : ( if_option_fml @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.case_eq_if
% 0.20/0.48 thf(fact_112_option_Ocase__eq__if,axiom,
% 0.20/0.48 ( case_o487727941rm_trm
% 0.20/0.48 = ( ^ [F12: option_trm,F23: trm > option_trm,Option2: option_trm] : ( if_option_trm @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.case_eq_if
% 0.20/0.48 thf(fact_113_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: $o,F22: game > $o] :
% 0.20/0.48 ( ( case_option_o_game @ F1 @ F22 @ none_game )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_114_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: $o,F22: trm > $o] :
% 0.20/0.48 ( ( case_option_o_trm @ F1 @ F22 @ none_trm )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_115_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: $o,F22: fml > $o] :
% 0.20/0.48 ( ( case_option_o_fml @ F1 @ F22 @ none_fml )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_116_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: option_fml,F22: fml > option_fml] :
% 0.20/0.48 ( ( case_o209804997ml_fml @ F1 @ F22 @ none_fml )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_117_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: option_fml,F22: trm > option_fml] :
% 0.20/0.48 ( ( case_o325794063ml_trm @ F1 @ F22 @ none_trm )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_118_option_Osimps_I4_J,axiom,
% 0.20/0.48 ! [F1: option_trm,F22: trm > option_trm] :
% 0.20/0.48 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 0.20/0.48 = F1 ) ).
% 0.20/0.48
% 0.20/0.48 % option.simps(4)
% 0.20/0.48 thf(fact_119_Existso_Oinduct,axiom,
% 0.20/0.48 ! [P3: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 0.20/0.48 ( ! [X5: variable,Phi2: fml] : ( P3 @ X5 @ ( some_fml @ Phi2 ) )
% 0.20/0.48 => ( ! [X5: variable] : ( P3 @ X5 @ none_fml )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Existso.induct
% 0.20/0.48 thf(fact_120_undeff__equiv,axiom,
% 0.20/0.48 ! [Phi: option_fml] :
% 0.20/0.48 ( ( Phi != none_fml )
% 0.20/0.48 = ( ? [F: fml] :
% 0.20/0.48 ( Phi
% 0.20/0.48 = ( some_fml @ F ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % undeff_equiv
% 0.20/0.48 thf(fact_121_Testo_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_fml > $o,A0: option_fml] :
% 0.20/0.48 ( ! [Phi2: fml] : ( P3 @ ( some_fml @ Phi2 ) )
% 0.20/0.48 => ( ( P3 @ none_fml )
% 0.20/0.48 => ( P3 @ A0 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Testo.induct
% 0.20/0.48 thf(fact_122_Testo_Ocases,axiom,
% 0.20/0.48 ! [X3: option_fml] :
% 0.20/0.48 ( ! [Phi2: fml] :
% 0.20/0.48 ( X3
% 0.20/0.48 != ( some_fml @ Phi2 ) )
% 0.20/0.48 => ( X3 = none_fml ) ) ).
% 0.20/0.48
% 0.20/0.48 % Testo.cases
% 0.20/0.48 thf(fact_123_mem__Collect__eq,axiom,
% 0.20/0.48 ! [A2: variable,P3: variable > $o] :
% 0.20/0.48 ( ( member_variable @ A2 @ ( collect_variable @ P3 ) )
% 0.20/0.48 = ( P3 @ A2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % mem_Collect_eq
% 0.20/0.48 thf(fact_124_Collect__mem__eq,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( collect_variable
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ A3 ) )
% 0.20/0.48 = A3 ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_mem_eq
% 0.20/0.48 thf(fact_125_Collect__cong,axiom,
% 0.20/0.48 ! [P3: variable > $o,Q: variable > $o] :
% 0.20/0.48 ( ! [X5: variable] :
% 0.20/0.48 ( ( P3 @ X5 )
% 0.20/0.48 = ( Q @ X5 ) )
% 0.20/0.48 => ( ( collect_variable @ P3 )
% 0.20/0.48 = ( collect_variable @ Q ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_cong
% 0.20/0.48 thf(fact_126_Ando_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 0.20/0.48 ( ! [Phi2: fml,Psi: fml] : ( P3 @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) )
% 0.20/0.48 => ( ! [X_1: option_fml] : ( P3 @ none_fml @ X_1 )
% 0.20/0.48 => ( ! [V6: fml] : ( P3 @ ( some_fml @ V6 ) @ none_fml )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Ando.induct
% 0.20/0.48 thf(fact_127_option_Oexpand,axiom,
% 0.20/0.48 ! [Option: option_fml,Option3: option_fml] :
% 0.20/0.48 ( ( ( Option = none_fml )
% 0.20/0.48 = ( Option3 = none_fml ) )
% 0.20/0.48 => ( ( ( Option != none_fml )
% 0.20/0.48 => ( ( Option3 != none_fml )
% 0.20/0.48 => ( ( the_fml @ Option )
% 0.20/0.48 = ( the_fml @ Option3 ) ) ) )
% 0.20/0.48 => ( Option = Option3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.expand
% 0.20/0.48 thf(fact_128_option_Oexpand,axiom,
% 0.20/0.48 ! [Option: option_trm,Option3: option_trm] :
% 0.20/0.48 ( ( ( Option = none_trm )
% 0.20/0.48 = ( Option3 = none_trm ) )
% 0.20/0.48 => ( ( ( Option != none_trm )
% 0.20/0.48 => ( ( Option3 != none_trm )
% 0.20/0.48 => ( ( the_trm @ Option )
% 0.20/0.48 = ( the_trm @ Option3 ) ) ) )
% 0.20/0.48 => ( Option = Option3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.expand
% 0.20/0.48 thf(fact_129_option_Oexpand,axiom,
% 0.20/0.48 ! [Option: option_game,Option3: option_game] :
% 0.20/0.48 ( ( ( Option = none_game )
% 0.20/0.48 = ( Option3 = none_game ) )
% 0.20/0.48 => ( ( ( Option != none_game )
% 0.20/0.48 => ( ( Option3 != none_game )
% 0.20/0.48 => ( ( the_game @ Option )
% 0.20/0.48 = ( the_game @ Option3 ) ) ) )
% 0.20/0.48 => ( Option = Option3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.expand
% 0.20/0.48 thf(fact_130_usubstappf__pred__conv,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,P2: char,Theta: trm] :
% 0.20/0.48 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.20/0.48 != none_fml )
% 0.20/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.48 != none_trm )
% 0.20/0.48 & ( ( ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ Sigma
% 0.20/0.48 @ P2 )
% 0.20/0.48 = none_fml )
% 0.20/0.48 | ? [R3: fml] :
% 0.20/0.48 ( ( ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ Sigma
% 0.20/0.48 @ P2 )
% 0.20/0.48 = ( some_fml @ R3 ) )
% 0.20/0.48 & ( ( inf_inf_set_variable @ ( static_FVF @ R3 ) @ U )
% 0.20/0.48 = bot_bot_set_variable ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf_pred_conv
% 0.20/0.48 thf(fact_131_f6,axiom,
% 0.20/0.48 ( ( case_o325794063ml_trm @ none_fml
% 0.20/0.48 @ ^ [T: trm] :
% 0.20/0.48 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.20/0.48 @ ^ [F: fml] :
% 0.20/0.48 ( if_option_fml
% 0.20/0.48 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F )
% 0.20/0.48 @ none_fml )
% 0.20/0.48 @ ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ sigma
% 0.20/0.48 @ p ) )
% 0.20/0.48 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 0.20/0.48 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) )
% 0.20/0.48 @ ^ [F: fml] :
% 0.20/0.48 ( if_option_fml
% 0.20/0.48 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) @ bot_bot_set_variable @ F )
% 0.20/0.48 @ none_fml )
% 0.20/0.48 @ ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ sigma
% 0.20/0.48 @ p ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % f6
% 0.20/0.48 thf(fact_132_f3,axiom,
% 0.20/0.48 ( ( case_o325794063ml_trm @ none_fml
% 0.20/0.48 @ ^ [T: trm] :
% 0.20/0.48 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.20/0.48 @ ^ [F: fml] :
% 0.20/0.48 ( if_option_fml
% 0.20/0.48 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F )
% 0.20/0.48 @ none_fml )
% 0.20/0.48 @ ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ sigma
% 0.20/0.48 @ p ) )
% 0.20/0.48 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 0.20/0.48 != none_fml ) ).
% 0.20/0.48
% 0.20/0.48 % f3
% 0.20/0.48 thf(fact_133_usubstappf_Osimps_I1_J,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,P2: char,Theta: trm] :
% 0.20/0.48 ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.20/0.48 = ( case_o325794063ml_trm @ none_fml
% 0.20/0.48 @ ^ [Sigma_theta: trm] :
% 0.20/0.48 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ P2 @ Sigma_theta ) )
% 0.20/0.48 @ ^ [R: fml] :
% 0.20/0.48 ( if_option_fml
% 0.20/0.48 @ ( ( inf_inf_set_variable @ ( static_FVF @ R ) @ U )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.20/0.48 @ none_fml )
% 0.20/0.48 @ ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ Sigma
% 0.20/0.48 @ P2 ) )
% 0.20/0.48 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf.simps(1)
% 0.20/0.48 thf(fact_134_Int__subset__iff,axiom,
% 0.20/0.48 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ C @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 = ( ( ord_le282106107riable @ C @ A3 )
% 0.20/0.48 & ( ord_le282106107riable @ C @ B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_subset_iff
% 0.20/0.48 thf(fact_135_inf__bot__left,axiom,
% 0.20/0.48 ! [X3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ bot_bot_variable_o @ X3 )
% 0.20/0.48 = bot_bot_variable_o ) ).
% 0.20/0.48
% 0.20/0.48 % inf_bot_left
% 0.20/0.48 thf(fact_136_inf__bot__left,axiom,
% 0.20/0.48 ! [X3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X3 )
% 0.20/0.48 = bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % inf_bot_left
% 0.20/0.48 thf(fact_137_inf__bot__right,axiom,
% 0.20/0.48 ! [X3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ X3 @ bot_bot_variable_o )
% 0.20/0.48 = bot_bot_variable_o ) ).
% 0.20/0.48
% 0.20/0.48 % inf_bot_right
% 0.20/0.48 thf(fact_138_inf__bot__right,axiom,
% 0.20/0.48 ! [X3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ bot_bot_set_variable )
% 0.20/0.48 = bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % inf_bot_right
% 0.20/0.48 thf(fact_139_subset__empty,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ bot_bot_set_variable )
% 0.20/0.48 = ( A3 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_empty
% 0.20/0.48 thf(fact_140_empty__subsetI,axiom,
% 0.20/0.48 ! [A3: set_variable] : ( ord_le282106107riable @ bot_bot_set_variable @ A3 ) ).
% 0.20/0.48
% 0.20/0.48 % empty_subsetI
% 0.20/0.48 thf(fact_141_le__inf__iff,axiom,
% 0.20/0.48 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 0.20/0.48 ( ( ord_le1407353162able_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) )
% 0.20/0.48 = ( ( ord_le1407353162able_o @ X3 @ Y3 )
% 0.20/0.48 & ( ord_le1407353162able_o @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_inf_iff
% 0.20/0.48 thf(fact_142_le__inf__iff,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 0.20/0.48 = ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 & ( ord_le282106107riable @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_inf_iff
% 0.20/0.48 thf(fact_143_inf_Obounded__iff,axiom,
% 0.20/0.48 ! [A2: variable > $o,B3: variable > $o,C2: variable > $o] :
% 0.20/0.48 ( ( ord_le1407353162able_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) )
% 0.20/0.48 = ( ( ord_le1407353162able_o @ A2 @ B3 )
% 0.20/0.48 & ( ord_le1407353162able_o @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.bounded_iff
% 0.20/0.48 thf(fact_144_inf_Obounded__iff,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 0.20/0.48 = ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 & ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.bounded_iff
% 0.20/0.48 thf(fact_145_f4,axiom,
% 0.20/0.48 ! [Z: option_fml,F3: trm > option_fml,Za: option_trm] :
% 0.20/0.48 ( ( ( Za = none_trm )
% 0.20/0.48 => ( ( case_o325794063ml_trm @ Z @ F3 @ Za )
% 0.20/0.48 = Z ) )
% 0.20/0.48 & ( ( Za != none_trm )
% 0.20/0.48 => ( ( case_o325794063ml_trm @ Z @ F3 @ Za )
% 0.20/0.48 = ( F3 @ ( the_trm @ Za ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % f4
% 0.20/0.48 thf(fact_146_empty__Collect__eq,axiom,
% 0.20/0.48 ! [P3: variable > $o] :
% 0.20/0.48 ( ( bot_bot_set_variable
% 0.20/0.48 = ( collect_variable @ P3 ) )
% 0.20/0.48 = ( ! [X: variable] :
% 0.20/0.48 ~ ( P3 @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % empty_Collect_eq
% 0.20/0.48 thf(fact_147_Collect__empty__eq,axiom,
% 0.20/0.48 ! [P3: variable > $o] :
% 0.20/0.48 ( ( ( collect_variable @ P3 )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 = ( ! [X: variable] :
% 0.20/0.48 ~ ( P3 @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_empty_eq
% 0.20/0.48 thf(fact_148_all__not__in__conv,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( ! [X: variable] :
% 0.20/0.48 ~ ( member_variable @ X @ A3 ) )
% 0.20/0.48 = ( A3 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % all_not_in_conv
% 0.20/0.48 thf(fact_149_empty__iff,axiom,
% 0.20/0.48 ! [C2: variable] :
% 0.20/0.48 ~ ( member_variable @ C2 @ bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % empty_iff
% 0.20/0.48 thf(fact_150_subset__antisym,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B2 @ A3 )
% 0.20/0.48 => ( A3 = B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_antisym
% 0.20/0.48 thf(fact_151_subsetI,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ! [X5: variable] :
% 0.20/0.48 ( ( member_variable @ X5 @ A3 )
% 0.20/0.48 => ( member_variable @ X5 @ B2 ) )
% 0.20/0.48 => ( ord_le282106107riable @ A3 @ B2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % subsetI
% 0.20/0.48 thf(fact_152_inf__right__idem,axiom,
% 0.20/0.48 ! [X3: variable > $o,Y3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ X3 @ Y3 ) @ Y3 )
% 0.20/0.48 = ( inf_inf_variable_o @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_right_idem
% 0.20/0.48 thf(fact_153_inf__right__idem,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 )
% 0.20/0.48 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_right_idem
% 0.20/0.48 thf(fact_154_inf_Oright__idem,axiom,
% 0.20/0.48 ! [A2: variable > $o,B3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ A2 @ B3 ) @ B3 )
% 0.20/0.48 = ( inf_inf_variable_o @ A2 @ B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.right_idem
% 0.20/0.48 thf(fact_155_inf_Oright__idem,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ B3 )
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.right_idem
% 0.20/0.48 thf(fact_156_inf__left__idem,axiom,
% 0.20/0.48 ! [X3: variable > $o,Y3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ X3 @ Y3 ) )
% 0.20/0.48 = ( inf_inf_variable_o @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_left_idem
% 0.20/0.48 thf(fact_157_inf__left__idem,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ X3 @ Y3 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_left_idem
% 0.20/0.48 thf(fact_158_inf_Oleft__idem,axiom,
% 0.20/0.48 ! [A2: variable > $o,B3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ A2 @ B3 ) )
% 0.20/0.48 = ( inf_inf_variable_o @ A2 @ B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.left_idem
% 0.20/0.48 thf(fact_159_inf_Oleft__idem,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.left_idem
% 0.20/0.48 thf(fact_160_inf__idem,axiom,
% 0.20/0.48 ! [X3: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ X3 @ X3 )
% 0.20/0.48 = X3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_idem
% 0.20/0.48 thf(fact_161_inf__idem,axiom,
% 0.20/0.48 ! [X3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ X3 )
% 0.20/0.48 = X3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_idem
% 0.20/0.48 thf(fact_162_inf_Oidem,axiom,
% 0.20/0.48 ! [A2: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ A2 @ A2 )
% 0.20/0.48 = A2 ) ).
% 0.20/0.48
% 0.20/0.48 % inf.idem
% 0.20/0.48 thf(fact_163_inf_Oidem,axiom,
% 0.20/0.48 ! [A2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A2 @ A2 )
% 0.20/0.48 = A2 ) ).
% 0.20/0.48
% 0.20/0.48 % inf.idem
% 0.20/0.48 thf(fact_164_inf__apply,axiom,
% 0.20/0.48 ( inf_inf_variable_o
% 0.20/0.48 = ( ^ [F: variable > $o,G: variable > $o,X: variable] : ( inf_inf_o @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_apply
% 0.20/0.48 thf(fact_165_Int__iff,axiom,
% 0.20/0.48 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 = ( ( member_variable @ C2 @ A3 )
% 0.20/0.48 & ( member_variable @ C2 @ B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_iff
% 0.20/0.48 thf(fact_166_IntI,axiom,
% 0.20/0.48 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( member_variable @ C2 @ A3 )
% 0.20/0.48 => ( ( member_variable @ C2 @ B2 )
% 0.20/0.48 => ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % IntI
% 0.20/0.48 thf(fact_167_usubstappf__pred,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,P2: char,R2: fml,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 0.20/0.48 ( ( ( produc1250175341on_fml
% 0.20/0.48 @ ^ [Uu: char > option_trm] :
% 0.20/0.48 ( produc1615133358on_fml
% 0.20/0.48 @ ^ [Uv: char > option_trm] :
% 0.20/0.48 ( produc1420172399on_fml
% 0.20/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.48 @ Sigma
% 0.20/0.48 @ P2 )
% 0.20/0.48 = ( some_fml @ R2 ) )
% 0.20/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.48 = ( some_trm @ Sigma_theta2 ) )
% 0.20/0.48 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 0.20/0.48 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf_pred
% 0.20/0.48 thf(fact_168_ODEo_Oinduct,axiom,
% 0.20/0.48 ! [P3: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.20/0.48 ( ! [X5: char,Theta2: trm] : ( P3 @ X5 @ ( some_trm @ Theta2 ) )
% 0.20/0.48 => ( ! [X5: char] : ( P3 @ X5 @ none_trm )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % ODEo.induct
% 0.20/0.48 thf(fact_169_undeft__None,axiom,
% 0.20/0.48 none_trm = none_trm ).
% 0.20/0.48
% 0.20/0.48 % undeft_None
% 0.20/0.48 thf(fact_170_undeft__equiv,axiom,
% 0.20/0.48 ! [Theta: option_trm] :
% 0.20/0.48 ( ( Theta != none_trm )
% 0.20/0.48 = ( ? [T: trm] :
% 0.20/0.48 ( Theta
% 0.20/0.48 = ( some_trm @ T ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % undeft_equiv
% 0.20/0.48 thf(fact_171_Timeso_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.20/0.48 ( ! [Theta2: trm,Eta: trm] : ( P3 @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) )
% 0.20/0.48 => ( ! [X_1: option_trm] : ( P3 @ none_trm @ X_1 )
% 0.20/0.48 => ( ! [V6: trm] : ( P3 @ ( some_trm @ V6 ) @ none_trm )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Timeso.induct
% 0.20/0.48 thf(fact_172_Assigno_Oinduct,axiom,
% 0.20/0.48 ! [P3: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.20/0.48 ( ! [X5: variable,Theta2: trm] : ( P3 @ X5 @ ( some_trm @ Theta2 ) )
% 0.20/0.48 => ( ! [X5: variable] : ( P3 @ X5 @ none_trm )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Assigno.induct
% 0.20/0.48 thf(fact_173_Differentialo_Ocases,axiom,
% 0.20/0.48 ! [X3: option_trm] :
% 0.20/0.48 ( ! [Theta2: trm] :
% 0.20/0.48 ( X3
% 0.20/0.48 != ( some_trm @ Theta2 ) )
% 0.20/0.48 => ( X3 = none_trm ) ) ).
% 0.20/0.48
% 0.20/0.48 % Differentialo.cases
% 0.20/0.48 thf(fact_174_Differentialo_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_trm > $o,A0: option_trm] :
% 0.20/0.48 ( ! [Theta2: trm] : ( P3 @ ( some_trm @ Theta2 ) )
% 0.20/0.48 => ( ( P3 @ none_trm )
% 0.20/0.48 => ( P3 @ A0 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Differentialo.induct
% 0.20/0.48 thf(fact_175_bot__set__def,axiom,
% 0.20/0.48 ( bot_bot_set_variable
% 0.20/0.48 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 0.20/0.48
% 0.20/0.48 % bot_set_def
% 0.20/0.48 thf(fact_176_inf__set__def,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ( collect_variable
% 0.20/0.48 @ ( inf_inf_variable_o
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ A4 )
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ B4 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_set_def
% 0.20/0.48 thf(fact_177_less__eq__set__def,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ( ord_le1407353162able_o
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ A4 )
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ B4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % less_eq_set_def
% 0.20/0.48 thf(fact_178_option_Odisc__eq__case_I2_J,axiom,
% 0.20/0.48 ! [Option: option_fml] :
% 0.20/0.48 ( ( Option != none_fml )
% 0.20/0.48 = ( case_option_o_fml @ $false
% 0.20/0.48 @ ^ [Uu: fml] : $true
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(2)
% 0.20/0.48 thf(fact_179_option_Odisc__eq__case_I2_J,axiom,
% 0.20/0.48 ! [Option: option_trm] :
% 0.20/0.48 ( ( Option != none_trm )
% 0.20/0.48 = ( case_option_o_trm @ $false
% 0.20/0.48 @ ^ [Uu: trm] : $true
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(2)
% 0.20/0.48 thf(fact_180_option_Odisc__eq__case_I2_J,axiom,
% 0.20/0.48 ! [Option: option_game] :
% 0.20/0.48 ( ( Option != none_game )
% 0.20/0.48 = ( case_option_o_game @ $false
% 0.20/0.48 @ ^ [Uu: game] : $true
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(2)
% 0.20/0.48 thf(fact_181_option_Odisc__eq__case_I1_J,axiom,
% 0.20/0.48 ! [Option: option_fml] :
% 0.20/0.48 ( ( Option = none_fml )
% 0.20/0.48 = ( case_option_o_fml @ $true
% 0.20/0.48 @ ^ [Uu: fml] : $false
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(1)
% 0.20/0.48 thf(fact_182_option_Odisc__eq__case_I1_J,axiom,
% 0.20/0.48 ! [Option: option_trm] :
% 0.20/0.48 ( ( Option = none_trm )
% 0.20/0.48 = ( case_option_o_trm @ $true
% 0.20/0.48 @ ^ [Uu: trm] : $false
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(1)
% 0.20/0.48 thf(fact_183_option_Odisc__eq__case_I1_J,axiom,
% 0.20/0.48 ! [Option: option_game] :
% 0.20/0.48 ( ( Option = none_game )
% 0.20/0.48 = ( case_option_o_game @ $true
% 0.20/0.48 @ ^ [Uu: game] : $false
% 0.20/0.48 @ Option ) ) ).
% 0.20/0.48
% 0.20/0.48 % option.disc_eq_case(1)
% 0.20/0.48 thf(fact_184_Diamondo_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 0.20/0.48 ( ! [Alpha: game,Phi2: fml] : ( P3 @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) )
% 0.20/0.48 => ( ! [X_1: option_fml] : ( P3 @ none_game @ X_1 )
% 0.20/0.48 => ( ! [V6: game] : ( P3 @ ( some_game @ V6 ) @ none_fml )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Diamondo.induct
% 0.20/0.48 thf(fact_185_case__optionE,axiom,
% 0.20/0.48 ! [P3: $o,Q: fml > $o,X3: option_fml] :
% 0.20/0.48 ( ( case_option_o_fml @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( ( X3 = none_fml )
% 0.20/0.48 => ~ P3 )
% 0.20/0.48 => ~ ! [Y4: fml] :
% 0.20/0.48 ( ( X3
% 0.20/0.48 = ( some_fml @ Y4 ) )
% 0.20/0.48 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % case_optionE
% 0.20/0.48 thf(fact_186_case__optionE,axiom,
% 0.20/0.48 ! [P3: $o,Q: trm > $o,X3: option_trm] :
% 0.20/0.48 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( ( X3 = none_trm )
% 0.20/0.48 => ~ P3 )
% 0.20/0.48 => ~ ! [Y4: trm] :
% 0.20/0.48 ( ( X3
% 0.20/0.48 = ( some_trm @ Y4 ) )
% 0.20/0.48 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % case_optionE
% 0.20/0.48 thf(fact_187_case__optionE,axiom,
% 0.20/0.48 ! [P3: $o,Q: game > $o,X3: option_game] :
% 0.20/0.48 ( ( case_option_o_game @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( ( X3 = none_game )
% 0.20/0.48 => ~ P3 )
% 0.20/0.48 => ~ ! [Y4: game] :
% 0.20/0.48 ( ( X3
% 0.20/0.48 = ( some_game @ Y4 ) )
% 0.20/0.48 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % case_optionE
% 0.20/0.48 thf(fact_188_ex__in__conv,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( ? [X: variable] : ( member_variable @ X @ A3 ) )
% 0.20/0.48 = ( A3 != bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % ex_in_conv
% 0.20/0.48 thf(fact_189_equals0I,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ! [Y4: variable] :
% 0.20/0.48 ~ ( member_variable @ Y4 @ A3 )
% 0.20/0.48 => ( A3 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % equals0I
% 0.20/0.48 thf(fact_190_equals0D,axiom,
% 0.20/0.48 ! [A3: set_variable,A2: variable] :
% 0.20/0.48 ( ( A3 = bot_bot_set_variable )
% 0.20/0.48 => ~ ( member_variable @ A2 @ A3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % equals0D
% 0.20/0.48 thf(fact_191_emptyE,axiom,
% 0.20/0.48 ! [A2: variable] :
% 0.20/0.48 ~ ( member_variable @ A2 @ bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % emptyE
% 0.20/0.48 thf(fact_192_Collect__mono__iff,axiom,
% 0.20/0.48 ! [P3: variable > $o,Q: variable > $o] :
% 0.20/0.48 ( ( ord_le282106107riable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) )
% 0.20/0.48 = ( ! [X: variable] :
% 0.20/0.48 ( ( P3 @ X )
% 0.20/0.48 => ( Q @ X ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_mono_iff
% 0.20/0.48 thf(fact_193_set__eq__subset,axiom,
% 0.20/0.48 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A4 @ B4 )
% 0.20/0.48 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % set_eq_subset
% 0.20/0.48 thf(fact_194_subset__trans,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B2 @ C )
% 0.20/0.48 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_trans
% 0.20/0.48 thf(fact_195_Collect__mono,axiom,
% 0.20/0.48 ! [P3: variable > $o,Q: variable > $o] :
% 0.20/0.48 ( ! [X5: variable] :
% 0.20/0.48 ( ( P3 @ X5 )
% 0.20/0.48 => ( Q @ X5 ) )
% 0.20/0.48 => ( ord_le282106107riable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_mono
% 0.20/0.48 thf(fact_196_subset__refl,axiom,
% 0.20/0.48 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 0.20/0.48
% 0.20/0.48 % subset_refl
% 0.20/0.48 thf(fact_197_subset__iff,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ! [T: variable] :
% 0.20/0.48 ( ( member_variable @ T @ A4 )
% 0.20/0.48 => ( member_variable @ T @ B4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_iff
% 0.20/0.48 thf(fact_198_equalityD2,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( A3 = B2 )
% 0.20/0.48 => ( ord_le282106107riable @ B2 @ A3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % equalityD2
% 0.20/0.48 thf(fact_199_equalityD1,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( A3 = B2 )
% 0.20/0.48 => ( ord_le282106107riable @ A3 @ B2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % equalityD1
% 0.20/0.48 thf(fact_200_subset__eq,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ! [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ A4 )
% 0.20/0.48 => ( member_variable @ X @ B4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_eq
% 0.20/0.48 thf(fact_201_equalityE,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( A3 = B2 )
% 0.20/0.48 => ~ ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ~ ( ord_le282106107riable @ B2 @ A3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % equalityE
% 0.20/0.48 thf(fact_202_subsetD,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,C2: variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ( member_variable @ C2 @ A3 )
% 0.20/0.48 => ( member_variable @ C2 @ B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % subsetD
% 0.20/0.48 thf(fact_203_in__mono,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,X3: variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ( member_variable @ X3 @ A3 )
% 0.20/0.48 => ( member_variable @ X3 @ B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % in_mono
% 0.20/0.48 thf(fact_204_inf__left__commute,axiom,
% 0.20/0.48 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) )
% 0.20/0.48 = ( inf_inf_variable_o @ Y3 @ ( inf_inf_variable_o @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_left_commute
% 0.20/0.48 thf(fact_205_inf__left__commute,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ Y3 @ ( inf_inf_set_variable @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_left_commute
% 0.20/0.48 thf(fact_206_inf_Oleft__commute,axiom,
% 0.20/0.48 ! [B3: variable > $o,A2: variable > $o,C2: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ B3 @ ( inf_inf_variable_o @ A2 @ C2 ) )
% 0.20/0.48 = ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.left_commute
% 0.20/0.48 thf(fact_207_inf_Oleft__commute,axiom,
% 0.20/0.48 ! [B3: set_variable,A2: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.left_commute
% 0.20/0.48 thf(fact_208_inf__commute,axiom,
% 0.20/0.48 ( inf_inf_variable_o
% 0.20/0.48 = ( ^ [X: variable > $o,Y: variable > $o] : ( inf_inf_variable_o @ Y @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_commute
% 0.20/0.48 thf(fact_209_inf__commute,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_commute
% 0.20/0.48 thf(fact_210_inf_Ocommute,axiom,
% 0.20/0.48 ( inf_inf_variable_o
% 0.20/0.48 = ( ^ [A5: variable > $o,B5: variable > $o] : ( inf_inf_variable_o @ B5 @ A5 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.commute
% 0.20/0.48 thf(fact_211_inf_Ocommute,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.commute
% 0.20/0.48 thf(fact_212_inf__assoc,axiom,
% 0.20/0.48 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ X3 @ Y3 ) @ Z2 )
% 0.20/0.48 = ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_assoc
% 0.20/0.48 thf(fact_213_inf__assoc,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Z2 )
% 0.20/0.48 = ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_assoc
% 0.20/0.48 thf(fact_214_inf_Oassoc,axiom,
% 0.20/0.48 ! [A2: variable > $o,B3: variable > $o,C2: variable > $o] :
% 0.20/0.48 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ A2 @ B3 ) @ C2 )
% 0.20/0.48 = ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.assoc
% 0.20/0.48 thf(fact_215_inf_Oassoc,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.assoc
% 0.20/0.48 thf(fact_216_boolean__algebra__cancel_Oinf2,axiom,
% 0.20/0.48 ! [B2: variable > $o,K: variable > $o,B3: variable > $o,A2: variable > $o] :
% 0.20/0.48 ( ( B2
% 0.20/0.48 = ( inf_inf_variable_o @ K @ B3 ) )
% 0.20/0.48 => ( ( inf_inf_variable_o @ A2 @ B2 )
% 0.20/0.48 = ( inf_inf_variable_o @ K @ ( inf_inf_variable_o @ A2 @ B3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % boolean_algebra_cancel.inf2
% 0.20/0.48 thf(fact_217_boolean__algebra__cancel_Oinf2,axiom,
% 0.20/0.48 ! [B2: set_variable,K: set_variable,B3: set_variable,A2: set_variable] :
% 0.20/0.48 ( ( B2
% 0.20/0.48 = ( inf_inf_set_variable @ K @ B3 ) )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A2 @ B2 )
% 0.20/0.48 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % boolean_algebra_cancel.inf2
% 0.20/0.48 thf(fact_218_boolean__algebra__cancel_Oinf1,axiom,
% 0.20/0.48 ! [A3: variable > $o,K: variable > $o,A2: variable > $o,B3: variable > $o] :
% 0.20/0.48 ( ( A3
% 0.20/0.48 = ( inf_inf_variable_o @ K @ A2 ) )
% 0.20/0.48 => ( ( inf_inf_variable_o @ A3 @ B3 )
% 0.20/0.48 = ( inf_inf_variable_o @ K @ ( inf_inf_variable_o @ A2 @ B3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % boolean_algebra_cancel.inf1
% 0.20/0.48 thf(fact_219_boolean__algebra__cancel_Oinf1,axiom,
% 0.20/0.48 ! [A3: set_variable,K: set_variable,A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( A3
% 0.20/0.48 = ( inf_inf_set_variable @ K @ A2 ) )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A3 @ B3 )
% 0.20/0.48 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % boolean_algebra_cancel.inf1
% 0.20/0.48 thf(fact_220_inf__sup__aci_I1_J,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_aci(1)
% 0.20/0.48 thf(fact_221_inf__sup__aci_I2_J,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Z2 )
% 0.20/0.48 = ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_aci(2)
% 0.20/0.48 thf(fact_222_inf__sup__aci_I3_J,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ Y3 @ ( inf_inf_set_variable @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_aci(3)
% 0.20/0.48 thf(fact_223_inf__sup__aci_I4_J,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ X3 @ Y3 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_aci(4)
% 0.20/0.48 thf(fact_224_Int__left__commute,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ B2 @ C ) )
% 0.20/0.48 = ( inf_inf_set_variable @ B2 @ ( inf_inf_set_variable @ A3 @ C ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_left_commute
% 0.20/0.48 thf(fact_225_Int__left__absorb,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 = ( inf_inf_set_variable @ A3 @ B2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_left_absorb
% 0.20/0.48 thf(fact_226_Int__commute,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] : ( inf_inf_set_variable @ B4 @ A4 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_commute
% 0.20/0.48 thf(fact_227_Int__absorb,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A3 @ A3 )
% 0.20/0.48 = A3 ) ).
% 0.20/0.48
% 0.20/0.48 % Int_absorb
% 0.20/0.48 thf(fact_228_Int__assoc,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A3 @ B2 ) @ C )
% 0.20/0.48 = ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ B2 @ C ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_assoc
% 0.20/0.48 thf(fact_229_IntD2,axiom,
% 0.20/0.48 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 => ( member_variable @ C2 @ B2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % IntD2
% 0.20/0.48 thf(fact_230_IntD1,axiom,
% 0.20/0.48 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 => ( member_variable @ C2 @ A3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % IntD1
% 0.20/0.48 thf(fact_231_IntE,axiom,
% 0.20/0.48 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 0.20/0.48 => ~ ( ( member_variable @ C2 @ A3 )
% 0.20/0.48 => ~ ( member_variable @ C2 @ B2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % IntE
% 0.20/0.48 thf(fact_232_empty__def,axiom,
% 0.20/0.48 ( bot_bot_set_variable
% 0.20/0.48 = ( collect_variable
% 0.20/0.48 @ ^ [X: variable] : $false ) ) ).
% 0.20/0.48
% 0.20/0.48 % empty_def
% 0.20/0.48 thf(fact_233_Collect__subset,axiom,
% 0.20/0.48 ! [A3: set_variable,P3: variable > $o] :
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 @ ( collect_variable
% 0.20/0.48 @ ^ [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ A3 )
% 0.20/0.48 & ( P3 @ X ) ) )
% 0.20/0.48 @ A3 ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_subset
% 0.20/0.48 thf(fact_234_Int__def,axiom,
% 0.20/0.48 ( inf_inf_set_variable
% 0.20/0.48 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.20/0.48 ( collect_variable
% 0.20/0.48 @ ^ [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ A4 )
% 0.20/0.48 & ( member_variable @ X @ B4 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_def
% 0.20/0.48 thf(fact_235_Int__Collect,axiom,
% 0.20/0.48 ! [X3: variable,A3: set_variable,P3: variable > $o] :
% 0.20/0.48 ( ( member_variable @ X3 @ ( inf_inf_set_variable @ A3 @ ( collect_variable @ P3 ) ) )
% 0.20/0.48 = ( ( member_variable @ X3 @ A3 )
% 0.20/0.48 & ( P3 @ X3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_Collect
% 0.20/0.48 thf(fact_236_Collect__conj__eq,axiom,
% 0.20/0.48 ! [P3: variable > $o,Q: variable > $o] :
% 0.20/0.48 ( ( collect_variable
% 0.20/0.48 @ ^ [X: variable] :
% 0.20/0.48 ( ( P3 @ X )
% 0.20/0.48 & ( Q @ X ) ) )
% 0.20/0.48 = ( inf_inf_set_variable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_conj_eq
% 0.20/0.48 thf(fact_237_inf_OcoboundedI2,axiom,
% 0.20/0.48 ! [B3: set_variable,C2: set_variable,A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B3 @ C2 )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.coboundedI2
% 0.20/0.48 thf(fact_238_inf_OcoboundedI1,axiom,
% 0.20/0.48 ! [A2: set_variable,C2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ C2 )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.coboundedI1
% 0.20/0.48 thf(fact_239_inf_Oabsorb__iff2,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [B5: set_variable,A5: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A5 @ B5 )
% 0.20/0.48 = B5 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.absorb_iff2
% 0.20/0.48 thf(fact_240_inf_Oabsorb__iff1,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A5 @ B5 )
% 0.20/0.48 = A5 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.absorb_iff1
% 0.20/0.48 thf(fact_241_inf_Ocobounded2,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ B3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf.cobounded2
% 0.20/0.48 thf(fact_242_inf_Ocobounded1,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ A2 ) ).
% 0.20/0.48
% 0.20/0.48 % inf.cobounded1
% 0.20/0.48 thf(fact_243_inf_Oorder__iff,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.20/0.48 ( A5
% 0.20/0.48 = ( inf_inf_set_variable @ A5 @ B5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.order_iff
% 0.20/0.48 thf(fact_244_inf__greatest,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ X3 @ Z2 )
% 0.20/0.48 => ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_greatest
% 0.20/0.48 thf(fact_245_inf_OboundedI,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ A2 @ C2 )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.boundedI
% 0.20/0.48 thf(fact_246_inf_OboundedE,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 0.20/0.48 => ~ ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ~ ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.boundedE
% 0.20/0.48 thf(fact_247_inf__absorb2,axiom,
% 0.20/0.48 ! [Y3: set_variable,X3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ Y3 @ X3 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 0.20/0.48 = Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_absorb2
% 0.20/0.48 thf(fact_248_inf__absorb1,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 0.20/0.48 = X3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_absorb1
% 0.20/0.48 thf(fact_249_inf_Oabsorb2,axiom,
% 0.20/0.48 ! [B3: set_variable,A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B3 @ A2 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.20/0.48 = B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.absorb2
% 0.20/0.48 thf(fact_250_inf_Oabsorb1,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.20/0.48 = A2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.absorb1
% 0.20/0.48 thf(fact_251_le__iff__inf,axiom,
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 = ( ^ [X: set_variable,Y: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ X @ Y )
% 0.20/0.48 = X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_iff_inf
% 0.20/0.48 thf(fact_252_inf__unique,axiom,
% 0.20/0.48 ! [F2: set_variable > set_variable > set_variable,X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ! [X5: set_variable,Y4: set_variable] : ( ord_le282106107riable @ ( F2 @ X5 @ Y4 ) @ X5 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable] : ( ord_le282106107riable @ ( F2 @ X5 @ Y4 ) @ Y4 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable,Z4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X5 @ Y4 )
% 0.20/0.48 => ( ( ord_le282106107riable @ X5 @ Z4 )
% 0.20/0.48 => ( ord_le282106107riable @ X5 @ ( F2 @ Y4 @ Z4 ) ) ) )
% 0.20/0.48 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 0.20/0.48 = ( F2 @ X3 @ Y3 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_unique
% 0.20/0.48 thf(fact_253_inf_OorderI,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( A2
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ B3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.orderI
% 0.20/0.48 thf(fact_254_inf_OorderE,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( A2
% 0.20/0.48 = ( inf_inf_set_variable @ A2 @ B3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf.orderE
% 0.20/0.48 thf(fact_255_le__infI2,axiom,
% 0.20/0.48 ! [B3: set_variable,X3: set_variable,A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B3 @ X3 )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ X3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_infI2
% 0.20/0.48 thf(fact_256_le__infI1,axiom,
% 0.20/0.48 ! [A2: set_variable,X3: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ X3 )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ X3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_infI1
% 0.20/0.48 thf(fact_257_inf__mono,axiom,
% 0.20/0.48 ! [A2: set_variable,C2: set_variable,B3: set_variable,D: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ C2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ D )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ ( inf_inf_set_variable @ C2 @ D ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_mono
% 0.20/0.48 thf(fact_258_le__infI,axiom,
% 0.20/0.48 ! [X3: set_variable,A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ A2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ X3 @ B3 )
% 0.20/0.48 => ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_infI
% 0.20/0.48 thf(fact_259_le__infE,axiom,
% 0.20/0.48 ! [X3: set_variable,A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.20/0.48 => ~ ( ( ord_le282106107riable @ X3 @ A2 )
% 0.20/0.48 => ~ ( ord_le282106107riable @ X3 @ B3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % le_infE
% 0.20/0.48 thf(fact_260_inf__le2,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_le2
% 0.20/0.48 thf(fact_261_inf__le1,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ X3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_le1
% 0.20/0.48 thf(fact_262_inf__sup__ord_I1_J,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ X3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_ord(1)
% 0.20/0.48 thf(fact_263_inf__sup__ord_I2_J,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 ) ).
% 0.20/0.48
% 0.20/0.48 % inf_sup_ord(2)
% 0.20/0.48 thf(fact_264_disjoint__iff__not__equal,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ( inf_inf_set_variable @ A3 @ B2 )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 = ( ! [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ A3 )
% 0.20/0.48 => ! [Y: variable] :
% 0.20/0.48 ( ( member_variable @ Y @ B2 )
% 0.20/0.48 => ( X != Y ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % disjoint_iff_not_equal
% 0.20/0.48 thf(fact_265_Int__empty__right,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ A3 @ bot_bot_set_variable )
% 0.20/0.48 = bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % Int_empty_right
% 0.20/0.48 thf(fact_266_Int__empty__left,axiom,
% 0.20/0.48 ! [B2: set_variable] :
% 0.20/0.48 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B2 )
% 0.20/0.48 = bot_bot_set_variable ) ).
% 0.20/0.48
% 0.20/0.48 % Int_empty_left
% 0.20/0.48 thf(fact_267_disjoint__iff,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ( inf_inf_set_variable @ A3 @ B2 )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 = ( ! [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ A3 )
% 0.20/0.48 => ~ ( member_variable @ X @ B2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % disjoint_iff
% 0.20/0.48 thf(fact_268_Int__emptyI,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ! [X5: variable] :
% 0.20/0.48 ( ( member_variable @ X5 @ A3 )
% 0.20/0.48 => ~ ( member_variable @ X5 @ B2 ) )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 0.20/0.48 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_emptyI
% 0.20/0.48 thf(fact_269_Int__Collect__mono,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable,P3: variable > $o,Q: variable > $o] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ! [X5: variable] :
% 0.20/0.48 ( ( member_variable @ X5 @ A3 )
% 0.20/0.48 => ( ( P3 @ X5 )
% 0.20/0.48 => ( Q @ X5 ) ) )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ ( collect_variable @ P3 ) ) @ ( inf_inf_set_variable @ B2 @ ( collect_variable @ Q ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_Collect_mono
% 0.20/0.48 thf(fact_270_Int__greatest,axiom,
% 0.20/0.48 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ C @ A3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ C @ B2 )
% 0.20/0.48 => ( ord_le282106107riable @ C @ ( inf_inf_set_variable @ A3 @ B2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_greatest
% 0.20/0.48 thf(fact_271_Int__absorb2,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ B2 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 0.20/0.48 = A3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_absorb2
% 0.20/0.48 thf(fact_272_Int__absorb1,axiom,
% 0.20/0.48 ! [B2: set_variable,A3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.20/0.48 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 0.20/0.48 = B2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_absorb1
% 0.20/0.48 thf(fact_273_Int__lower2,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ B2 ) ).
% 0.20/0.48
% 0.20/0.48 % Int_lower2
% 0.20/0.48 thf(fact_274_Int__lower1,axiom,
% 0.20/0.48 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ A3 ) ).
% 0.20/0.48
% 0.20/0.48 % Int_lower1
% 0.20/0.48 thf(fact_275_Int__mono,axiom,
% 0.20/0.48 ! [A3: set_variable,C: set_variable,B2: set_variable,D2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A3 @ C )
% 0.20/0.48 => ( ( ord_le282106107riable @ B2 @ D2 )
% 0.20/0.48 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ ( inf_inf_set_variable @ C @ D2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Int_mono
% 0.20/0.48 thf(fact_276_order__refl,axiom,
% 0.20/0.48 ! [X3: set_variable] : ( ord_le282106107riable @ X3 @ X3 ) ).
% 0.20/0.48
% 0.20/0.48 % order_refl
% 0.20/0.48 thf(fact_277_subset__emptyI,axiom,
% 0.20/0.48 ! [A3: set_variable] :
% 0.20/0.48 ( ! [X5: variable] :
% 0.20/0.48 ~ ( member_variable @ X5 @ A3 )
% 0.20/0.48 => ( ord_le282106107riable @ A3 @ bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % subset_emptyI
% 0.20/0.48 thf(fact_278_bot_Oextremum__uniqueI,axiom,
% 0.20/0.48 ! [A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ bot_bot_set_variable )
% 0.20/0.48 => ( A2 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % bot.extremum_uniqueI
% 0.20/0.48 thf(fact_279_bot_Oextremum__unique,axiom,
% 0.20/0.48 ! [A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ bot_bot_set_variable )
% 0.20/0.48 = ( A2 = bot_bot_set_variable ) ) ).
% 0.20/0.48
% 0.20/0.48 % bot.extremum_unique
% 0.20/0.48 thf(fact_280_bot_Oextremum,axiom,
% 0.20/0.48 ! [A2: set_variable] : ( ord_le282106107riable @ bot_bot_set_variable @ A2 ) ).
% 0.20/0.48
% 0.20/0.48 % bot.extremum
% 0.20/0.48 thf(fact_281_usubstappf__geqr,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.20/0.48 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.20/0.48 != none_fml )
% 0.20/0.48 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.20/0.48 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf_geqr
% 0.20/0.48 thf(fact_282_fml_Oinject_I2_J,axiom,
% 0.20/0.48 ! [X21: trm,X222: trm,Y21: trm,Y22: trm] :
% 0.20/0.48 ( ( ( geq @ X21 @ X222 )
% 0.20/0.48 = ( geq @ Y21 @ Y22 ) )
% 0.20/0.48 = ( ( X21 = Y21 )
% 0.20/0.48 & ( X222 = Y22 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % fml.inject(2)
% 0.20/0.48 thf(fact_283_Aterm__Some,axiom,
% 0.20/0.48 some_trm = some_trm ).
% 0.20/0.48
% 0.20/0.48 % Aterm_Some
% 0.20/0.48 thf(fact_284_Loopo_Ocases,axiom,
% 0.20/0.48 ! [X3: option_game] :
% 0.20/0.48 ( ! [Alpha: game] :
% 0.20/0.48 ( X3
% 0.20/0.48 != ( some_game @ Alpha ) )
% 0.20/0.48 => ( X3 = none_game ) ) ).
% 0.20/0.48
% 0.20/0.48 % Loopo.cases
% 0.20/0.48 thf(fact_285_Loopo_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_game > $o,A0: option_game] :
% 0.20/0.48 ( ! [Alpha: game] : ( P3 @ ( some_game @ Alpha ) )
% 0.20/0.48 => ( ( P3 @ none_game )
% 0.20/0.48 => ( P3 @ A0 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Loopo.induct
% 0.20/0.48 thf(fact_286_undefg__equiv,axiom,
% 0.20/0.48 ! [Alpha2: option_game] :
% 0.20/0.48 ( ( Alpha2 != none_game )
% 0.20/0.48 = ( ? [G: game] :
% 0.20/0.48 ( Alpha2
% 0.20/0.48 = ( some_game @ G ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % undefg_equiv
% 0.20/0.48 thf(fact_287_Composeo_Oinduct,axiom,
% 0.20/0.48 ! [P3: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 0.20/0.48 ( ! [Alpha: game,Beta: game] : ( P3 @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.20/0.48 => ( ! [Alpha: option_game] : ( P3 @ Alpha @ none_game )
% 0.20/0.48 => ( ! [V6: game] : ( P3 @ none_game @ ( some_game @ V6 ) )
% 0.20/0.48 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Composeo.induct
% 0.20/0.48 thf(fact_288_fml_Odistinct_I1_J,axiom,
% 0.20/0.48 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 0.20/0.48 ( ( pred @ X11 @ X12 )
% 0.20/0.48 != ( geq @ X21 @ X222 ) ) ).
% 0.20/0.48
% 0.20/0.48 % fml.distinct(1)
% 0.20/0.48 thf(fact_289_order__subst1,axiom,
% 0.20/0.48 ! [A2: set_variable,F2: set_variable > set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ ( F2 @ B3 ) )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ C2 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X5 @ Y4 )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order_subst1
% 0.20/0.48 thf(fact_290_order__subst2,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ ( F2 @ B3 ) @ C2 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X5 @ Y4 )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order_subst2
% 0.20/0.48 thf(fact_291_ord__eq__le__subst,axiom,
% 0.20/0.48 ! [A2: set_variable,F2: set_variable > set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( A2
% 0.20/0.48 = ( F2 @ B3 ) )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ C2 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X5 @ Y4 )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % ord_eq_le_subst
% 0.20/0.48 thf(fact_292_ord__le__eq__subst,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( ( F2 @ B3 )
% 0.20/0.48 = C2 )
% 0.20/0.48 => ( ! [X5: set_variable,Y4: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X5 @ Y4 )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 0.20/0.48 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % ord_le_eq_subst
% 0.20/0.48 thf(fact_293_eq__iff,axiom,
% 0.20/0.48 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 0.20/0.48 = ( ^ [X: set_variable,Y: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X @ Y )
% 0.20/0.48 & ( ord_le282106107riable @ Y @ X ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % eq_iff
% 0.20/0.48 thf(fact_294_antisym,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ Y3 @ X3 )
% 0.20/0.48 => ( X3 = Y3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % antisym
% 0.20/0.48 thf(fact_295_eq__refl,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable] :
% 0.20/0.48 ( ( X3 = Y3 )
% 0.20/0.48 => ( ord_le282106107riable @ X3 @ Y3 ) ) ).
% 0.20/0.48
% 0.20/0.48 % eq_refl
% 0.20/0.48 thf(fact_296_order_Otrans,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ C2 )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order.trans
% 0.20/0.48 thf(fact_297_antisym__conv,axiom,
% 0.20/0.48 ! [Y3: set_variable,X3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ Y3 @ X3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 = ( X3 = Y3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % antisym_conv
% 0.20/0.48 thf(fact_298_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.48 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 0.20/0.48 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A5 @ B5 )
% 0.20/0.48 & ( ord_le282106107riable @ B5 @ A5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order_class.order.eq_iff
% 0.20/0.48 thf(fact_299_ord__eq__le__trans,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( A2 = B3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ C2 )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % ord_eq_le_trans
% 0.20/0.48 thf(fact_300_ord__le__eq__trans,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( B3 = C2 )
% 0.20/0.48 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % ord_le_eq_trans
% 0.20/0.48 thf(fact_301_order__class_Oorder_Oantisym,axiom,
% 0.20/0.48 ! [A2: set_variable,B3: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ B3 @ A2 )
% 0.20/0.48 => ( A2 = B3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order_class.order.antisym
% 0.20/0.48 thf(fact_302_order__trans,axiom,
% 0.20/0.48 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.20/0.48 => ( ( ord_le282106107riable @ Y3 @ Z2 )
% 0.20/0.48 => ( ord_le282106107riable @ X3 @ Z2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % order_trans
% 0.20/0.48 thf(fact_303_dual__order_Orefl,axiom,
% 0.20/0.48 ! [A2: set_variable] : ( ord_le282106107riable @ A2 @ A2 ) ).
% 0.20/0.48
% 0.20/0.48 % dual_order.refl
% 0.20/0.48 thf(fact_304_dual__order_Otrans,axiom,
% 0.20/0.48 ! [B3: set_variable,A2: set_variable,C2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B3 @ A2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ C2 @ B3 )
% 0.20/0.48 => ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % dual_order.trans
% 0.20/0.48 thf(fact_305_dual__order_Oeq__iff,axiom,
% 0.20/0.48 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 0.20/0.48 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B5 @ A5 )
% 0.20/0.48 & ( ord_le282106107riable @ A5 @ B5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % dual_order.eq_iff
% 0.20/0.48 thf(fact_306_dual__order_Oantisym,axiom,
% 0.20/0.48 ! [B3: set_variable,A2: set_variable] :
% 0.20/0.48 ( ( ord_le282106107riable @ B3 @ A2 )
% 0.20/0.48 => ( ( ord_le282106107riable @ A2 @ B3 )
% 0.20/0.48 => ( A2 = B3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % dual_order.antisym
% 0.20/0.48 thf(fact_307_prop__restrict,axiom,
% 0.20/0.48 ! [X3: variable,Z5: set_variable,X6: set_variable,P3: variable > $o] :
% 0.20/0.48 ( ( member_variable @ X3 @ Z5 )
% 0.20/0.48 => ( ( ord_le282106107riable @ Z5
% 0.20/0.48 @ ( collect_variable
% 0.20/0.48 @ ^ [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ X6 )
% 0.20/0.48 & ( P3 @ X ) ) ) )
% 0.20/0.48 => ( P3 @ X3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % prop_restrict
% 0.20/0.48 thf(fact_308_Collect__restrict,axiom,
% 0.20/0.48 ! [X6: set_variable,P3: variable > $o] :
% 0.20/0.48 ( ord_le282106107riable
% 0.20/0.48 @ ( collect_variable
% 0.20/0.48 @ ^ [X: variable] :
% 0.20/0.48 ( ( member_variable @ X @ X6 )
% 0.20/0.48 & ( P3 @ X ) ) )
% 0.20/0.48 @ X6 ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_restrict
% 0.20/0.48 thf(fact_309_usubstappf__geq__conv,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.20/0.48 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.20/0.48 != none_fml )
% 0.20/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.48 != none_trm )
% 0.20/0.48 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.20/0.48 != none_trm ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf_geq_conv
% 0.20/0.48 thf(fact_310_usubstappf__geq,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.20/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.20/0.48 != none_trm )
% 0.20/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.20/0.48 != none_trm )
% 0.20/0.48 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.20/0.48 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf_geq
% 0.20/0.48 thf(fact_311_disjE__realizer2,axiom,
% 0.20/0.48 ! [P3: $o,Q: fml > $o,X3: option_fml,R4: option_fml > $o,F2: option_fml,G2: fml > option_fml] :
% 0.20/0.48 ( ( case_option_o_fml @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( P3
% 0.20/0.48 => ( R4 @ F2 ) )
% 0.20/0.48 => ( ! [Q2: fml] :
% 0.20/0.48 ( ( Q @ Q2 )
% 0.20/0.48 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.20/0.48 => ( R4 @ ( case_o209804997ml_fml @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % disjE_realizer2
% 0.20/0.48 thf(fact_312_disjE__realizer2,axiom,
% 0.20/0.48 ! [P3: $o,Q: trm > $o,X3: option_trm,R4: option_fml > $o,F2: option_fml,G2: trm > option_fml] :
% 0.20/0.48 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( P3
% 0.20/0.48 => ( R4 @ F2 ) )
% 0.20/0.48 => ( ! [Q2: trm] :
% 0.20/0.48 ( ( Q @ Q2 )
% 0.20/0.48 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.20/0.48 => ( R4 @ ( case_o325794063ml_trm @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % disjE_realizer2
% 0.20/0.48 thf(fact_313_disjE__realizer2,axiom,
% 0.20/0.48 ! [P3: $o,Q: trm > $o,X3: option_trm,R4: option_trm > $o,F2: option_trm,G2: trm > option_trm] :
% 0.20/0.48 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 0.20/0.48 => ( ( P3
% 0.20/0.48 => ( R4 @ F2 ) )
% 0.20/0.48 => ( ! [Q2: trm] :
% 0.20/0.48 ( ( Q @ Q2 )
% 0.20/0.48 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.20/0.48 => ( R4 @ ( case_o487727941rm_trm @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % disjE_realizer2
% 0.20/0.48 thf(fact_314_Geqo_Oelims,axiom,
% 0.20/0.48 ! [X3: option_trm,Xa: option_trm,Y3: option_fml] :
% 0.20/0.48 ( ( ( uSubst152838031e_Geqo @ X3 @ Xa )
% 0.20/0.48 = Y3 )
% 0.20/0.48 => ( ! [Theta2: trm] :
% 0.20/0.48 ( ( X3
% 0.20/0.48 = ( some_trm @ Theta2 ) )
% 0.20/0.48 => ! [Eta: trm] :
% 0.20/0.48 ( ( Xa
% 0.20/0.48 = ( some_trm @ Eta ) )
% 0.20/0.48 => ( Y3
% 0.20/0.48 != ( some_fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 0.20/0.48 => ( ( ( X3 = none_trm )
% 0.20/0.48 => ( Y3 != none_fml ) )
% 0.20/0.48 => ~ ( ? [V6: trm] :
% 0.20/0.48 ( X3
% 0.20/0.48 = ( some_trm @ V6 ) )
% 0.20/0.48 => ( ( Xa = none_trm )
% 0.20/0.48 => ( Y3 != none_fml ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Geqo.elims
% 0.20/0.48 thf(fact_315_inf__Int__eq,axiom,
% 0.20/0.48 ! [R4: set_variable,S: set_variable] :
% 0.20/0.48 ( ( inf_inf_variable_o
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 0.20/0.48 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % inf_Int_eq
% 0.20/0.48 thf(fact_316_Geqo_Osimps_I2_J,axiom,
% 0.20/0.48 ! [Eta2: option_trm] :
% 0.20/0.48 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 0.20/0.48 = none_fml ) ).
% 0.20/0.48
% 0.20/0.48 % Geqo.simps(2)
% 0.20/0.48 thf(fact_317_Geqo__undef,axiom,
% 0.20/0.48 ! [Theta: option_trm,Eta2: option_trm] :
% 0.20/0.48 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta2 )
% 0.20/0.48 = none_fml )
% 0.20/0.48 = ( ( Theta = none_trm )
% 0.20/0.48 | ( Eta2 = none_trm ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Geqo_undef
% 0.20/0.48 thf(fact_318_Geqo_Osimps_I3_J,axiom,
% 0.20/0.48 ! [V7: trm] :
% 0.20/0.48 ( ( uSubst152838031e_Geqo @ ( some_trm @ V7 ) @ none_trm )
% 0.20/0.48 = none_fml ) ).
% 0.20/0.48
% 0.20/0.48 % Geqo.simps(3)
% 0.20/0.48 thf(fact_319_Geqo_Osimps_I1_J,axiom,
% 0.20/0.48 ! [Theta: trm,Eta2: trm] :
% 0.20/0.48 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta2 ) )
% 0.20/0.48 = ( some_fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Geqo.simps(1)
% 0.20/0.48 thf(fact_320_usubstappf_Osimps_I2_J,axiom,
% 0.20/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.20/0.48 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.20/0.48 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % usubstappf.simps(2)
% 0.20/0.48 thf(fact_321_bot__empty__eq,axiom,
% 0.20/0.48 ( bot_bot_variable_o
% 0.20/0.48 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % bot_empty_eq
% 0.20/0.48 thf(fact_322_pred__subset__eq,axiom,
% 0.20/0.48 ! [R4: set_variable,S: set_variable] :
% 0.20/0.48 ( ( ord_le1407353162able_o
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 0.20/0.48 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 0.20/0.48 = ( ord_le282106107riable @ R4 @ S ) ) ).
% 0.20/0.48
% 0.20/0.48 % pred_subset_eq
% 0.20/0.48 thf(fact_323_Collect__empty__eq__bot,axiom,
% 0.20/0.48 ! [P3: variable > $o] :
% 0.20/0.48 ( ( ( collect_variable @ P3 )
% 0.20/0.48 = bot_bot_set_variable )
% 0.20/0.48 = ( P3 = bot_bot_variable_o ) ) ).
% 0.20/0.48
% 0.20/0.48 % Collect_empty_eq_bot
% 0.20/0.48 thf(fact_324_Set_Ois__empty__def,axiom,
% 0.20/0.48 ( is_empty_variable
% 0.20/0.48 = ( ^ [A4: set_variable] : ( A4 = bot_bot_set_variable ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % Set.is_empty_def
% 0.20/0.48 thf(fact_325_internal__case__prod__def,axiom,
% 0.20/0.48 produc1278328899on_fml = produc1250175341on_fml ).
% 0.20/0.48
% 0.20/0.48 % internal_case_prod_def
% 0.20/0.48 thf(fact_326_internal__case__prod__def,axiom,
% 0.20/0.48 produc2141841102on_trm = produc1231571704on_trm ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_327_internal__case__prod__def,axiom,
% 0.31/0.48 produc377919108on_fml = produc1615133358on_fml ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_328_internal__case__prod__def,axiom,
% 0.31/0.48 produc1214549391on_trm = produc1036610745on_trm ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_329_internal__case__prod__def,axiom,
% 0.31/0.48 produc1598111045on_fml = produc1420172399on_fml ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_330_internal__case__prod__def,axiom,
% 0.31/0.48 produc1591622303on_fml = produc347802313on_fml ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_331_internal__case__prod__def,axiom,
% 0.31/0.48 produc2129367017on_trm = produc885547027on_trm ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_332_internal__case__prod__def,axiom,
% 0.31/0.48 produc1903410526on_fml = produc154833544on_fml ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_333_internal__case__prod__def,axiom,
% 0.31/0.48 produc293671592on_trm = produc692578258on_trm ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_334_internal__case__prod__def,axiom,
% 0.31/0.48 produc724717725on_fml = produc1499310791on_fml ).
% 0.31/0.48
% 0.31/0.48 % internal_case_prod_def
% 0.31/0.48 thf(fact_335_usubstappt_Osimps_I4_J,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char,Theta: trm] :
% 0.31/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.31/0.48 = ( case_o487727941rm_trm @ none_trm
% 0.31/0.48 @ ^ [Sigma_theta: trm] :
% 0.31/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F2 @ Sigma_theta ) )
% 0.31/0.48 @ ^ [R: trm] :
% 0.31/0.48 ( if_option_trm
% 0.31/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.31/0.48 @ none_trm )
% 0.31/0.48 @ ( produc866613687on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [F4: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 ) )
% 0.31/0.48 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.simps(4)
% 0.31/0.48 thf(fact_336_trm_Oinject_I4_J,axiom,
% 0.31/0.48 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.31/0.48 ( ( ( func @ X41 @ X42 )
% 0.31/0.48 = ( func @ Y41 @ Y42 ) )
% 0.31/0.48 = ( ( X41 = Y41 )
% 0.31/0.48 & ( X42 = Y42 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % trm.inject(4)
% 0.31/0.48 thf(fact_337_usubstappt__func2,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable,Theta: trm] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [F4: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.31/0.48 != bot_bot_set_variable )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.31/0.48 = none_trm ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt_func2
% 0.31/0.48 thf(fact_338_usubstappt__func,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [F4: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.31/0.48 = ( some_trm @ Sigma_theta2 ) )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.31/0.48 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt_func
% 0.31/0.48 thf(fact_339_usubstappt__func__conv,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char,Theta: trm] :
% 0.31/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 0.31/0.48 != none_trm )
% 0.31/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.31/0.48 != none_trm )
% 0.31/0.48 & ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [F4: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = none_trm )
% 0.31/0.48 | ? [R3: trm] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [F4: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R3 ) )
% 0.31/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.31/0.48 = bot_bot_set_variable ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt_func_conv
% 0.31/0.48 thf(fact_340_usappconst__simp,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 => ( ( uSubst1559070963pconst @ Sigma @ U @ F2 )
% 0.31/0.48 = ( some_trm @ R2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usappconst_simp
% 0.31/0.48 thf(fact_341_usappconst__conv,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 0.31/0.48 ( ( ( uSubst1559070963pconst @ Sigma @ U @ F2 )
% 0.31/0.48 != none_trm )
% 0.31/0.48 => ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = none_trm )
% 0.31/0.48 | ? [R3: trm] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R3 ) )
% 0.31/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.31/0.48 = bot_bot_set_variable ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usappconst_conv
% 0.31/0.48 thf(fact_342_usappconst__def,axiom,
% 0.31/0.48 ( uSubst1559070963pconst
% 0.31/0.48 = ( ^ [Sigma2: produc1418842292n_game,U2: set_variable,F: char] :
% 0.31/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F ) )
% 0.31/0.48 @ ^ [R: trm] :
% 0.31/0.48 ( if_option_trm
% 0.31/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 @ ( some_trm @ R )
% 0.31/0.48 @ none_trm )
% 0.31/0.48 @ ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma2
% 0.31/0.48 @ F ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usappconst_def
% 0.31/0.48 thf(fact_343_usubstappt__const,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 0.31/0.48 = ( some_trm @ R2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt_const
% 0.31/0.48 thf(fact_344_trm_Oinject_I3_J,axiom,
% 0.31/0.48 ! [X32: char,Y32: char] :
% 0.31/0.48 ( ( ( const @ X32 )
% 0.31/0.48 = ( const @ Y32 ) )
% 0.31/0.48 = ( X32 = Y32 ) ) ).
% 0.31/0.48
% 0.31/0.48 % trm.inject(3)
% 0.31/0.48 thf(fact_345_usubstappt_Osimps_I3_J,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 0.31/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 0.31/0.48 = ( uSubst1559070963pconst @ Sigma @ U @ F2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.simps(3)
% 0.31/0.48 thf(fact_346_trm_Odistinct_I23_J,axiom,
% 0.31/0.48 ! [X32: char,X41: char,X42: trm] :
% 0.31/0.48 ( ( const @ X32 )
% 0.31/0.48 != ( func @ X41 @ X42 ) ) ).
% 0.31/0.48
% 0.31/0.48 % trm.distinct(23)
% 0.31/0.48 thf(fact_347_usubstappt__const__conv,axiom,
% 0.31/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 0.31/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 0.31/0.48 != none_trm )
% 0.31/0.48 => ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = none_trm )
% 0.31/0.48 | ? [R3: trm] :
% 0.31/0.48 ( ( ( produc866613687on_trm
% 0.31/0.48 @ ^ [F0: char > option_trm] :
% 0.31/0.48 ( produc1231571704on_trm
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1036610745on_trm
% 0.31/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.48 @ Sigma
% 0.31/0.48 @ F2 )
% 0.31/0.48 = ( some_trm @ R3 ) )
% 0.31/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.31/0.48 = bot_bot_set_variable ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt_const_conv
% 0.31/0.48 thf(fact_348_subset__Collect__iff,axiom,
% 0.31/0.48 ! [B2: set_variable,A3: set_variable,P3: variable > $o] :
% 0.31/0.48 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.31/0.48 => ( ( ord_le282106107riable @ B2
% 0.31/0.48 @ ( collect_variable
% 0.31/0.48 @ ^ [X: variable] :
% 0.31/0.48 ( ( member_variable @ X @ A3 )
% 0.31/0.48 & ( P3 @ X ) ) ) )
% 0.31/0.48 = ( ! [X: variable] :
% 0.31/0.48 ( ( member_variable @ X @ B2 )
% 0.31/0.48 => ( P3 @ X ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subset_Collect_iff
% 0.31/0.48 thf(fact_349_subset__CollectI,axiom,
% 0.31/0.48 ! [B2: set_variable,A3: set_variable,Q: variable > $o,P3: variable > $o] :
% 0.31/0.48 ( ( ord_le282106107riable @ B2 @ A3 )
% 0.31/0.48 => ( ! [X5: variable] :
% 0.31/0.48 ( ( member_variable @ X5 @ B2 )
% 0.31/0.48 => ( ( Q @ X5 )
% 0.31/0.48 => ( P3 @ X5 ) ) )
% 0.31/0.48 => ( ord_le282106107riable
% 0.31/0.48 @ ( collect_variable
% 0.31/0.48 @ ^ [X: variable] :
% 0.31/0.48 ( ( member_variable @ X @ B2 )
% 0.31/0.48 & ( Q @ X ) ) )
% 0.31/0.48 @ ( collect_variable
% 0.31/0.48 @ ^ [X: variable] :
% 0.31/0.48 ( ( member_variable @ X @ A3 )
% 0.31/0.48 & ( P3 @ X ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subset_CollectI
% 0.31/0.48 thf(fact_350_conj__subset__def,axiom,
% 0.31/0.48 ! [A3: set_variable,P3: variable > $o,Q: variable > $o] :
% 0.31/0.48 ( ( ord_le282106107riable @ A3
% 0.31/0.48 @ ( collect_variable
% 0.31/0.48 @ ^ [X: variable] :
% 0.31/0.48 ( ( P3 @ X )
% 0.31/0.48 & ( Q @ X ) ) ) )
% 0.31/0.48 = ( ( ord_le282106107riable @ A3 @ ( collect_variable @ P3 ) )
% 0.31/0.48 & ( ord_le282106107riable @ A3 @ ( collect_variable @ Q ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % conj_subset_def
% 0.31/0.48 thf(fact_351_Diamondo_Ocases,axiom,
% 0.31/0.48 ! [X3: produc1739631244on_fml] :
% 0.31/0.48 ( ! [Alpha: game,Phi2: fml] :
% 0.31/0.48 ( X3
% 0.31/0.48 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) ) )
% 0.31/0.48 => ( ! [Phi2: option_fml] :
% 0.31/0.48 ( X3
% 0.31/0.48 != ( produc2124676926on_fml @ none_game @ Phi2 ) )
% 0.31/0.48 => ~ ! [V6: game] :
% 0.31/0.48 ( X3
% 0.31/0.48 != ( produc2124676926on_fml @ ( some_game @ V6 ) @ none_fml ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Diamondo.cases
% 0.31/0.48
% 0.31/0.48 % Helper facts (5)
% 0.31/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 0.31/0.48 ! [X3: option_fml,Y3: option_fml] :
% 0.31/0.48 ( ( if_option_fml @ $false @ X3 @ Y3 )
% 0.31/0.48 = Y3 ) ).
% 0.31/0.48
% 0.31/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 0.31/0.48 ! [X3: option_fml,Y3: option_fml] :
% 0.31/0.48 ( ( if_option_fml @ $true @ X3 @ Y3 )
% 0.31/0.48 = X3 ) ).
% 0.31/0.48
% 0.31/0.48 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.31/0.48 ! [P3: $o] :
% 0.31/0.48 ( ( P3 = $true )
% 0.31/0.48 | ( P3 = $false ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.31/0.48 ! [X3: option_trm,Y3: option_trm] :
% 0.31/0.48 ( ( if_option_trm @ $false @ X3 @ Y3 )
% 0.31/0.48 = Y3 ) ).
% 0.31/0.48
% 0.31/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.31/0.48 ! [X3: option_trm,Y3: option_trm] :
% 0.31/0.48 ( ( if_option_trm @ $true @ X3 @ Y3 )
% 0.31/0.48 = X3 ) ).
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 0.31/0.48 ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 0.31/0.48 != none_fml )
% 0.31/0.48 | ( ( produc1250175341on_fml
% 0.31/0.48 @ ^ [Uu: char > option_trm] :
% 0.31/0.48 ( produc1615133358on_fml
% 0.31/0.48 @ ^ [Uv: char > option_trm] :
% 0.31/0.48 ( produc1420172399on_fml
% 0.31/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.31/0.48 @ sigma
% 0.31/0.48 @ p )
% 0.31/0.48 = none_fml ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.94/1.56 ---- Embedded in THF ---
% 2.94/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.94/1.56 %%% Generated on Tue Feb 24 08:30:03 EST 2026
% 2.94/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.94/1.56 %%% Logic specification used:
% 2.94/1.56 %%% thf(spec, logic, $$dhol).
% 2.94/1.56
% 2.94/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2DTF7804.p
% See solution above
% 2.94/1.56 ------------------------
% 3.15/1.60 ---- Cleaned THF ---
% 3.15/1.60 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,
% 3.15/1.60 produc1418842292n_game: $tType ).
% 3.15/1.60
% 3.15/1.60 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__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J,type,
% 3.15/1.60 produc62062515n_game: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__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,type,
% 3.15/1.60 produc799602994n_game: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1739631244on_fml: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 3.15/1.60 option_game: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 option_trm: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 option_fml: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.15/1.60 set_variable: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Syntax__Ovariable,type,
% 3.15/1.60 variable: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Syntax__Ogame,type,
% 3.15/1.60 game: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__String__Ochar,type,
% 3.15/1.60 char: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Syntax__Otrm,type,
% 3.15/1.60 trm: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(ty_n_t__Syntax__Ofml,type,
% 3.15/1.60 fml: $tType ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 if_option_fml: $o > option_fml > option_fml > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 3.15/1.60 inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
% 3.15/1.60 inf_inf_o: $o > $o > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.15/1.60 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 3.15/1.60 none_fml: option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 3.15/1.60 none_game: option_game ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 3.15/1.60 none_trm: option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 3.15/1.60 some_fml: fml > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 3.15/1.60 some_game: game > option_game ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 3.15/1.60 some_trm: trm > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 3.15/1.60 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 3.15/1.60 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 3.15/1.60 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Ofml,type,
% 3.15/1.60 case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Otrm,type,
% 3.15/1.60 case_o325794063ml_trm: option_fml > ( trm > option_fml ) > option_trm > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Syntax__Otrm,type,
% 3.15/1.60 case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 3.15/1.60 the_fml: option_fml > fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 3.15/1.60 the_game: option_game > game ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 3.15/1.60 the_trm: option_trm > trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 3.15/1.60 bot_bot_variable_o: variable > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.15/1.60 bot_bot_set_variable: set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 3.15/1.60 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.15/1.60 ord_le282106107riable: set_variable > set_variable > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.15/1.60 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.15/1.60 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.15/1.60 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.15/1.60 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.15/1.60 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.15/1.60 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.15/1.60 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.15/1.60 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 3.15/1.60 collect_variable: ( variable > $o ) > set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 3.15/1.60 is_empty_variable: set_variable > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Static__Semantics_OFVF,type,
% 3.15/1.60 static_FVF: fml > set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Static__Semantics_OFVT,type,
% 3.15/1.60 static_FVT: trm > set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Syntax_Ofml_OGeq,type,
% 3.15/1.60 geq: trm > trm > fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Syntax_Ofml_OPred,type,
% 3.15/1.60 pred: char > trm > fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Syntax_Otrm_OConst,type,
% 3.15/1.60 const: char > trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_Syntax_Otrm_OFunc,type,
% 3.15/1.60 func: char > trm > trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 3.15/1.60 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 3.15/1.60 uSubst1408967625substt: trm > produc1418842292n_game ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 3.15/1.60 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 3.15/1.60 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 3.15/1.60 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 3.15/1.60 member_variable: variable > set_variable > $o ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v_Ua____,type,
% 3.15/1.60 ua: set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v_Va____,type,
% 3.15/1.60 va: set_variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v__092_060sigma_062,type,
% 3.15/1.60 sigma: produc1418842292n_game ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v__092_060theta_062____,type,
% 3.15/1.60 theta: trm ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v_p____,type,
% 3.15/1.60 p: char ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v_vv____,type,
% 3.15/1.60 vv: set_variable > set_variable > variable ).
% 3.15/1.60
% 3.15/1.60 thf(sy_v_vva____,type,
% 3.15/1.60 vva: set_variable > set_variable > variable ).
% 3.15/1.60
% 3.15/1.60 thf(fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062,axiom,
% 3.15/1.60 ! [X0: set_variable,X1: set_variable] :
% 3.15/1.60 ( ( ? [V2: variable] :
% 3.15/1.60 ( ( member_variable @ V2 @ X1 )
% 3.15/1.60 & ? [V3: variable] :
% 3.15/1.60 ( ( member_variable @ V3 @ X0 )
% 3.15/1.60 & ( V2 = V3 ) ) ) )
% 3.15/1.60 = ( ( member_variable @ ( vv @ X0 @ X1 ) @ X1 )
% 3.15/1.60 & ? [V3: variable] :
% 3.15/1.60 ( ( member_variable @ V3 @ X0 )
% 3.15/1.60 & ( ( vv @ X0 @ X1 )
% 3.15/1.60 = V3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 3.15/1.60 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.15/1.60 != none_fml ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
% 3.15/1.60 ~ ( ( ( inf_inf_set_variable
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 = none_fml ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
% 3.15/1.60 ( ~ ( ( ( ( inf_inf_set_variable
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
% 3.15/1.60 & ( ( ( inf_inf_set_variable
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 => ( none_fml
% 3.15/1.60 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
% 3.15/1.60 => ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p )
% 3.15/1.60 = none_fml ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_4_usubstappf__det,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Phi: fml,V: set_variable] :
% 3.15/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 3.15/1.60 != none_fml )
% 3.15/1.60 => ( ( ( uSubst516392804stappf @ Sigma @ V @ Phi )
% 3.15/1.60 != none_fml )
% 3.15/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 3.15/1.60 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_5_f8,axiom,
% 3.15/1.60 ( ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p )
% 3.15/1.60 = none_fml )
% 3.15/1.60 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.15/1.60 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062,axiom,
% 3.15/1.60 ( ~ ( member_variable
% 3.15/1.60 @ ( vv @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 | ~ ( member_variable
% 3.15/1.60 @ ( vva @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 | ( ( vv @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 != ( vva @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_7_fml_Oinject_I1_J,axiom,
% 3.15/1.60 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 3.15/1.60 ( ( ( pred @ X11 @ X12 )
% 3.15/1.60 = ( pred @ Y11 @ Y12 ) )
% 3.15/1.60 = ( ( X11 = Y11 )
% 3.15/1.60 & ( X12 = Y12 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_8_f7,axiom,
% 3.15/1.60 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 3.15/1.60 = ( uSubst516392818stappt @ sigma @ va @ theta ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_9_case__prod__app,axiom,
% 3.15/1.60 ( produc1250175341on_fml
% 3.15/1.60 = ( ^ [F: ( char > option_trm ) > produc62062515n_game > char > option_fml,X: produc1418842292n_game,Y: char] :
% 3.15/1.60 ( produc1499310791on_fml
% 3.15/1.60 @ ^ [L: char > option_trm,R: produc62062515n_game] : ( F @ L @ R @ Y )
% 3.15/1.60 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_10_case__prod__app,axiom,
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 = ( ^ [F: ( char > option_trm ) > produc799602994n_game > char > option_trm,X: produc62062515n_game,Y: char] :
% 3.15/1.60 ( produc692578258on_trm
% 3.15/1.60 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F @ L @ R @ Y )
% 3.15/1.60 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_11_case__prod__app,axiom,
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 = ( ^ [F: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 3.15/1.60 ( produc154833544on_fml
% 3.15/1.60 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F @ L @ R @ Y )
% 3.15/1.60 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_12_case__prod__app,axiom,
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 = ( ^ [F: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 3.15/1.60 ( produc885547027on_trm
% 3.15/1.60 @ ^ [L: char > option_fml,R: char > option_game] : ( F @ L @ R @ Y )
% 3.15/1.60 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_13_case__prod__app,axiom,
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 = ( ^ [F: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 3.15/1.60 ( produc347802313on_fml
% 3.15/1.60 @ ^ [L: char > option_fml,R: char > option_game] : ( F @ L @ R @ Y )
% 3.15/1.60 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_14_f1,axiom,
% 3.15/1.60 ! [V4: variable] :
% 3.15/1.60 ( ~ ( member_variable @ V4 @ va )
% 3.15/1.60 | ( member_variable @ V4 @ ua ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_15_f10,axiom,
% 3.15/1.60 ( ( ( ( inf_inf_set_variable
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 | ! [V4: variable] :
% 3.15/1.60 ( ~ ( member_variable @ V4
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 | ! [Va: variable] :
% 3.15/1.60 ( ~ ( member_variable @ Va @ va )
% 3.15/1.60 | ( V4 != Va ) ) ) )
% 3.15/1.60 & ( ( ( inf_inf_set_variable
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 | ( ( member_variable
% 3.15/1.60 @ ( vv @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 & ( member_variable
% 3.15/1.60 @ ( vva @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 @ va )
% 3.15/1.60 & ( ( vv @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) )
% 3.15/1.60 = ( vva @ va
% 3.15/1.60 @ ( static_FVF
% 3.15/1.60 @ ( the_fml
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_16_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc347802313on_fml
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_17_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc885547027on_trm
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_18_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_trm > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc885547027on_trm @ F2 @ Prod ) )
% 3.15/1.60 = ( produc347802313on_fml
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_19_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_trm > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc885547027on_trm @ F2 @ Prod ) )
% 3.15/1.60 = ( produc885547027on_trm
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_20_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: ( char > option_trm ) > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc1036610745on_trm @ F2 @ Prod ) )
% 3.15/1.60 = ( produc347802313on_fml
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_21_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: ( char > option_trm ) > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc1036610745on_trm @ F2 @ Prod ) )
% 3.15/1.60 = ( produc885547027on_trm
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_22_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: ( char > option_fml ) > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc1420172399on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc347802313on_fml
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_23_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: ( char > option_fml ) > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc1420172399on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc885547027on_trm
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_24_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > char > option_trm,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc1036610745on_trm
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_25_prod_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > char > option_fml,F2: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 3.15/1.60 ( ( H @ ( produc347802313on_fml @ F2 @ Prod ) )
% 3.15/1.60 = ( produc1420172399on_fml
% 3.15/1.60 @ ^ [X13: char > option_fml,X2: char > option_game] : ( H @ ( F2 @ X13 @ X2 ) )
% 3.15/1.60 @ Prod ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_26_usubstappf__pred2,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,P2: char,R2: fml,U: set_variable,Theta: trm] :
% 3.15/1.60 ( ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ P2 )
% 3.15/1.60 = ( some_fml @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 3.15/1.60 = none_fml ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_27_f2,axiom,
% 3.15/1.60 ! [Z: option_fml,F3: fml > option_fml,Za: option_fml] :
% 3.15/1.60 ( ( ( Za = none_fml )
% 3.15/1.60 => ( ( case_o209804997ml_fml @ Z @ F3 @ Za )
% 3.15/1.60 = Z ) )
% 3.15/1.60 & ( ( Za != none_fml )
% 3.15/1.60 => ( ( case_o209804997ml_fml @ Z @ F3 @ Za )
% 3.15/1.60 = ( F3 @ ( the_fml @ Za ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_28_Pred_Oprems_I1_J,axiom,
% 3.15/1.60 ord_le282106107riable @ va @ ua ).
% 3.15/1.60
% 3.15/1.60 thf(fact_29_f9,axiom,
% 3.15/1.60 ! [V5: set_variable,Va2: set_variable] :
% 3.15/1.60 ( ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 | ! [V4: variable] :
% 3.15/1.60 ( ~ ( member_variable @ V4 @ V5 )
% 3.15/1.60 | ! [Va: variable] :
% 3.15/1.60 ( ~ ( member_variable @ Va @ Va2 )
% 3.15/1.60 | ( V4 != Va ) ) ) )
% 3.15/1.60 & ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 | ( ( member_variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 3.15/1.60 & ( member_variable @ ( vva @ Va2 @ V5 ) @ Va2 )
% 3.15/1.60 & ( ( vv @ Va2 @ V5 )
% 3.15/1.60 = ( vva @ Va2 @ V5 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_30__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.15/1.60 ~ ! [Vva: set_variable > set_variable > variable] :
% 3.15/1.60 ~ ! [V5: set_variable,Va2: set_variable] :
% 3.15/1.60 ( ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 | ! [V4: variable] :
% 3.15/1.60 ( ~ ( member_variable @ V4 @ V5 )
% 3.15/1.60 | ! [Va: variable] :
% 3.15/1.60 ( ~ ( member_variable @ Va @ Va2 )
% 3.15/1.60 | ( V4 != Va ) ) ) )
% 3.15/1.60 & ( ( ( inf_inf_set_variable @ V5 @ Va2 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 | ( ( member_variable @ ( vv @ Va2 @ V5 ) @ V5 )
% 3.15/1.60 & ( member_variable @ ( Vva @ Va2 @ V5 ) @ Va2 )
% 3.15/1.60 & ( ( vv @ Va2 @ V5 )
% 3.15/1.60 = ( Vva @ Va2 @ V5 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_31_option_Oinject,axiom,
% 3.15/1.60 ! [X22: fml,Y2: fml] :
% 3.15/1.60 ( ( ( some_fml @ X22 )
% 3.15/1.60 = ( some_fml @ Y2 ) )
% 3.15/1.60 = ( X22 = Y2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_32_option_Oinject,axiom,
% 3.15/1.60 ! [X22: trm,Y2: trm] :
% 3.15/1.60 ( ( ( some_trm @ X22 )
% 3.15/1.60 = ( some_trm @ Y2 ) )
% 3.15/1.60 = ( X22 = Y2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_33_option_Oinject,axiom,
% 3.15/1.60 ! [X22: game,Y2: game] :
% 3.15/1.60 ( ( ( some_game @ X22 )
% 3.15/1.60 = ( some_game @ Y2 ) )
% 3.15/1.60 = ( X22 = Y2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_34_f5,axiom,
% 3.15/1.60 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 3.15/1.60 != none_trm ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_35_not__Some__eq,axiom,
% 3.15/1.60 ! [X3: option_fml] :
% 3.15/1.60 ( ( ! [Y: fml] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_fml @ Y ) ) )
% 3.15/1.60 = ( X3 = none_fml ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_36_not__Some__eq,axiom,
% 3.15/1.60 ! [X3: option_trm] :
% 3.15/1.60 ( ( ! [Y: trm] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_trm @ Y ) ) )
% 3.15/1.60 = ( X3 = none_trm ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_37_not__Some__eq,axiom,
% 3.15/1.60 ! [X3: option_game] :
% 3.15/1.60 ( ( ! [Y: game] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_game @ Y ) ) )
% 3.15/1.60 = ( X3 = none_game ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_38_not__None__eq,axiom,
% 3.15/1.60 ! [X3: option_fml] :
% 3.15/1.60 ( ( X3 != none_fml )
% 3.15/1.60 = ( ? [Y: fml] :
% 3.15/1.60 ( X3
% 3.15/1.60 = ( some_fml @ Y ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_39_not__None__eq,axiom,
% 3.15/1.60 ! [X3: option_trm] :
% 3.15/1.60 ( ( X3 != none_trm )
% 3.15/1.60 = ( ? [Y: trm] :
% 3.15/1.60 ( X3
% 3.15/1.60 = ( some_trm @ Y ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_40_not__None__eq,axiom,
% 3.15/1.60 ! [X3: option_game] :
% 3.15/1.60 ( ( X3 != none_game )
% 3.15/1.60 = ( ? [Y: game] :
% 3.15/1.60 ( X3
% 3.15/1.60 = ( some_game @ Y ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_41_option_Ocollapse,axiom,
% 3.15/1.60 ! [Option: option_fml] :
% 3.15/1.60 ( ( Option != none_fml )
% 3.15/1.60 => ( ( some_fml @ ( the_fml @ Option ) )
% 3.15/1.60 = Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_42_option_Ocollapse,axiom,
% 3.15/1.60 ! [Option: option_trm] :
% 3.15/1.60 ( ( Option != none_trm )
% 3.15/1.60 => ( ( some_trm @ ( the_trm @ Option ) )
% 3.15/1.60 = Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_43_option_Ocollapse,axiom,
% 3.15/1.60 ! [Option: option_game] :
% 3.15/1.60 ( ( Option != none_game )
% 3.15/1.60 => ( ( some_game @ ( the_game @ Option ) )
% 3.15/1.60 = Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_44_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: game > $o,X22: game] :
% 3.15/1.60 ( ( case_option_o_game @ F1 @ F22 @ ( some_game @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_45_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: trm > $o,X22: trm] :
% 3.15/1.60 ( ( case_option_o_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_46_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: fml > $o,X22: fml] :
% 3.15/1.60 ( ( case_option_o_fml @ F1 @ F22 @ ( some_fml @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_47_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: option_fml,F22: fml > option_fml,X22: fml] :
% 3.15/1.60 ( ( case_o209804997ml_fml @ F1 @ F22 @ ( some_fml @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_48_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: option_fml,F22: trm > option_fml,X22: trm] :
% 3.15/1.60 ( ( case_o325794063ml_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_49_option_Osimps_I5_J,axiom,
% 3.15/1.60 ! [F1: option_trm,F22: trm > option_trm,X22: trm] :
% 3.15/1.60 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 3.15/1.60 = ( F22 @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_50_option_Osel,axiom,
% 3.15/1.60 ! [X22: fml] :
% 3.15/1.60 ( ( the_fml @ ( some_fml @ X22 ) )
% 3.15/1.60 = X22 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_51_option_Osel,axiom,
% 3.15/1.60 ! [X22: trm] :
% 3.15/1.60 ( ( the_trm @ ( some_trm @ X22 ) )
% 3.15/1.60 = X22 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_52_option_Osel,axiom,
% 3.15/1.60 ! [X22: game] :
% 3.15/1.60 ( ( the_game @ ( some_game @ X22 ) )
% 3.15/1.60 = X22 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_53_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_game )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_game @ ( the_game @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_game @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_54_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_trm )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_55_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_fml )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_56_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.15/1.60 ( ( P3 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_fml )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_57_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_trm )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_58_option_Osplit__sel,axiom,
% 3.15/1.60 ! [P3: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ( ( Option = none_trm )
% 3.15/1.60 => ( P3 @ F1 ) )
% 3.15/1.60 & ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 => ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_59_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > option_fml,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.15/1.60 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_o209804997ml_fml @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_60_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > option_fml,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_o325794063ml_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_61_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > option_trm,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_o487727941rm_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_62_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_trm > option_fml,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_o325794063ml_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_63_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_o487727941rm_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_64_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 3.15/1.60 ( ( H @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_option_o_game @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: game] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_65_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_option_o_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_66_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 3.15/1.60 ( ( H @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_option_o_fml @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_67_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.15/1.60 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_option_o_fml @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_68_option_Ocase__distrib,axiom,
% 3.15/1.60 ! [H: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.15/1.60 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( case_option_o_trm @ ( H @ F1 )
% 3.15/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_69_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: game > $o,Option: option_game] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_game @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_game )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_game @ ( the_game @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_game @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_70_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: trm > $o,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_trm )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_71_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: $o > $o,F1: $o,F22: fml > $o,Option: option_fml] :
% 3.15/1.60 ( ( P3 @ ( case_option_o_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_fml )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_72_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.15/1.60 ( ( P3 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_fml )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_73_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_trm )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_74_option_Osplit__sel__asm,axiom,
% 3.15/1.60 ! [P3: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.15/1.60 = ( ~ ( ( ( Option = none_trm )
% 3.15/1.60 & ~ ( P3 @ F1 ) )
% 3.15/1.60 | ( ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.15/1.60 & ~ ( P3 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_75_usubstappt__det,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 3.15/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_76_usubstappt__antimon,axiom,
% 3.15/1.60 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Theta: trm] :
% 3.15/1.60 ( ( ord_le282106107riable @ V @ U )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_77_option_Oexhaust__sel,axiom,
% 3.15/1.60 ! [Option: option_fml] :
% 3.15/1.60 ( ( Option != none_fml )
% 3.15/1.60 => ( Option
% 3.15/1.60 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_78_option_Oexhaust__sel,axiom,
% 3.15/1.60 ! [Option: option_trm] :
% 3.15/1.60 ( ( Option != none_trm )
% 3.15/1.60 => ( Option
% 3.15/1.60 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_79_option_Oexhaust__sel,axiom,
% 3.15/1.60 ! [Option: option_game] :
% 3.15/1.60 ( ( Option != none_game )
% 3.15/1.60 => ( Option
% 3.15/1.60 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_80_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_fml,P3: option_fml > option_fml > $o,Y3: option_fml] :
% 3.15/1.60 ( ( ( X3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: fml,B: fml] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_fml @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_fml @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_81_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_fml,P3: option_fml > option_trm > $o,Y3: option_trm] :
% 3.15/1.60 ( ( ( X3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: fml,B: trm] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_fml @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_trm @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_82_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_fml,P3: option_fml > option_game > $o,Y3: option_game] :
% 3.15/1.60 ( ( ( X3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: fml,B: game] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_fml @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_game @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_83_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_trm,P3: option_trm > option_fml > $o,Y3: option_fml] :
% 3.15/1.60 ( ( ( X3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: trm,B: fml] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_trm @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_fml @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_84_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_trm,P3: option_trm > option_trm > $o,Y3: option_trm] :
% 3.15/1.60 ( ( ( X3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: trm,B: trm] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_trm @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_trm @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_85_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_trm,P3: option_trm > option_game > $o,Y3: option_game] :
% 3.15/1.60 ( ( ( X3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: trm,B: game] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_trm @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_game @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_86_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_game,P3: option_game > option_fml > $o,Y3: option_fml] :
% 3.15/1.60 ( ( ( X3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_fml )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: game,B: fml] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_game @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_fml @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_87_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_game,P3: option_game > option_trm > $o,Y3: option_trm] :
% 3.15/1.60 ( ( ( X3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_trm )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: game,B: trm] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_game @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_trm @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_88_combine__options__cases,axiom,
% 3.15/1.60 ! [X3: option_game,P3: option_game > option_game > $o,Y3: option_game] :
% 3.15/1.60 ( ( ( X3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ( ( Y3 = none_game )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) )
% 3.15/1.60 => ( ! [A: game,B: game] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_game @ A ) )
% 3.15/1.60 => ( ( Y3
% 3.15/1.60 = ( some_game @ B ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) )
% 3.15/1.60 => ( P3 @ X3 @ Y3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_89_split__option__all,axiom,
% 3.15/1.60 ( ( ^ [P4: option_fml > $o] :
% 3.15/1.60 ! [X4: option_fml] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_fml > $o] :
% 3.15/1.60 ( ( P @ none_fml )
% 3.15/1.60 & ! [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_90_split__option__all,axiom,
% 3.15/1.60 ( ( ^ [P4: option_trm > $o] :
% 3.15/1.60 ! [X4: option_trm] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_trm > $o] :
% 3.15/1.60 ( ( P @ none_trm )
% 3.15/1.60 & ! [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_91_split__option__all,axiom,
% 3.15/1.60 ( ( ^ [P4: option_game > $o] :
% 3.15/1.60 ! [X4: option_game] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_game > $o] :
% 3.15/1.60 ( ( P @ none_game )
% 3.15/1.60 & ! [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_92_split__option__ex,axiom,
% 3.15/1.60 ( ( ^ [P4: option_fml > $o] :
% 3.15/1.60 ? [X4: option_fml] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_fml > $o] :
% 3.15/1.60 ( ( P @ none_fml )
% 3.15/1.60 | ? [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_93_split__option__ex,axiom,
% 3.15/1.60 ( ( ^ [P4: option_trm > $o] :
% 3.15/1.60 ? [X4: option_trm] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_trm > $o] :
% 3.15/1.60 ( ( P @ none_trm )
% 3.15/1.60 | ? [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_94_split__option__ex,axiom,
% 3.15/1.60 ( ( ^ [P4: option_game > $o] :
% 3.15/1.60 ? [X4: option_game] : ( P4 @ X4 ) )
% 3.15/1.60 = ( ^ [P: option_game > $o] :
% 3.15/1.60 ( ( P @ none_game )
% 3.15/1.60 | ? [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_95_option_Oinducts,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,Option: option_fml] :
% 3.15/1.60 ( ( P3 @ none_fml )
% 3.15/1.60 => ( ! [X5: fml] : ( P3 @ ( some_fml @ X5 ) )
% 3.15/1.60 => ( P3 @ Option ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_96_option_Oinducts,axiom,
% 3.15/1.60 ! [P3: option_trm > $o,Option: option_trm] :
% 3.15/1.60 ( ( P3 @ none_trm )
% 3.15/1.60 => ( ! [X5: trm] : ( P3 @ ( some_trm @ X5 ) )
% 3.15/1.60 => ( P3 @ Option ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_97_option_Oinducts,axiom,
% 3.15/1.60 ! [P3: option_game > $o,Option: option_game] :
% 3.15/1.60 ( ( P3 @ none_game )
% 3.15/1.60 => ( ! [X5: game] : ( P3 @ ( some_game @ X5 ) )
% 3.15/1.60 => ( P3 @ Option ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_98_option_Oexhaust,axiom,
% 3.15/1.60 ! [Y3: option_fml] :
% 3.15/1.60 ( ( Y3 != none_fml )
% 3.15/1.60 => ~ ! [X23: fml] :
% 3.15/1.60 ( Y3
% 3.15/1.60 != ( some_fml @ X23 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_99_option_Oexhaust,axiom,
% 3.15/1.60 ! [Y3: option_trm] :
% 3.15/1.60 ( ( Y3 != none_trm )
% 3.15/1.60 => ~ ! [X23: trm] :
% 3.15/1.60 ( Y3
% 3.15/1.60 != ( some_trm @ X23 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_100_option_Oexhaust,axiom,
% 3.15/1.60 ! [Y3: option_game] :
% 3.15/1.60 ( ( Y3 != none_game )
% 3.15/1.60 => ~ ! [X23: game] :
% 3.15/1.60 ( Y3
% 3.15/1.60 != ( some_game @ X23 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_101_option_OdiscI,axiom,
% 3.15/1.60 ! [Option: option_fml,X22: fml] :
% 3.15/1.60 ( ( Option
% 3.15/1.60 = ( some_fml @ X22 ) )
% 3.15/1.60 => ( Option != none_fml ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_102_option_OdiscI,axiom,
% 3.15/1.60 ! [Option: option_trm,X22: trm] :
% 3.15/1.60 ( ( Option
% 3.15/1.60 = ( some_trm @ X22 ) )
% 3.15/1.60 => ( Option != none_trm ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_103_option_OdiscI,axiom,
% 3.15/1.60 ! [Option: option_game,X22: game] :
% 3.15/1.60 ( ( Option
% 3.15/1.60 = ( some_game @ X22 ) )
% 3.15/1.60 => ( Option != none_game ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_104_option_Odistinct_I1_J,axiom,
% 3.15/1.60 ! [X22: fml] :
% 3.15/1.60 ( none_fml
% 3.15/1.60 != ( some_fml @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_105_option_Odistinct_I1_J,axiom,
% 3.15/1.60 ! [X22: trm] :
% 3.15/1.60 ( none_trm
% 3.15/1.60 != ( some_trm @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_106_option_Odistinct_I1_J,axiom,
% 3.15/1.60 ! [X22: game] :
% 3.15/1.60 ( none_game
% 3.15/1.60 != ( some_game @ X22 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_107_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_option_o_game
% 3.15/1.60 = ( ^ [F12: $o,F23: game > $o,Option2: option_game] :
% 3.15/1.60 ( ( ( Option2 = none_game )
% 3.15/1.60 => F12 )
% 3.15/1.60 & ( ( Option2 != none_game )
% 3.15/1.60 => ( F23 @ ( the_game @ Option2 ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_108_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_option_o_trm
% 3.15/1.60 = ( ^ [F12: $o,F23: trm > $o,Option2: option_trm] :
% 3.15/1.60 ( ( ( Option2 = none_trm )
% 3.15/1.60 => F12 )
% 3.15/1.60 & ( ( Option2 != none_trm )
% 3.15/1.60 => ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_109_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_option_o_fml
% 3.15/1.60 = ( ^ [F12: $o,F23: fml > $o,Option2: option_fml] :
% 3.15/1.60 ( ( ( Option2 = none_fml )
% 3.15/1.60 => F12 )
% 3.15/1.60 & ( ( Option2 != none_fml )
% 3.15/1.60 => ( F23 @ ( the_fml @ Option2 ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_110_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_o209804997ml_fml
% 3.15/1.60 = ( ^ [F12: option_fml,F23: fml > option_fml,Option2: option_fml] : ( if_option_fml @ ( Option2 = none_fml ) @ F12 @ ( F23 @ ( the_fml @ Option2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_111_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_o325794063ml_trm
% 3.15/1.60 = ( ^ [F12: option_fml,F23: trm > option_fml,Option2: option_trm] : ( if_option_fml @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_112_option_Ocase__eq__if,axiom,
% 3.15/1.60 ( case_o487727941rm_trm
% 3.15/1.60 = ( ^ [F12: option_trm,F23: trm > option_trm,Option2: option_trm] : ( if_option_trm @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_113_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: game > $o] :
% 3.15/1.60 ( ( case_option_o_game @ F1 @ F22 @ none_game )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_114_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: trm > $o] :
% 3.15/1.60 ( ( case_option_o_trm @ F1 @ F22 @ none_trm )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_115_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: $o,F22: fml > $o] :
% 3.15/1.60 ( ( case_option_o_fml @ F1 @ F22 @ none_fml )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_116_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: option_fml,F22: fml > option_fml] :
% 3.15/1.60 ( ( case_o209804997ml_fml @ F1 @ F22 @ none_fml )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_117_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: option_fml,F22: trm > option_fml] :
% 3.15/1.60 ( ( case_o325794063ml_trm @ F1 @ F22 @ none_trm )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_118_option_Osimps_I4_J,axiom,
% 3.15/1.60 ! [F1: option_trm,F22: trm > option_trm] :
% 3.15/1.60 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 3.15/1.60 = F1 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_119_Existso_Oinduct,axiom,
% 3.15/1.60 ! [P3: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 3.15/1.60 ( ! [X5: variable,Phi2: fml] : ( P3 @ X5 @ ( some_fml @ Phi2 ) )
% 3.15/1.60 => ( ! [X5: variable] : ( P3 @ X5 @ none_fml )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_120_undeff__equiv,axiom,
% 3.15/1.60 ! [Phi: option_fml] :
% 3.15/1.60 ( ( Phi != none_fml )
% 3.15/1.60 = ( ? [F: fml] :
% 3.15/1.60 ( Phi
% 3.15/1.60 = ( some_fml @ F ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_121_Testo_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_fml > $o,A0: option_fml] :
% 3.15/1.60 ( ! [Phi2: fml] : ( P3 @ ( some_fml @ Phi2 ) )
% 3.15/1.60 => ( ( P3 @ none_fml )
% 3.15/1.60 => ( P3 @ A0 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_122_Testo_Ocases,axiom,
% 3.15/1.60 ! [X3: option_fml] :
% 3.15/1.60 ( ! [Phi2: fml] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_fml @ Phi2 ) )
% 3.15/1.60 => ( X3 = none_fml ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_123_mem__Collect__eq,axiom,
% 3.15/1.60 ! [A2: variable,P3: variable > $o] :
% 3.15/1.60 ( ( member_variable @ A2 @ ( collect_variable @ P3 ) )
% 3.15/1.60 = ( P3 @ A2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_124_Collect__mem__eq,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( collect_variable
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ A3 ) )
% 3.15/1.60 = A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_125_Collect__cong,axiom,
% 3.15/1.60 ! [P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ! [X5: variable] :
% 3.15/1.60 ( ( P3 @ X5 )
% 3.15/1.60 = ( Q @ X5 ) )
% 3.15/1.60 => ( ( collect_variable @ P3 )
% 3.15/1.60 = ( collect_variable @ Q ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_126_Ando_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 3.15/1.60 ( ! [Phi2: fml,Psi: fml] : ( P3 @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) )
% 3.15/1.60 => ( ! [X_1: option_fml] : ( P3 @ none_fml @ X_1 )
% 3.15/1.60 => ( ! [V6: fml] : ( P3 @ ( some_fml @ V6 ) @ none_fml )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_127_option_Oexpand,axiom,
% 3.15/1.60 ! [Option: option_fml,Option3: option_fml] :
% 3.15/1.60 ( ( ( Option = none_fml )
% 3.15/1.60 = ( Option3 = none_fml ) )
% 3.15/1.60 => ( ( ( Option != none_fml )
% 3.15/1.60 => ( ( Option3 != none_fml )
% 3.15/1.60 => ( ( the_fml @ Option )
% 3.15/1.60 = ( the_fml @ Option3 ) ) ) )
% 3.15/1.60 => ( Option = Option3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_128_option_Oexpand,axiom,
% 3.15/1.60 ! [Option: option_trm,Option3: option_trm] :
% 3.15/1.60 ( ( ( Option = none_trm )
% 3.15/1.60 = ( Option3 = none_trm ) )
% 3.15/1.60 => ( ( ( Option != none_trm )
% 3.15/1.60 => ( ( Option3 != none_trm )
% 3.15/1.60 => ( ( the_trm @ Option )
% 3.15/1.60 = ( the_trm @ Option3 ) ) ) )
% 3.15/1.60 => ( Option = Option3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_129_option_Oexpand,axiom,
% 3.15/1.60 ! [Option: option_game,Option3: option_game] :
% 3.15/1.60 ( ( ( Option = none_game )
% 3.15/1.60 = ( Option3 = none_game ) )
% 3.15/1.60 => ( ( ( Option != none_game )
% 3.15/1.60 => ( ( Option3 != none_game )
% 3.15/1.60 => ( ( the_game @ Option )
% 3.15/1.60 = ( the_game @ Option3 ) ) ) )
% 3.15/1.60 => ( Option = Option3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_130_usubstappf__pred__conv,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,P2: char,Theta: trm] :
% 3.15/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 3.15/1.60 != none_fml )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 & ( ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ P2 )
% 3.15/1.60 = none_fml )
% 3.15/1.60 | ? [R3: fml] :
% 3.15/1.60 ( ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ P2 )
% 3.15/1.60 = ( some_fml @ R3 ) )
% 3.15/1.60 & ( ( inf_inf_set_variable @ ( static_FVF @ R3 ) @ U )
% 3.15/1.60 = bot_bot_set_variable ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_131_f6,axiom,
% 3.15/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.15/1.60 @ ^ [T: trm] :
% 3.15/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.15/1.60 @ ^ [F: fml] :
% 3.15/1.60 ( if_option_fml
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F )
% 3.15/1.60 @ none_fml )
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) )
% 3.15/1.60 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 3.15/1.60 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) )
% 3.15/1.60 @ ^ [F: fml] :
% 3.15/1.60 ( if_option_fml
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) @ bot_bot_set_variable @ F )
% 3.15/1.60 @ none_fml )
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_132_f3,axiom,
% 3.15/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.15/1.60 @ ^ [T: trm] :
% 3.15/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.15/1.60 @ ^ [F: fml] :
% 3.15/1.60 ( if_option_fml
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F ) @ ua )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F )
% 3.15/1.60 @ none_fml )
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p ) )
% 3.15/1.60 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 3.15/1.60 != none_fml ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_133_usubstappf_Osimps_I1_J,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,P2: char,Theta: trm] :
% 3.15/1.60 ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 3.15/1.60 = ( case_o325794063ml_trm @ none_fml
% 3.15/1.60 @ ^ [Sigma_theta: trm] :
% 3.15/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ P2 @ Sigma_theta ) )
% 3.15/1.60 @ ^ [R: fml] :
% 3.15/1.60 ( if_option_fml
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ R ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.15/1.60 @ none_fml )
% 3.15/1.60 @ ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ P2 ) )
% 3.15/1.60 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_134_Int__subset__iff,axiom,
% 3.15/1.60 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ C @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 = ( ( ord_le282106107riable @ C @ A3 )
% 3.15/1.60 & ( ord_le282106107riable @ C @ B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_135_inf__bot__left,axiom,
% 3.15/1.60 ! [X3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ bot_bot_variable_o @ X3 )
% 3.15/1.60 = bot_bot_variable_o ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_136_inf__bot__left,axiom,
% 3.15/1.60 ! [X3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X3 )
% 3.15/1.60 = bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_137_inf__bot__right,axiom,
% 3.15/1.60 ! [X3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ X3 @ bot_bot_variable_o )
% 3.15/1.60 = bot_bot_variable_o ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_138_inf__bot__right,axiom,
% 3.15/1.60 ! [X3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ bot_bot_set_variable )
% 3.15/1.60 = bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_139_subset__empty,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ bot_bot_set_variable )
% 3.15/1.60 = ( A3 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_140_empty__subsetI,axiom,
% 3.15/1.60 ! [A3: set_variable] : ( ord_le282106107riable @ bot_bot_set_variable @ A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_141_le__inf__iff,axiom,
% 3.15/1.60 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 3.15/1.60 ( ( ord_le1407353162able_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) )
% 3.15/1.60 = ( ( ord_le1407353162able_o @ X3 @ Y3 )
% 3.15/1.60 & ( ord_le1407353162able_o @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_142_le__inf__iff,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 3.15/1.60 = ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 & ( ord_le282106107riable @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_143_inf_Obounded__iff,axiom,
% 3.15/1.60 ! [A2: variable > $o,B3: variable > $o,C2: variable > $o] :
% 3.15/1.60 ( ( ord_le1407353162able_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) )
% 3.15/1.60 = ( ( ord_le1407353162able_o @ A2 @ B3 )
% 3.15/1.60 & ( ord_le1407353162able_o @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_144_inf_Obounded__iff,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 3.15/1.60 = ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 & ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_145_f4,axiom,
% 3.15/1.60 ! [Z: option_fml,F3: trm > option_fml,Za: option_trm] :
% 3.15/1.60 ( ( ( Za = none_trm )
% 3.15/1.60 => ( ( case_o325794063ml_trm @ Z @ F3 @ Za )
% 3.15/1.60 = Z ) )
% 3.15/1.60 & ( ( Za != none_trm )
% 3.15/1.60 => ( ( case_o325794063ml_trm @ Z @ F3 @ Za )
% 3.15/1.60 = ( F3 @ ( the_trm @ Za ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_146_empty__Collect__eq,axiom,
% 3.15/1.60 ! [P3: variable > $o] :
% 3.15/1.60 ( ( bot_bot_set_variable
% 3.15/1.60 = ( collect_variable @ P3 ) )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ~ ( P3 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_147_Collect__empty__eq,axiom,
% 3.15/1.60 ! [P3: variable > $o] :
% 3.15/1.60 ( ( ( collect_variable @ P3 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ~ ( P3 @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_148_all__not__in__conv,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( ! [X: variable] :
% 3.15/1.60 ~ ( member_variable @ X @ A3 ) )
% 3.15/1.60 = ( A3 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_149_empty__iff,axiom,
% 3.15/1.60 ! [C2: variable] :
% 3.15/1.60 ~ ( member_variable @ C2 @ bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_150_subset__antisym,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B2 @ A3 )
% 3.15/1.60 => ( A3 = B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_151_subsetI,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ! [X5: variable] :
% 3.15/1.60 ( ( member_variable @ X5 @ A3 )
% 3.15/1.60 => ( member_variable @ X5 @ B2 ) )
% 3.15/1.60 => ( ord_le282106107riable @ A3 @ B2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_152_inf__right__idem,axiom,
% 3.15/1.60 ! [X3: variable > $o,Y3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ X3 @ Y3 ) @ Y3 )
% 3.15/1.60 = ( inf_inf_variable_o @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_153_inf__right__idem,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 )
% 3.15/1.60 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_154_inf_Oright__idem,axiom,
% 3.15/1.60 ! [A2: variable > $o,B3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ A2 @ B3 ) @ B3 )
% 3.15/1.60 = ( inf_inf_variable_o @ A2 @ B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_155_inf_Oright__idem,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ B3 )
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_156_inf__left__idem,axiom,
% 3.15/1.60 ! [X3: variable > $o,Y3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ X3 @ Y3 ) )
% 3.15/1.60 = ( inf_inf_variable_o @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_157_inf__left__idem,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ X3 @ Y3 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_158_inf_Oleft__idem,axiom,
% 3.15/1.60 ! [A2: variable > $o,B3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ A2 @ B3 ) )
% 3.15/1.60 = ( inf_inf_variable_o @ A2 @ B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_159_inf_Oleft__idem,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_160_inf__idem,axiom,
% 3.15/1.60 ! [X3: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ X3 @ X3 )
% 3.15/1.60 = X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_161_inf__idem,axiom,
% 3.15/1.60 ! [X3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ X3 )
% 3.15/1.60 = X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_162_inf_Oidem,axiom,
% 3.15/1.60 ! [A2: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ A2 @ A2 )
% 3.15/1.60 = A2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_163_inf_Oidem,axiom,
% 3.15/1.60 ! [A2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A2 @ A2 )
% 3.15/1.60 = A2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_164_inf__apply,axiom,
% 3.15/1.60 ( inf_inf_variable_o
% 3.15/1.60 = ( ^ [F: variable > $o,G: variable > $o,X: variable] : ( inf_inf_o @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_165_Int__iff,axiom,
% 3.15/1.60 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 = ( ( member_variable @ C2 @ A3 )
% 3.15/1.60 & ( member_variable @ C2 @ B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_166_IntI,axiom,
% 3.15/1.60 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( member_variable @ C2 @ A3 )
% 3.15/1.60 => ( ( member_variable @ C2 @ B2 )
% 3.15/1.60 => ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_167_usubstappf__pred,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,P2: char,R2: fml,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 3.15/1.60 ( ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ P2 )
% 3.15/1.60 = ( some_fml @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 = ( some_trm @ Sigma_theta2 ) )
% 3.15/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P2 @ Theta ) )
% 3.15/1.60 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_168_ODEo_Oinduct,axiom,
% 3.15/1.60 ! [P3: char > option_trm > $o,A0: char,A1: option_trm] :
% 3.15/1.60 ( ! [X5: char,Theta2: trm] : ( P3 @ X5 @ ( some_trm @ Theta2 ) )
% 3.15/1.60 => ( ! [X5: char] : ( P3 @ X5 @ none_trm )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_169_undeft__None,axiom,
% 3.15/1.60 none_trm = none_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_170_undeft__equiv,axiom,
% 3.15/1.60 ! [Theta: option_trm] :
% 3.15/1.60 ( ( Theta != none_trm )
% 3.15/1.60 = ( ? [T: trm] :
% 3.15/1.60 ( Theta
% 3.15/1.60 = ( some_trm @ T ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_171_Timeso_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 3.15/1.60 ( ! [Theta2: trm,Eta: trm] : ( P3 @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) )
% 3.15/1.60 => ( ! [X_1: option_trm] : ( P3 @ none_trm @ X_1 )
% 3.15/1.60 => ( ! [V6: trm] : ( P3 @ ( some_trm @ V6 ) @ none_trm )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_172_Assigno_Oinduct,axiom,
% 3.15/1.60 ! [P3: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 3.15/1.60 ( ! [X5: variable,Theta2: trm] : ( P3 @ X5 @ ( some_trm @ Theta2 ) )
% 3.15/1.60 => ( ! [X5: variable] : ( P3 @ X5 @ none_trm )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_173_Differentialo_Ocases,axiom,
% 3.15/1.60 ! [X3: option_trm] :
% 3.15/1.60 ( ! [Theta2: trm] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_trm @ Theta2 ) )
% 3.15/1.60 => ( X3 = none_trm ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_174_Differentialo_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_trm > $o,A0: option_trm] :
% 3.15/1.60 ( ! [Theta2: trm] : ( P3 @ ( some_trm @ Theta2 ) )
% 3.15/1.60 => ( ( P3 @ none_trm )
% 3.15/1.60 => ( P3 @ A0 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_175_bot__set__def,axiom,
% 3.15/1.60 ( bot_bot_set_variable
% 3.15/1.60 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_176_inf__set__def,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ( collect_variable
% 3.15/1.60 @ ( inf_inf_variable_o
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ A4 )
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ B4 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_177_less__eq__set__def,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ( ord_le1407353162able_o
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ A4 )
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ B4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_178_option_Odisc__eq__case_I2_J,axiom,
% 3.15/1.60 ! [Option: option_fml] :
% 3.15/1.60 ( ( Option != none_fml )
% 3.15/1.60 = ( case_option_o_fml @ $false
% 3.15/1.60 @ ^ [Uu: fml] : $true
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_179_option_Odisc__eq__case_I2_J,axiom,
% 3.15/1.60 ! [Option: option_trm] :
% 3.15/1.60 ( ( Option != none_trm )
% 3.15/1.60 = ( case_option_o_trm @ $false
% 3.15/1.60 @ ^ [Uu: trm] : $true
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_180_option_Odisc__eq__case_I2_J,axiom,
% 3.15/1.60 ! [Option: option_game] :
% 3.15/1.60 ( ( Option != none_game )
% 3.15/1.60 = ( case_option_o_game @ $false
% 3.15/1.60 @ ^ [Uu: game] : $true
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_181_option_Odisc__eq__case_I1_J,axiom,
% 3.15/1.60 ! [Option: option_fml] :
% 3.15/1.60 ( ( Option = none_fml )
% 3.15/1.60 = ( case_option_o_fml @ $true
% 3.15/1.60 @ ^ [Uu: fml] : $false
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_182_option_Odisc__eq__case_I1_J,axiom,
% 3.15/1.60 ! [Option: option_trm] :
% 3.15/1.60 ( ( Option = none_trm )
% 3.15/1.60 = ( case_option_o_trm @ $true
% 3.15/1.60 @ ^ [Uu: trm] : $false
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_183_option_Odisc__eq__case_I1_J,axiom,
% 3.15/1.60 ! [Option: option_game] :
% 3.15/1.60 ( ( Option = none_game )
% 3.15/1.60 = ( case_option_o_game @ $true
% 3.15/1.60 @ ^ [Uu: game] : $false
% 3.15/1.60 @ Option ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_184_Diamondo_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 3.15/1.60 ( ! [Alpha: game,Phi2: fml] : ( P3 @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) )
% 3.15/1.60 => ( ! [X_1: option_fml] : ( P3 @ none_game @ X_1 )
% 3.15/1.60 => ( ! [V6: game] : ( P3 @ ( some_game @ V6 ) @ none_fml )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_185_case__optionE,axiom,
% 3.15/1.60 ! [P3: $o,Q: fml > $o,X3: option_fml] :
% 3.15/1.60 ( ( case_option_o_fml @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( ( X3 = none_fml )
% 3.15/1.60 => ~ P3 )
% 3.15/1.60 => ~ ! [Y4: fml] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_fml @ Y4 ) )
% 3.15/1.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_186_case__optionE,axiom,
% 3.15/1.60 ! [P3: $o,Q: trm > $o,X3: option_trm] :
% 3.15/1.60 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( ( X3 = none_trm )
% 3.15/1.60 => ~ P3 )
% 3.15/1.60 => ~ ! [Y4: trm] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_trm @ Y4 ) )
% 3.15/1.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_187_case__optionE,axiom,
% 3.15/1.60 ! [P3: $o,Q: game > $o,X3: option_game] :
% 3.15/1.60 ( ( case_option_o_game @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( ( X3 = none_game )
% 3.15/1.60 => ~ P3 )
% 3.15/1.60 => ~ ! [Y4: game] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_game @ Y4 ) )
% 3.15/1.60 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_188_ex__in__conv,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( ? [X: variable] : ( member_variable @ X @ A3 ) )
% 3.15/1.60 = ( A3 != bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_189_equals0I,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ! [Y4: variable] :
% 3.15/1.60 ~ ( member_variable @ Y4 @ A3 )
% 3.15/1.60 => ( A3 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_190_equals0D,axiom,
% 3.15/1.60 ! [A3: set_variable,A2: variable] :
% 3.15/1.60 ( ( A3 = bot_bot_set_variable )
% 3.15/1.60 => ~ ( member_variable @ A2 @ A3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_191_emptyE,axiom,
% 3.15/1.60 ! [A2: variable] :
% 3.15/1.60 ~ ( member_variable @ A2 @ bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_192_Collect__mono__iff,axiom,
% 3.15/1.60 ! [P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ( ord_le282106107riable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ( ( P3 @ X )
% 3.15/1.60 => ( Q @ X ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_193_set__eq__subset,axiom,
% 3.15/1.60 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A4 @ B4 )
% 3.15/1.60 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_194_subset__trans,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B2 @ C )
% 3.15/1.60 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_195_Collect__mono,axiom,
% 3.15/1.60 ! [P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ! [X5: variable] :
% 3.15/1.60 ( ( P3 @ X5 )
% 3.15/1.60 => ( Q @ X5 ) )
% 3.15/1.60 => ( ord_le282106107riable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_196_subset__refl,axiom,
% 3.15/1.60 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_197_subset__iff,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ! [T: variable] :
% 3.15/1.60 ( ( member_variable @ T @ A4 )
% 3.15/1.60 => ( member_variable @ T @ B4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_198_equalityD2,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( A3 = B2 )
% 3.15/1.60 => ( ord_le282106107riable @ B2 @ A3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_199_equalityD1,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( A3 = B2 )
% 3.15/1.60 => ( ord_le282106107riable @ A3 @ B2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_200_subset__eq,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ! [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A4 )
% 3.15/1.60 => ( member_variable @ X @ B4 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_201_equalityE,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( A3 = B2 )
% 3.15/1.60 => ~ ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ~ ( ord_le282106107riable @ B2 @ A3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_202_subsetD,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,C2: variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ( member_variable @ C2 @ A3 )
% 3.15/1.60 => ( member_variable @ C2 @ B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_203_in__mono,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,X3: variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ( member_variable @ X3 @ A3 )
% 3.15/1.60 => ( member_variable @ X3 @ B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_204_inf__left__commute,axiom,
% 3.15/1.60 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) )
% 3.15/1.60 = ( inf_inf_variable_o @ Y3 @ ( inf_inf_variable_o @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_205_inf__left__commute,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ Y3 @ ( inf_inf_set_variable @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_206_inf_Oleft__commute,axiom,
% 3.15/1.60 ! [B3: variable > $o,A2: variable > $o,C2: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ B3 @ ( inf_inf_variable_o @ A2 @ C2 ) )
% 3.15/1.60 = ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_207_inf_Oleft__commute,axiom,
% 3.15/1.60 ! [B3: set_variable,A2: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_208_inf__commute,axiom,
% 3.15/1.60 ( inf_inf_variable_o
% 3.15/1.60 = ( ^ [X: variable > $o,Y: variable > $o] : ( inf_inf_variable_o @ Y @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_209_inf__commute,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_210_inf_Ocommute,axiom,
% 3.15/1.60 ( inf_inf_variable_o
% 3.15/1.60 = ( ^ [A5: variable > $o,B5: variable > $o] : ( inf_inf_variable_o @ B5 @ A5 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_211_inf_Ocommute,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_212_inf__assoc,axiom,
% 3.15/1.60 ! [X3: variable > $o,Y3: variable > $o,Z2: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ X3 @ Y3 ) @ Z2 )
% 3.15/1.60 = ( inf_inf_variable_o @ X3 @ ( inf_inf_variable_o @ Y3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_213_inf__assoc,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Z2 )
% 3.15/1.60 = ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_214_inf_Oassoc,axiom,
% 3.15/1.60 ! [A2: variable > $o,B3: variable > $o,C2: variable > $o] :
% 3.15/1.60 ( ( inf_inf_variable_o @ ( inf_inf_variable_o @ A2 @ B3 ) @ C2 )
% 3.15/1.60 = ( inf_inf_variable_o @ A2 @ ( inf_inf_variable_o @ B3 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_215_inf_Oassoc,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_216_boolean__algebra__cancel_Oinf2,axiom,
% 3.15/1.60 ! [B2: variable > $o,K: variable > $o,B3: variable > $o,A2: variable > $o] :
% 3.15/1.60 ( ( B2
% 3.15/1.60 = ( inf_inf_variable_o @ K @ B3 ) )
% 3.15/1.60 => ( ( inf_inf_variable_o @ A2 @ B2 )
% 3.15/1.60 = ( inf_inf_variable_o @ K @ ( inf_inf_variable_o @ A2 @ B3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_217_boolean__algebra__cancel_Oinf2,axiom,
% 3.15/1.60 ! [B2: set_variable,K: set_variable,B3: set_variable,A2: set_variable] :
% 3.15/1.60 ( ( B2
% 3.15/1.60 = ( inf_inf_set_variable @ K @ B3 ) )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A2 @ B2 )
% 3.15/1.60 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_218_boolean__algebra__cancel_Oinf1,axiom,
% 3.15/1.60 ! [A3: variable > $o,K: variable > $o,A2: variable > $o,B3: variable > $o] :
% 3.15/1.60 ( ( A3
% 3.15/1.60 = ( inf_inf_variable_o @ K @ A2 ) )
% 3.15/1.60 => ( ( inf_inf_variable_o @ A3 @ B3 )
% 3.15/1.60 = ( inf_inf_variable_o @ K @ ( inf_inf_variable_o @ A2 @ B3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_219_boolean__algebra__cancel_Oinf1,axiom,
% 3.15/1.60 ! [A3: set_variable,K: set_variable,A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( A3
% 3.15/1.60 = ( inf_inf_set_variable @ K @ A2 ) )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A3 @ B3 )
% 3.15/1.60 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_220_inf__sup__aci_I1_J,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_221_inf__sup__aci_I2_J,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Z2 )
% 3.15/1.60 = ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_222_inf__sup__aci_I3_J,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ Y3 @ ( inf_inf_set_variable @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_223_inf__sup__aci_I4_J,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X3 @ ( inf_inf_set_variable @ X3 @ Y3 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_224_Int__left__commute,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ B2 @ C ) )
% 3.15/1.60 = ( inf_inf_set_variable @ B2 @ ( inf_inf_set_variable @ A3 @ C ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_225_Int__left__absorb,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 = ( inf_inf_set_variable @ A3 @ B2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_226_Int__commute,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] : ( inf_inf_set_variable @ B4 @ A4 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_227_Int__absorb,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A3 @ A3 )
% 3.15/1.60 = A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_228_Int__assoc,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,C: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A3 @ B2 ) @ C )
% 3.15/1.60 = ( inf_inf_set_variable @ A3 @ ( inf_inf_set_variable @ B2 @ C ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_229_IntD2,axiom,
% 3.15/1.60 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 => ( member_variable @ C2 @ B2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_230_IntD1,axiom,
% 3.15/1.60 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 => ( member_variable @ C2 @ A3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_231_IntE,axiom,
% 3.15/1.60 ! [C2: variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A3 @ B2 ) )
% 3.15/1.60 => ~ ( ( member_variable @ C2 @ A3 )
% 3.15/1.60 => ~ ( member_variable @ C2 @ B2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_232_empty__def,axiom,
% 3.15/1.60 ( bot_bot_set_variable
% 3.15/1.60 = ( collect_variable
% 3.15/1.60 @ ^ [X: variable] : $false ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_233_Collect__subset,axiom,
% 3.15/1.60 ! [A3: set_variable,P3: variable > $o] :
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A3 )
% 3.15/1.60 & ( P3 @ X ) ) )
% 3.15/1.60 @ A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_234_Int__def,axiom,
% 3.15/1.60 ( inf_inf_set_variable
% 3.15/1.60 = ( ^ [A4: set_variable,B4: set_variable] :
% 3.15/1.60 ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A4 )
% 3.15/1.60 & ( member_variable @ X @ B4 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_235_Int__Collect,axiom,
% 3.15/1.60 ! [X3: variable,A3: set_variable,P3: variable > $o] :
% 3.15/1.60 ( ( member_variable @ X3 @ ( inf_inf_set_variable @ A3 @ ( collect_variable @ P3 ) ) )
% 3.15/1.60 = ( ( member_variable @ X3 @ A3 )
% 3.15/1.60 & ( P3 @ X3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_236_Collect__conj__eq,axiom,
% 3.15/1.60 ! [P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( P3 @ X )
% 3.15/1.60 & ( Q @ X ) ) )
% 3.15/1.60 = ( inf_inf_set_variable @ ( collect_variable @ P3 ) @ ( collect_variable @ Q ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_237_inf_OcoboundedI2,axiom,
% 3.15/1.60 ! [B3: set_variable,C2: set_variable,A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B3 @ C2 )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_238_inf_OcoboundedI1,axiom,
% 3.15/1.60 ! [A2: set_variable,C2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ C2 )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_239_inf_Oabsorb__iff2,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [B5: set_variable,A5: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A5 @ B5 )
% 3.15/1.60 = B5 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_240_inf_Oabsorb__iff1,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A5 @ B5 )
% 3.15/1.60 = A5 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_241_inf_Ocobounded2,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ B3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_242_inf_Ocobounded1,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ A2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_243_inf_Oorder__iff,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.15/1.60 ( A5
% 3.15/1.60 = ( inf_inf_set_variable @ A5 @ B5 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_244_inf__greatest,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ X3 @ Z2 )
% 3.15/1.60 => ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ Y3 @ Z2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_245_inf_OboundedI,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ A2 @ C2 )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_246_inf_OboundedE,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 3.15/1.60 => ~ ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ~ ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_247_inf__absorb2,axiom,
% 3.15/1.60 ! [Y3: set_variable,X3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ Y3 @ X3 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 3.15/1.60 = Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_248_inf__absorb1,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 3.15/1.60 = X3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_249_inf_Oabsorb2,axiom,
% 3.15/1.60 ! [B3: set_variable,A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B3 @ A2 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.15/1.60 = B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_250_inf_Oabsorb1,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.15/1.60 = A2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_251_le__iff__inf,axiom,
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 = ( ^ [X: set_variable,Y: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ X @ Y )
% 3.15/1.60 = X ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_252_inf__unique,axiom,
% 3.15/1.60 ! [F2: set_variable > set_variable > set_variable,X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ! [X5: set_variable,Y4: set_variable] : ( ord_le282106107riable @ ( F2 @ X5 @ Y4 ) @ X5 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable] : ( ord_le282106107riable @ ( F2 @ X5 @ Y4 ) @ Y4 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable,Z4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X5 @ Y4 )
% 3.15/1.60 => ( ( ord_le282106107riable @ X5 @ Z4 )
% 3.15/1.60 => ( ord_le282106107riable @ X5 @ ( F2 @ Y4 @ Z4 ) ) ) )
% 3.15/1.60 => ( ( inf_inf_set_variable @ X3 @ Y3 )
% 3.15/1.60 = ( F2 @ X3 @ Y3 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_253_inf_OorderI,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( A2
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ B3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_254_inf_OorderE,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( A2
% 3.15/1.60 = ( inf_inf_set_variable @ A2 @ B3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_255_le__infI2,axiom,
% 3.15/1.60 ! [B3: set_variable,X3: set_variable,A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B3 @ X3 )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ X3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_256_le__infI1,axiom,
% 3.15/1.60 ! [A2: set_variable,X3: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ X3 )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ X3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_257_inf__mono,axiom,
% 3.15/1.60 ! [A2: set_variable,C2: set_variable,B3: set_variable,D: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ C2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ D )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A2 @ B3 ) @ ( inf_inf_set_variable @ C2 @ D ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_258_le__infI,axiom,
% 3.15/1.60 ! [X3: set_variable,A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ A2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ X3 @ B3 )
% 3.15/1.60 => ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_259_le__infE,axiom,
% 3.15/1.60 ! [X3: set_variable,A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.15/1.60 => ~ ( ( ord_le282106107riable @ X3 @ A2 )
% 3.15/1.60 => ~ ( ord_le282106107riable @ X3 @ B3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_260_inf__le2,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_261_inf__le1,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_262_inf__sup__ord_I1_J,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_263_inf__sup__ord_I2_J,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ X3 @ Y3 ) @ Y3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_264_disjoint__iff__not__equal,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ( inf_inf_set_variable @ A3 @ B2 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A3 )
% 3.15/1.60 => ! [Y: variable] :
% 3.15/1.60 ( ( member_variable @ Y @ B2 )
% 3.15/1.60 => ( X != Y ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_265_Int__empty__right,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ A3 @ bot_bot_set_variable )
% 3.15/1.60 = bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_266_Int__empty__left,axiom,
% 3.15/1.60 ! [B2: set_variable] :
% 3.15/1.60 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B2 )
% 3.15/1.60 = bot_bot_set_variable ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_267_disjoint__iff,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ( inf_inf_set_variable @ A3 @ B2 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A3 )
% 3.15/1.60 => ~ ( member_variable @ X @ B2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_268_Int__emptyI,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ! [X5: variable] :
% 3.15/1.60 ( ( member_variable @ X5 @ A3 )
% 3.15/1.60 => ~ ( member_variable @ X5 @ B2 ) )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 3.15/1.60 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_269_Int__Collect__mono,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable,P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ! [X5: variable] :
% 3.15/1.60 ( ( member_variable @ X5 @ A3 )
% 3.15/1.60 => ( ( P3 @ X5 )
% 3.15/1.60 => ( Q @ X5 ) ) )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ ( collect_variable @ P3 ) ) @ ( inf_inf_set_variable @ B2 @ ( collect_variable @ Q ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_270_Int__greatest,axiom,
% 3.15/1.60 ! [C: set_variable,A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ C @ A3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ C @ B2 )
% 3.15/1.60 => ( ord_le282106107riable @ C @ ( inf_inf_set_variable @ A3 @ B2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_271_Int__absorb2,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ B2 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 3.15/1.60 = A3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_272_Int__absorb1,axiom,
% 3.15/1.60 ! [B2: set_variable,A3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B2 @ A3 )
% 3.15/1.60 => ( ( inf_inf_set_variable @ A3 @ B2 )
% 3.15/1.60 = B2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_273_Int__lower2,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ B2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_274_Int__lower1,axiom,
% 3.15/1.60 ! [A3: set_variable,B2: set_variable] : ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ A3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_275_Int__mono,axiom,
% 3.15/1.60 ! [A3: set_variable,C: set_variable,B2: set_variable,D2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3 @ C )
% 3.15/1.60 => ( ( ord_le282106107riable @ B2 @ D2 )
% 3.15/1.60 => ( ord_le282106107riable @ ( inf_inf_set_variable @ A3 @ B2 ) @ ( inf_inf_set_variable @ C @ D2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_276_order__refl,axiom,
% 3.15/1.60 ! [X3: set_variable] : ( ord_le282106107riable @ X3 @ X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_277_subset__emptyI,axiom,
% 3.15/1.60 ! [A3: set_variable] :
% 3.15/1.60 ( ! [X5: variable] :
% 3.15/1.60 ~ ( member_variable @ X5 @ A3 )
% 3.15/1.60 => ( ord_le282106107riable @ A3 @ bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_278_bot_Oextremum__uniqueI,axiom,
% 3.15/1.60 ! [A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ bot_bot_set_variable )
% 3.15/1.60 => ( A2 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_279_bot_Oextremum__unique,axiom,
% 3.15/1.60 ! [A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ bot_bot_set_variable )
% 3.15/1.60 = ( A2 = bot_bot_set_variable ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_280_bot_Oextremum,axiom,
% 3.15/1.60 ! [A2: set_variable] : ( ord_le282106107riable @ bot_bot_set_variable @ A2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_281_usubstappf__geqr,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.15/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.15/1.60 != none_fml )
% 3.15/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.15/1.60 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_282_fml_Oinject_I2_J,axiom,
% 3.15/1.60 ! [X21: trm,X222: trm,Y21: trm,Y22: trm] :
% 3.15/1.60 ( ( ( geq @ X21 @ X222 )
% 3.15/1.60 = ( geq @ Y21 @ Y22 ) )
% 3.15/1.60 = ( ( X21 = Y21 )
% 3.15/1.60 & ( X222 = Y22 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_283_Aterm__Some,axiom,
% 3.15/1.60 some_trm = some_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_284_Loopo_Ocases,axiom,
% 3.15/1.60 ! [X3: option_game] :
% 3.15/1.60 ( ! [Alpha: game] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( some_game @ Alpha ) )
% 3.15/1.60 => ( X3 = none_game ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_285_Loopo_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_game > $o,A0: option_game] :
% 3.15/1.60 ( ! [Alpha: game] : ( P3 @ ( some_game @ Alpha ) )
% 3.15/1.60 => ( ( P3 @ none_game )
% 3.15/1.60 => ( P3 @ A0 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_286_undefg__equiv,axiom,
% 3.15/1.60 ! [Alpha2: option_game] :
% 3.15/1.60 ( ( Alpha2 != none_game )
% 3.15/1.60 = ( ? [G: game] :
% 3.15/1.60 ( Alpha2
% 3.15/1.60 = ( some_game @ G ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_287_Composeo_Oinduct,axiom,
% 3.15/1.60 ! [P3: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 3.15/1.60 ( ! [Alpha: game,Beta: game] : ( P3 @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 3.15/1.60 => ( ! [Alpha: option_game] : ( P3 @ Alpha @ none_game )
% 3.15/1.60 => ( ! [V6: game] : ( P3 @ none_game @ ( some_game @ V6 ) )
% 3.15/1.60 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_288_fml_Odistinct_I1_J,axiom,
% 3.15/1.60 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 3.15/1.60 ( ( pred @ X11 @ X12 )
% 3.15/1.60 != ( geq @ X21 @ X222 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_289_order__subst1,axiom,
% 3.15/1.60 ! [A2: set_variable,F2: set_variable > set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ ( F2 @ B3 ) )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ C2 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X5 @ Y4 )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_290_order__subst2,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ ( F2 @ B3 ) @ C2 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X5 @ Y4 )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_291_ord__eq__le__subst,axiom,
% 3.15/1.60 ! [A2: set_variable,F2: set_variable > set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( A2
% 3.15/1.60 = ( F2 @ B3 ) )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ C2 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X5 @ Y4 )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ ( F2 @ C2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_292_ord__le__eq__subst,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,F2: set_variable > set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( ( F2 @ B3 )
% 3.15/1.60 = C2 )
% 3.15/1.60 => ( ! [X5: set_variable,Y4: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X5 @ Y4 )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
% 3.15/1.60 => ( ord_le282106107riable @ ( F2 @ A2 ) @ C2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_293_eq__iff,axiom,
% 3.15/1.60 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 3.15/1.60 = ( ^ [X: set_variable,Y: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X @ Y )
% 3.15/1.60 & ( ord_le282106107riable @ Y @ X ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_294_antisym,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ Y3 @ X3 )
% 3.15/1.60 => ( X3 = Y3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_295_eq__refl,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable] :
% 3.15/1.60 ( ( X3 = Y3 )
% 3.15/1.60 => ( ord_le282106107riable @ X3 @ Y3 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_296_order_Otrans,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ C2 )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_297_antisym__conv,axiom,
% 3.15/1.60 ! [Y3: set_variable,X3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ Y3 @ X3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 = ( X3 = Y3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_298_order__class_Oorder_Oeq__iff,axiom,
% 3.15/1.60 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 3.15/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A5 @ B5 )
% 3.15/1.60 & ( ord_le282106107riable @ B5 @ A5 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_299_ord__eq__le__trans,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( A2 = B3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ C2 )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_300_ord__le__eq__trans,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( B3 = C2 )
% 3.15/1.60 => ( ord_le282106107riable @ A2 @ C2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_301_order__class_Oorder_Oantisym,axiom,
% 3.15/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B3 @ A2 )
% 3.15/1.60 => ( A2 = B3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_302_order__trans,axiom,
% 3.15/1.60 ! [X3: set_variable,Y3: set_variable,Z2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ X3 @ Y3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ Y3 @ Z2 )
% 3.15/1.60 => ( ord_le282106107riable @ X3 @ Z2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_303_dual__order_Orefl,axiom,
% 3.15/1.60 ! [A2: set_variable] : ( ord_le282106107riable @ A2 @ A2 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_304_dual__order_Otrans,axiom,
% 3.15/1.60 ! [B3: set_variable,A2: set_variable,C2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B3 @ A2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ C2 @ B3 )
% 3.15/1.60 => ( ord_le282106107riable @ C2 @ A2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_305_dual__order_Oeq__iff,axiom,
% 3.15/1.60 ( ( ^ [Y5: set_variable,Z3: set_variable] : ( Y5 = Z3 ) )
% 3.15/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B5 @ A5 )
% 3.15/1.60 & ( ord_le282106107riable @ A5 @ B5 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_306_dual__order_Oantisym,axiom,
% 3.15/1.60 ! [B3: set_variable,A2: set_variable] :
% 3.15/1.60 ( ( ord_le282106107riable @ B3 @ A2 )
% 3.15/1.60 => ( ( ord_le282106107riable @ A2 @ B3 )
% 3.15/1.60 => ( A2 = B3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_307_prop__restrict,axiom,
% 3.15/1.60 ! [X3: variable,Z5: set_variable,X6: set_variable,P3: variable > $o] :
% 3.15/1.60 ( ( member_variable @ X3 @ Z5 )
% 3.15/1.60 => ( ( ord_le282106107riable @ Z5
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ X6 )
% 3.15/1.60 & ( P3 @ X ) ) ) )
% 3.15/1.60 => ( P3 @ X3 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_308_Collect__restrict,axiom,
% 3.15/1.60 ! [X6: set_variable,P3: variable > $o] :
% 3.15/1.60 ( ord_le282106107riable
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ X6 )
% 3.15/1.60 & ( P3 @ X ) ) )
% 3.15/1.60 @ X6 ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_309_usubstappf__geq__conv,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.15/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.15/1.60 != none_fml )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.15/1.60 != none_trm ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_310_usubstappf__geq,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.15/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.15/1.60 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_311_disjE__realizer2,axiom,
% 3.15/1.60 ! [P3: $o,Q: fml > $o,X3: option_fml,R4: option_fml > $o,F2: option_fml,G2: fml > option_fml] :
% 3.15/1.60 ( ( case_option_o_fml @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( P3
% 3.15/1.60 => ( R4 @ F2 ) )
% 3.15/1.60 => ( ! [Q2: fml] :
% 3.15/1.60 ( ( Q @ Q2 )
% 3.15/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.15/1.60 => ( R4 @ ( case_o209804997ml_fml @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_312_disjE__realizer2,axiom,
% 3.15/1.60 ! [P3: $o,Q: trm > $o,X3: option_trm,R4: option_fml > $o,F2: option_fml,G2: trm > option_fml] :
% 3.15/1.60 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( P3
% 3.15/1.60 => ( R4 @ F2 ) )
% 3.15/1.60 => ( ! [Q2: trm] :
% 3.15/1.60 ( ( Q @ Q2 )
% 3.15/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.15/1.60 => ( R4 @ ( case_o325794063ml_trm @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_313_disjE__realizer2,axiom,
% 3.15/1.60 ! [P3: $o,Q: trm > $o,X3: option_trm,R4: option_trm > $o,F2: option_trm,G2: trm > option_trm] :
% 3.15/1.60 ( ( case_option_o_trm @ P3 @ Q @ X3 )
% 3.15/1.60 => ( ( P3
% 3.15/1.60 => ( R4 @ F2 ) )
% 3.15/1.60 => ( ! [Q2: trm] :
% 3.15/1.60 ( ( Q @ Q2 )
% 3.15/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.15/1.60 => ( R4 @ ( case_o487727941rm_trm @ F2 @ G2 @ X3 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_314_Geqo_Oelims,axiom,
% 3.15/1.60 ! [X3: option_trm,Xa: option_trm,Y3: option_fml] :
% 3.15/1.60 ( ( ( uSubst152838031e_Geqo @ X3 @ Xa )
% 3.15/1.60 = Y3 )
% 3.15/1.60 => ( ! [Theta2: trm] :
% 3.15/1.60 ( ( X3
% 3.15/1.60 = ( some_trm @ Theta2 ) )
% 3.15/1.60 => ! [Eta: trm] :
% 3.15/1.60 ( ( Xa
% 3.15/1.60 = ( some_trm @ Eta ) )
% 3.15/1.60 => ( Y3
% 3.15/1.60 != ( some_fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 3.15/1.60 => ( ( ( X3 = none_trm )
% 3.15/1.60 => ( Y3 != none_fml ) )
% 3.15/1.60 => ~ ( ? [V6: trm] :
% 3.15/1.60 ( X3
% 3.15/1.60 = ( some_trm @ V6 ) )
% 3.15/1.60 => ( ( Xa = none_trm )
% 3.15/1.60 => ( Y3 != none_fml ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_315_inf__Int__eq,axiom,
% 3.15/1.60 ! [R4: set_variable,S: set_variable] :
% 3.15/1.60 ( ( inf_inf_variable_o
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 3.15/1.60 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_316_Geqo_Osimps_I2_J,axiom,
% 3.15/1.60 ! [Eta2: option_trm] :
% 3.15/1.60 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 3.15/1.60 = none_fml ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_317_Geqo__undef,axiom,
% 3.15/1.60 ! [Theta: option_trm,Eta2: option_trm] :
% 3.15/1.60 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta2 )
% 3.15/1.60 = none_fml )
% 3.15/1.60 = ( ( Theta = none_trm )
% 3.15/1.60 | ( Eta2 = none_trm ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_318_Geqo_Osimps_I3_J,axiom,
% 3.15/1.60 ! [V7: trm] :
% 3.15/1.60 ( ( uSubst152838031e_Geqo @ ( some_trm @ V7 ) @ none_trm )
% 3.15/1.60 = none_fml ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_319_Geqo_Osimps_I1_J,axiom,
% 3.15/1.60 ! [Theta: trm,Eta2: trm] :
% 3.15/1.60 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta2 ) )
% 3.15/1.60 = ( some_fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_320_usubstappf_Osimps_I2_J,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.15/1.60 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.15/1.60 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_321_bot__empty__eq,axiom,
% 3.15/1.60 ( bot_bot_variable_o
% 3.15/1.60 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_322_pred__subset__eq,axiom,
% 3.15/1.60 ! [R4: set_variable,S: set_variable] :
% 3.15/1.60 ( ( ord_le1407353162able_o
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 3.15/1.60 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 3.15/1.60 = ( ord_le282106107riable @ R4 @ S ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_323_Collect__empty__eq__bot,axiom,
% 3.15/1.60 ! [P3: variable > $o] :
% 3.15/1.60 ( ( ( collect_variable @ P3 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 = ( P3 = bot_bot_variable_o ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_324_Set_Ois__empty__def,axiom,
% 3.15/1.60 ( is_empty_variable
% 3.15/1.60 = ( ^ [A4: set_variable] : ( A4 = bot_bot_set_variable ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_325_internal__case__prod__def,axiom,
% 3.15/1.60 produc1278328899on_fml = produc1250175341on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_326_internal__case__prod__def,axiom,
% 3.15/1.60 produc2141841102on_trm = produc1231571704on_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_327_internal__case__prod__def,axiom,
% 3.15/1.60 produc377919108on_fml = produc1615133358on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_328_internal__case__prod__def,axiom,
% 3.15/1.60 produc1214549391on_trm = produc1036610745on_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_329_internal__case__prod__def,axiom,
% 3.15/1.60 produc1598111045on_fml = produc1420172399on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_330_internal__case__prod__def,axiom,
% 3.15/1.60 produc1591622303on_fml = produc347802313on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_331_internal__case__prod__def,axiom,
% 3.15/1.60 produc2129367017on_trm = produc885547027on_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_332_internal__case__prod__def,axiom,
% 3.15/1.60 produc1903410526on_fml = produc154833544on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_333_internal__case__prod__def,axiom,
% 3.15/1.60 produc293671592on_trm = produc692578258on_trm ).
% 3.15/1.60
% 3.15/1.60 thf(fact_334_internal__case__prod__def,axiom,
% 3.15/1.60 produc724717725on_fml = produc1499310791on_fml ).
% 3.15/1.60
% 3.15/1.60 thf(fact_335_usubstappt_Osimps_I4_J,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char,Theta: trm] :
% 3.15/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 3.15/1.60 = ( case_o487727941rm_trm @ none_trm
% 3.15/1.60 @ ^ [Sigma_theta: trm] :
% 3.15/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F2 @ Sigma_theta ) )
% 3.15/1.60 @ ^ [R: trm] :
% 3.15/1.60 ( if_option_trm
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.15/1.60 @ none_trm )
% 3.15/1.60 @ ( produc866613687on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [F4: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 ) )
% 3.15/1.60 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_336_trm_Oinject_I4_J,axiom,
% 3.15/1.60 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 3.15/1.60 ( ( ( func @ X41 @ X42 )
% 3.15/1.60 = ( func @ Y41 @ Y42 ) )
% 3.15/1.60 = ( ( X41 = Y41 )
% 3.15/1.60 & ( X42 = Y42 ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_337_usubstappt__func2,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable,Theta: trm] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [F4: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.15/1.60 != bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 3.15/1.60 = none_trm ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_338_usubstappt__func,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [F4: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 = ( some_trm @ Sigma_theta2 ) )
% 3.15/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 3.15/1.60 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_339_usubstappt__func__conv,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char,Theta: trm] :
% 3.15/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F2 @ Theta ) )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.15/1.60 != none_trm )
% 3.15/1.60 & ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [F4: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = none_trm )
% 3.15/1.60 | ? [R3: trm] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [F4: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R3 ) )
% 3.15/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.15/1.60 = bot_bot_set_variable ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_340_usappconst__simp,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst1559070963pconst @ Sigma @ U @ F2 )
% 3.15/1.60 = ( some_trm @ R2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_341_usappconst__conv,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 3.15/1.60 ( ( ( uSubst1559070963pconst @ Sigma @ U @ F2 )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = none_trm )
% 3.15/1.60 | ? [R3: trm] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R3 ) )
% 3.15/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.15/1.60 = bot_bot_set_variable ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_342_usappconst__def,axiom,
% 3.15/1.60 ( uSubst1559070963pconst
% 3.15/1.60 = ( ^ [Sigma2: produc1418842292n_game,U2: set_variable,F: char] :
% 3.15/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F ) )
% 3.15/1.60 @ ^ [R: trm] :
% 3.15/1.60 ( if_option_trm
% 3.15/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 @ ( some_trm @ R )
% 3.15/1.60 @ none_trm )
% 3.15/1.60 @ ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma2
% 3.15/1.60 @ F ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_343_usubstappt__const,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,F2: char,R2: trm,U: set_variable] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R2 ) )
% 3.15/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.15/1.60 = bot_bot_set_variable )
% 3.15/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 3.15/1.60 = ( some_trm @ R2 ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_344_trm_Oinject_I3_J,axiom,
% 3.15/1.60 ! [X32: char,Y32: char] :
% 3.15/1.60 ( ( ( const @ X32 )
% 3.15/1.60 = ( const @ Y32 ) )
% 3.15/1.60 = ( X32 = Y32 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_345_usubstappt_Osimps_I3_J,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 3.15/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 3.15/1.60 = ( uSubst1559070963pconst @ Sigma @ U @ F2 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_346_trm_Odistinct_I23_J,axiom,
% 3.15/1.60 ! [X32: char,X41: char,X42: trm] :
% 3.15/1.60 ( ( const @ X32 )
% 3.15/1.60 != ( func @ X41 @ X42 ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_347_usubstappt__const__conv,axiom,
% 3.15/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 3.15/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F2 ) )
% 3.15/1.60 != none_trm )
% 3.15/1.60 => ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = none_trm )
% 3.15/1.60 | ? [R3: trm] :
% 3.15/1.60 ( ( ( produc866613687on_trm
% 3.15/1.60 @ ^ [F0: char > option_trm] :
% 3.15/1.60 ( produc1231571704on_trm
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1036610745on_trm
% 3.15/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.15/1.60 @ Sigma
% 3.15/1.60 @ F2 )
% 3.15/1.60 = ( some_trm @ R3 ) )
% 3.15/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.15/1.60 = bot_bot_set_variable ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_348_subset__Collect__iff,axiom,
% 3.15/1.60 ! [B2: set_variable,A3: set_variable,P3: variable > $o] :
% 3.15/1.60 ( ( ord_le282106107riable @ B2 @ A3 )
% 3.15/1.60 => ( ( ord_le282106107riable @ B2
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A3 )
% 3.15/1.60 & ( P3 @ X ) ) ) )
% 3.15/1.60 = ( ! [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ B2 )
% 3.15/1.60 => ( P3 @ X ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_349_subset__CollectI,axiom,
% 3.15/1.60 ! [B2: set_variable,A3: set_variable,Q: variable > $o,P3: variable > $o] :
% 3.15/1.60 ( ( ord_le282106107riable @ B2 @ A3 )
% 3.15/1.60 => ( ! [X5: variable] :
% 3.15/1.60 ( ( member_variable @ X5 @ B2 )
% 3.15/1.60 => ( ( Q @ X5 )
% 3.15/1.60 => ( P3 @ X5 ) ) )
% 3.15/1.60 => ( ord_le282106107riable
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ B2 )
% 3.15/1.60 & ( Q @ X ) ) )
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( member_variable @ X @ A3 )
% 3.15/1.60 & ( P3 @ X ) ) ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_350_conj__subset__def,axiom,
% 3.15/1.60 ! [A3: set_variable,P3: variable > $o,Q: variable > $o] :
% 3.15/1.60 ( ( ord_le282106107riable @ A3
% 3.15/1.60 @ ( collect_variable
% 3.15/1.60 @ ^ [X: variable] :
% 3.15/1.60 ( ( P3 @ X )
% 3.15/1.60 & ( Q @ X ) ) ) )
% 3.15/1.60 = ( ( ord_le282106107riable @ A3 @ ( collect_variable @ P3 ) )
% 3.15/1.60 & ( ord_le282106107riable @ A3 @ ( collect_variable @ Q ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(fact_351_Diamondo_Ocases,axiom,
% 3.15/1.60 ! [X3: produc1739631244on_fml] :
% 3.15/1.60 ( ! [Alpha: game,Phi2: fml] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) ) )
% 3.15/1.60 => ( ! [Phi2: option_fml] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( produc2124676926on_fml @ none_game @ Phi2 ) )
% 3.15/1.60 => ~ ! [V6: game] :
% 3.15/1.60 ( X3
% 3.15/1.60 != ( produc2124676926on_fml @ ( some_game @ V6 ) @ none_fml ) ) ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 3.15/1.60 ! [X3: option_fml,Y3: option_fml] :
% 3.15/1.60 ( ( if_option_fml @ $false @ X3 @ Y3 )
% 3.15/1.60 = Y3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 3.15/1.60 ! [X3: option_fml,Y3: option_fml] :
% 3.15/1.60 ( ( if_option_fml @ $true @ X3 @ Y3 )
% 3.15/1.60 = X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.15/1.60 ! [P3: $o] :
% 3.15/1.60 ( ( P3 = $true )
% 3.15/1.60 | ( P3 = $false ) ) ).
% 3.15/1.60
% 3.15/1.60 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.15/1.60 ! [X3: option_trm,Y3: option_trm] :
% 3.15/1.60 ( ( if_option_trm @ $false @ X3 @ Y3 )
% 3.15/1.60 = Y3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.15/1.60 ! [X3: option_trm,Y3: option_trm] :
% 3.15/1.60 ( ( if_option_trm @ $true @ X3 @ Y3 )
% 3.15/1.60 = X3 ) ).
% 3.15/1.60
% 3.15/1.60 thf(conj_0,conjecture,
% 3.15/1.60 ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 3.15/1.60 != none_fml )
% 3.15/1.60 | ( ( produc1250175341on_fml
% 3.15/1.60 @ ^ [Uu: char > option_trm] :
% 3.15/1.60 ( produc1615133358on_fml
% 3.15/1.60 @ ^ [Uv: char > option_trm] :
% 3.15/1.60 ( produc1420172399on_fml
% 3.15/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.15/1.60 @ sigma
% 3.15/1.60 @ p )
% 3.15/1.60 = none_fml ) ) ).
% 3.15/1.60 ------------------------
% 3.15/1.63 % (7998)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_7804 for (2999ds/27Mi)
% 3.15/1.63 % (8002)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/18Mi)
% 3.15/1.63 % (7996)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/183Mi)
% 3.15/1.64 % (8002)Instruction limit reached!
% 3.15/1.64 % (8002)------------------------------
% 3.15/1.64 % (8002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.64 % (8002)Termination reason: Unknown
% 3.15/1.64 % (8002)Termination phase: shuffling
% 3.15/1.64
% 3.15/1.64 % (8002)Memory used [KB]: 1918
% 3.15/1.64 % (8002)Time elapsed: 0.008 s
% 3.15/1.64 % (8002)Instructions burned: 19 (million)
% 3.15/1.64 % (8002)------------------------------
% 3.15/1.64 % (8002)------------------------------
% 3.15/1.64 % (8001)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_7804 for (2999ds/275Mi)
% 3.15/1.64 % (7998)Instruction limit reached!
% 3.15/1.64 % (7998)------------------------------
% 3.15/1.64 % (7998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.64 % (7998)Termination reason: Unknown
% 3.15/1.64 % (7998)Termination phase: shuffling
% 3.15/1.64
% 3.15/1.64 % (7998)Memory used [KB]: 2046
% 3.15/1.64 % (7998)Time elapsed: 0.011 s
% 3.15/1.64 % (7998)Instructions burned: 28 (million)
% 3.15/1.64 % (7998)------------------------------
% 3.15/1.64 % (7998)------------------------------
% 3.15/1.65 % (7999)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/2Mi)
% 3.15/1.65 % (7997)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_7804 for (2999ds/4Mi)
% 3.15/1.65 % (8003)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/3Mi)
% 3.15/1.65 % (7999)Instruction limit reached!
% 3.15/1.65 % (7999)------------------------------
% 3.15/1.65 % (7999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.65 % (7999)Termination reason: Unknown
% 3.15/1.65 % (7999)Termination phase: shuffling
% 3.15/1.65
% 3.15/1.65 % (7999)Memory used [KB]: 1535
% 3.15/1.65 % (7999)Time elapsed: 0.003 s
% 3.15/1.65 % (7999)Instructions burned: 2 (million)
% 3.15/1.65 % (7999)------------------------------
% 3.15/1.65 % (7999)------------------------------
% 3.15/1.65 % (8003)Instruction limit reached!
% 3.15/1.65 % (8003)------------------------------
% 3.15/1.65 % (8003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.65 % (8003)Termination reason: Unknown
% 3.15/1.65 % (8003)Termination phase: shuffling
% 3.15/1.65 % (7997)Instruction limit reached!
% 3.15/1.65 % (7997)------------------------------
% 3.15/1.65 % (7997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.65 % (7997)Termination reason: Unknown
% 3.15/1.65 % (7997)Termination phase: shuffling
% 3.15/1.65
% 3.15/1.65 % (7997)Memory used [KB]: 1535
% 3.15/1.65 % (7997)Time elapsed: 0.003 s
% 3.15/1.65 % (7997)Instructions burned: 4 (million)
% 3.15/1.65 % (7997)------------------------------
% 3.15/1.65 % (7997)------------------------------
% 3.15/1.65
% 3.15/1.65 % (8003)Memory used [KB]: 1535
% 3.15/1.65 % (8003)Time elapsed: 0.003 s
% 3.15/1.65 % (8003)Instructions burned: 3 (million)
% 3.15/1.65 % (8003)------------------------------
% 3.15/1.65 % (8003)------------------------------
% 3.15/1.65 % (8000)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_7804 for (2999ds/2Mi)
% 3.15/1.65 % (8004)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_7804 for (2999ds/37Mi)
% 3.15/1.65 % (8000)Instruction limit reached!
% 3.15/1.65 % (8000)------------------------------
% 3.15/1.65 % (8000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.65 % (8000)Termination reason: Unknown
% 3.15/1.65 % (8000)Termination phase: shuffling
% 3.15/1.65
% 3.15/1.65 % (8000)Memory used [KB]: 1535
% 3.15/1.65 % (8000)Time elapsed: 0.002 s
% 3.15/1.65 % (8000)Instructions burned: 3 (million)
% 3.15/1.65 % (8000)------------------------------
% 3.15/1.65 % (8000)------------------------------
% 3.15/1.66 % (8006)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_7804 for (2999ds/3Mi)
% 3.15/1.66 % (8007)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_7804 for (2999ds/1041Mi)
% 3.15/1.66 % (8006)Instruction limit reached!
% 3.15/1.66 % (8006)------------------------------
% 3.15/1.66 % (8006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.66 % (8006)Termination reason: Unknown
% 3.15/1.66 % (8006)Termination phase: shuffling
% 3.15/1.66
% 3.15/1.66 % (8006)Memory used [KB]: 1663
% 3.15/1.66 % (8006)Time elapsed: 0.004 s
% 3.15/1.66 % (8006)Instructions burned: 5 (million)
% 3.15/1.66 % (8006)------------------------------
% 3.15/1.66 % (8006)------------------------------
% 3.15/1.66 % (8004)Instruction limit reached!
% 3.15/1.66 % (8004)------------------------------
% 3.15/1.66 % (8004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.66 % (8004)Termination reason: Unknown
% 3.15/1.66 % (8004)Termination phase: shuffling
% 3.15/1.66
% 3.15/1.66 % (8004)Memory used [KB]: 2302
% 3.15/1.66 % (8004)Time elapsed: 0.013 s
% 3.15/1.66 % (8004)Instructions burned: 40 (million)
% 3.15/1.66 % (8004)------------------------------
% 3.15/1.66 % (8004)------------------------------
% 3.15/1.66 % (8005)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_7804 for (2999ds/15Mi)
% 3.15/1.67 % (8008)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/7Mi)
% 3.15/1.67 % (8008)Instruction limit reached!
% 3.15/1.67 % (8008)------------------------------
% 3.15/1.67 % (8008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.67 % (8008)Termination reason: Unknown
% 3.15/1.67 % (8008)Termination phase: shuffling
% 3.15/1.67
% 3.15/1.67 % (8008)Memory used [KB]: 1663
% 3.15/1.67 % (8008)Time elapsed: 0.005 s
% 3.15/1.67 % (8008)Instructions burned: 7 (million)
% 3.15/1.67 % (8008)------------------------------
% 3.15/1.67 % (8008)------------------------------
% 3.15/1.67 % (8009)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/16Mi)
% 3.15/1.67 % (8005)Instruction limit reached!
% 3.15/1.67 % (8005)------------------------------
% 3.15/1.67 % (8005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.67 % (8005)Termination reason: Unknown
% 3.15/1.67 % (8005)Termination phase: shuffling
% 3.15/1.67
% 3.15/1.67 % (8005)Memory used [KB]: 1791
% 3.15/1.67 % (8005)Time elapsed: 0.010 s
% 3.15/1.67 % (8005)Instructions burned: 15 (million)
% 3.15/1.67 % (8005)------------------------------
% 3.15/1.67 % (8005)------------------------------
% 3.15/1.67 % (8010)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_7804 for (2999ds/3Mi)
% 3.15/1.67 % (8010)Instruction limit reached!
% 3.15/1.67 % (8010)------------------------------
% 3.15/1.67 % (8010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.67 % (8010)Termination reason: Unknown
% 3.15/1.67 % (8010)Termination phase: shuffling
% 3.15/1.67
% 3.15/1.67 % (8010)Memory used [KB]: 1535
% 3.15/1.67 % (8010)Time elapsed: 0.003 s
% 3.15/1.67 % (8010)Instructions burned: 5 (million)
% 3.15/1.67 % (8010)------------------------------
% 3.15/1.67 % (8010)------------------------------
% 3.15/1.68 % (8009)Instruction limit reached!
% 3.15/1.68 % (8009)------------------------------
% 3.15/1.68 % (8009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.68 % (8009)Termination reason: Unknown
% 3.15/1.68 % (8009)Termination phase: shuffling
% 3.15/1.68
% 3.15/1.68 % (8009)Memory used [KB]: 1918
% 3.15/1.68 % (8009)Time elapsed: 0.007 s
% 3.15/1.68 % (8009)Instructions burned: 17 (million)
% 3.15/1.68 % (8009)------------------------------
% 3.15/1.68 % (8009)------------------------------
% 3.15/1.69 % (8013)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/3Mi)
% 3.15/1.69 % (8013)Instruction limit reached!
% 3.15/1.69 % (8013)------------------------------
% 3.15/1.69 % (8013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.69 % (8013)Termination reason: Unknown
% 3.15/1.69 % (8013)Termination phase: shuffling
% 3.15/1.69
% 3.15/1.69 % (8013)Memory used [KB]: 1535
% 3.15/1.69 % (8013)Time elapsed: 0.003 s
% 3.15/1.69 % (8013)Instructions burned: 3 (million)
% 3.15/1.69 % (8013)------------------------------
% 3.15/1.69 % (8013)------------------------------
% 3.15/1.69 % (8011)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_7804 for (2999ds/3Mi)
% 3.15/1.69 % (8014)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/4Mi)
% 3.15/1.69 % (8011)Instruction limit reached!
% 3.15/1.69 % (8011)------------------------------
% 3.15/1.69 % (8011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.69 % (8011)Termination reason: Unknown
% 3.15/1.69 % (8011)Termination phase: shuffling
% 3.15/1.69
% 3.15/1.69 % (8011)Memory used [KB]: 1535
% 3.15/1.69 % (8011)Time elapsed: 0.003 s
% 3.15/1.69 % (8011)Instructions burned: 3 (million)
% 3.15/1.69 % (8011)------------------------------
% 3.15/1.69 % (8011)------------------------------
% 3.15/1.69 % (8012)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/7Mi)
% 3.15/1.69 % (8014)Instruction limit reached!
% 3.15/1.69 % (8014)------------------------------
% 3.15/1.69 % (8014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.69 % (8014)Termination reason: Unknown
% 3.15/1.69 % (8014)Termination phase: shuffling
% 3.15/1.69
% 3.15/1.69 % (8014)Memory used [KB]: 1535
% 3.15/1.69 % (8014)Time elapsed: 0.004 s
% 3.15/1.69 % (8014)Instructions burned: 4 (million)
% 3.15/1.69 % (8014)------------------------------
% 3.15/1.69 % (8014)------------------------------
% 3.15/1.69 % (8012)Instruction limit reached!
% 3.15/1.69 % (8012)------------------------------
% 3.15/1.69 % (8012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.15/1.69 % (8012)Termination reason: Unknown
% 3.15/1.69 % (8012)Termination phase: shuffling
% 3.15/1.69
% 3.15/1.69 % (8012)Memory used [KB]: 1663
% 3.15/1.69 % (8012)Time elapsed: 0.005 s
% 3.15/1.69 % (8012)Instructions burned: 9 (million)
% 3.15/1.69 % (8012)------------------------------
% 3.15/1.69 % (8012)------------------------------
% 3.18/1.70 % (8015)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/18Mi)
% 3.18/1.70 % (7996)Instruction limit reached!
% 3.18/1.70 % (7996)------------------------------
% 3.18/1.70 % (7996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70 % (7996)Termination reason: Unknown
% 3.18/1.70 % (7996)Termination phase: Saturation
% 3.18/1.70
% 3.18/1.70 % (7996)Memory used [KB]: 7419
% 3.18/1.70 % (7996)Time elapsed: 0.070 s
% 3.18/1.70 % (7996)Instructions burned: 185 (million)
% 3.18/1.70 % (7996)------------------------------
% 3.18/1.70 % (7996)------------------------------
% 3.18/1.70 % (8018)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_7804 for (2999ds/902Mi)
% 3.18/1.70 % (8015)Instruction limit reached!
% 3.18/1.70 % (8015)------------------------------
% 3.18/1.70 % (8015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70 % (8015)Termination reason: Unknown
% 3.18/1.70 % (8015)Termination phase: shuffling
% 3.18/1.70
% 3.18/1.70 % (8015)Memory used [KB]: 1918
% 3.18/1.70 % (8015)Time elapsed: 0.009 s
% 3.18/1.70 % (8015)Instructions burned: 20 (million)
% 3.18/1.70 % (8015)------------------------------
% 3.18/1.70 % (8015)------------------------------
% 3.18/1.70 % (8016)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/710Mi)
% 3.18/1.71 % (8017)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/6Mi)
% 3.18/1.71 % (8017)Instruction limit reached!
% 3.18/1.71 % (8017)------------------------------
% 3.18/1.71 % (8017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (8017)Termination reason: Unknown
% 3.18/1.71 % (8017)Termination phase: shuffling
% 3.18/1.71
% 3.18/1.71 % (8017)Memory used [KB]: 1663
% 3.18/1.71 % (8017)Time elapsed: 0.005 s
% 3.18/1.71 % (8017)Instructions burned: 6 (million)
% 3.18/1.71 % (8017)------------------------------
% 3.18/1.71 % (8017)------------------------------
% 3.18/1.71 % (8019)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_7804 for (2999ds/21Mi)
% 3.18/1.71 % (8020)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/5Mi)
% 3.18/1.72 % (8020)Instruction limit reached!
% 3.18/1.72 % (8020)------------------------------
% 3.18/1.72 % (8020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.72 % (8020)Termination reason: Unknown
% 3.18/1.72 % (8020)Termination phase: shuffling
% 3.18/1.72
% 3.18/1.72 % (8020)Memory used [KB]: 1663
% 3.18/1.72 % (8020)Time elapsed: 0.004 s
% 3.18/1.72 % (8020)Instructions burned: 7 (million)
% 3.18/1.72 % (8020)------------------------------
% 3.18/1.72 % (8020)------------------------------
% 3.18/1.72 % (8019)Instruction limit reached!
% 3.18/1.72 % (8019)------------------------------
% 3.18/1.72 % (8019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.72 % (8019)Termination reason: Unknown
% 3.18/1.72 % (8019)Termination phase: shuffling
% 3.18/1.72
% 3.18/1.72 % (8019)Memory used [KB]: 1918
% 3.18/1.72 % (8019)Time elapsed: 0.008 s
% 3.18/1.72 % (8019)Instructions burned: 22 (million)
% 3.18/1.72 % (8019)------------------------------
% 3.18/1.72 % (8019)------------------------------
% 3.18/1.73 % (8022)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7804 for (2999ds/377Mi)
% 3.18/1.73 % (8021)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_7804 for (2999ds/6Mi)
% 3.18/1.73 % (8023)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_7804 for (2999ds/779Mi)
% 3.18/1.73 % (8021)Instruction limit reached!
% 3.18/1.73 % (8021)------------------------------
% 3.18/1.73 % (8021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.73 % (8021)Termination reason: Unknown
% 3.18/1.73 % (8021)Termination phase: shuffling
% 3.18/1.73
% 3.18/1.73 % (8021)Memory used [KB]: 1663
% 3.18/1.73 % (8021)Time elapsed: 0.005 s
% 3.18/1.73 % (8021)Instructions burned: 8 (million)
% 3.18/1.73 % (8021)------------------------------
% 3.18/1.73 % (8021)------------------------------
% 3.18/1.75 % (8024)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_7804 for (2998ds/19Mi)
% 3.18/1.76 % (8024)Instruction limit reached!
% 3.18/1.76 % (8024)------------------------------
% 3.18/1.76 % (8024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.76 % (8024)Termination reason: Unknown
% 3.18/1.76 % (8024)Termination phase: shuffling
% 3.18/1.76
% 3.18/1.76 % (8024)Memory used [KB]: 1918
% 3.18/1.76 % (8024)Time elapsed: 0.011 s
% 3.18/1.76 % (8024)Instructions burned: 20 (million)
% 3.18/1.76 % (8024)------------------------------
% 3.18/1.76 % (8024)------------------------------
% 3.18/1.76 % (8001)Instruction limit reached!
% 3.18/1.76 % (8001)------------------------------
% 3.18/1.76 % (8001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.76 % (8001)Termination reason: Unknown
% 3.18/1.76 % (8001)Termination phase: Saturation
% 3.18/1.76
% 3.18/1.76 % (8001)Memory used [KB]: 6780
% 3.18/1.76 % (8001)Time elapsed: 0.124 s
% 3.18/1.76 % (8001)Instructions burned: 275 (million)
% 3.18/1.76 % (8001)------------------------------
% 3.18/1.76 % (8001)------------------------------
% 3.18/1.77 % (8025)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7804 for (2998ds/879Mi)
% 3.18/1.78 % (8026)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7804 for (2998ds/17Mi)
% 3.18/1.79 % (8026)Instruction limit reached!
% 3.18/1.79 % (8026)------------------------------
% 3.18/1.79 % (8026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.79 % (8026)Termination reason: Unknown
% 3.18/1.79 % (8026)Termination phase: shuffling
% 3.18/1.79
% 3.18/1.79 % (8026)Memory used [KB]: 1918
% 3.18/1.79 % (8026)Time elapsed: 0.011 s
% 3.18/1.79 % (8026)Instructions burned: 17 (million)
% 3.18/1.79 % (8026)------------------------------
% 3.18/1.79 % (8026)------------------------------
% 3.18/1.80 % (8027)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7804 for (2998ds/3Mi)
% 3.18/1.80 % (8027)Instruction limit reached!
% 3.18/1.80 % (8027)------------------------------
% 3.18/1.80 % (8027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.80 % (8027)Termination reason: Unknown
% 3.18/1.80 % (8027)Termination phase: shuffling
% 3.18/1.80
% 3.18/1.80 % (8027)Memory used [KB]: 1535
% 3.18/1.80 % (8027)Time elapsed: 0.003 s
% 3.18/1.80 % (8027)Instructions burned: 3 (million)
% 3.18/1.80 % (8027)------------------------------
% 3.18/1.80 % (8027)------------------------------
% 3.18/1.82 % (8028)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7804 for (2997ds/30Mi)
% 3.18/1.82 % (8025)First to succeed.
% 3.18/1.82 % (8025)Refutation found. Thanks to Tanya!
% 3.18/1.82 % SZS status Theorem for DTF2THF_7804
% 3.18/1.82 % SZS output start Proof for DTF2THF_7804
% 3.18/1.82 thf(type_def_5, type, option_fml: $tType).
% 3.18/1.82 thf(type_def_7, type, option_trm: $tType).
% 3.18/1.82 thf(type_def_8, type, variable: $tType).
% 3.18/1.82 thf(type_def_9, type, set_variable: $tType).
% 3.18/1.82 thf(type_def_10, type, option_game: $tType).
% 3.18/1.82 thf(type_def_11, type, fml: $tType).
% 3.18/1.82 thf(type_def_12, type, game: $tType).
% 3.18/1.82 thf(type_def_13, type, trm: $tType).
% 3.18/1.82 thf(type_def_14, type, produc1739631244on_fml: $tType).
% 3.18/1.82 thf(type_def_15, type, char: $tType).
% 3.18/1.82 thf(type_def_16, type, produc799602994n_game: $tType).
% 3.18/1.82 thf(type_def_17, type, produc62062515n_game: $tType).
% 3.18/1.82 thf(type_def_18, type, produc1418842292n_game: $tType).
% 3.18/1.82 thf(func_def_0, type, produc1418842292n_game: $tType).
% 3.18/1.82 thf(func_def_1, type, produc62062515n_game: $tType).
% 3.18/1.82 thf(func_def_2, type, produc799602994n_game: $tType).
% 3.18/1.82 thf(func_def_3, type, produc1739631244on_fml: $tType).
% 3.18/1.82 thf(func_def_4, type, option_game: $tType).
% 3.18/1.82 thf(func_def_5, type, option_trm: $tType).
% 3.18/1.82 thf(func_def_6, type, option_fml: $tType).
% 3.18/1.82 thf(func_def_7, type, set_variable: $tType).
% 3.18/1.82 thf(func_def_8, type, variable: $tType).
% 3.18/1.82 thf(func_def_9, type, game: $tType).
% 3.18/1.82 thf(func_def_10, type, char: $tType).
% 3.18/1.82 thf(func_def_11, type, trm: $tType).
% 3.18/1.82 thf(func_def_12, type, fml: $tType).
% 3.18/1.82 thf(func_def_13, type, if_option_fml: $o > option_fml > option_fml > option_fml).
% 3.18/1.82 thf(func_def_14, type, if_option_trm: $o > option_trm > option_trm > option_trm).
% 3.18/1.82 thf(func_def_15, type, inf_inf_variable_o: (variable > $o) > (variable > $o) > variable > $o).
% 3.18/1.82 thf(func_def_16, type, inf_inf_o: $o > $o > $o).
% 3.18/1.82 thf(func_def_17, type, inf_inf_set_variable: set_variable > set_variable > set_variable).
% 3.18/1.82 thf(func_def_18, type, none_fml: option_fml).
% 3.18/1.82 thf(func_def_19, type, none_game: option_game).
% 3.18/1.82 thf(func_def_20, type, none_trm: option_trm).
% 3.18/1.82 thf(func_def_21, type, some_fml: fml > option_fml).
% 3.18/1.82 thf(func_def_22, type, some_game: game > option_game).
% 3.18/1.82 thf(func_def_23, type, some_trm: trm > option_trm).
% 3.18/1.82 thf(func_def_24, type, case_option_o_fml: $o > (fml > $o) > option_fml > $o).
% 3.18/1.82 thf(func_def_25, type, case_option_o_game: $o > (game > $o) > option_game > $o).
% 3.18/1.82 thf(func_def_26, type, case_option_o_trm: $o > (trm > $o) > option_trm > $o).
% 3.18/1.82 thf(func_def_27, type, case_o209804997ml_fml: option_fml > (fml > option_fml) > option_fml > option_fml).
% 3.18/1.82 thf(func_def_28, type, case_o325794063ml_trm: option_fml > (trm > option_fml) > option_trm > option_fml).
% 3.18/1.82 thf(func_def_29, type, case_o487727941rm_trm: option_trm > (trm > option_trm) > option_trm > option_trm).
% 3.18/1.82 thf(func_def_30, type, the_fml: option_fml > fml).
% 3.18/1.82 thf(func_def_31, type, the_game: option_game > game).
% 3.18/1.82 thf(func_def_32, type, the_trm: option_trm > trm).
% 3.18/1.82 thf(func_def_33, type, bot_bot_variable_o: variable > $o).
% 3.18/1.82 thf(func_def_34, type, bot_bot_set_variable: set_variable).
% 3.18/1.82 thf(func_def_35, type, ord_le1407353162able_o: (variable > $o) > (variable > $o) > $o).
% 3.18/1.82 thf(func_def_36, type, ord_le282106107riable: set_variable > set_variable > $o).
% 3.18/1.82 thf(func_def_37, type, produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml).
% 3.18/1.82 thf(func_def_38, type, produc1598111045on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 3.18/1.82 thf(func_def_39, type, produc1214549391on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 3.18/1.82 thf(func_def_40, type, produc1591622303on_fml: ((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml).
% 3.18/1.82 thf(func_def_41, type, produc2129367017on_trm: ((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm).
% 3.18/1.82 thf(func_def_42, type, produc377919108on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 3.18/1.82 thf(func_def_43, type, produc2141841102on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 3.18/1.82 thf(func_def_44, type, produc1903410526on_fml: ((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml).
% 3.18/1.82 thf(func_def_45, type, produc293671592on_trm: ((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm).
% 3.18/1.82 thf(func_def_46, type, produc1278328899on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 3.18/1.82 thf(func_def_47, type, produc724717725on_fml: ((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml).
% 3.18/1.82 thf(func_def_48, type, produc1420172399on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 3.18/1.82 thf(func_def_49, type, produc1036610745on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 3.18/1.82 thf(func_def_50, type, produc347802313on_fml: ((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml).
% 3.18/1.82 thf(func_def_51, type, produc885547027on_trm: ((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm).
% 3.18/1.82 thf(func_def_52, type, produc1615133358on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 3.18/1.82 thf(func_def_53, type, produc1231571704on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 3.18/1.82 thf(func_def_54, type, produc154833544on_fml: ((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml).
% 3.18/1.82 thf(func_def_55, type, produc692578258on_trm: ((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm).
% 3.18/1.82 thf(func_def_56, type, produc1250175341on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 3.18/1.82 thf(func_def_57, type, produc866613687on_trm: ((char > option_trm) > produc62062515n_game > char > option_trm) > produc1418842292n_game > char > option_trm).
% 3.18/1.82 thf(func_def_58, type, produc1499310791on_fml: ((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml).
% 3.18/1.82 thf(func_def_59, type, collect_variable: (variable > $o) > set_variable).
% 3.18/1.82 thf(func_def_60, type, is_empty_variable: set_variable > $o).
% 3.18/1.82 thf(func_def_61, type, static_FVF: fml > set_variable).
% 3.18/1.82 thf(func_def_62, type, static_FVT: trm > set_variable).
% 3.18/1.82 thf(func_def_63, type, geq: trm > trm > fml).
% 3.18/1.82 thf(func_def_64, type, pred: char > trm > fml).
% 3.18/1.82 thf(func_def_65, type, const: char > trm).
% 3.18/1.82 thf(func_def_66, type, func: char > trm > trm).
% 3.18/1.82 thf(func_def_67, type, uSubst152838031e_Geqo: option_trm > option_trm > option_fml).
% 3.18/1.82 thf(func_def_68, type, uSubst1408967625substt: trm > produc1418842292n_game).
% 3.18/1.82 thf(func_def_69, type, uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm).
% 3.18/1.82 thf(func_def_70, type, uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml).
% 3.18/1.82 thf(func_def_71, type, uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm).
% 3.18/1.82 thf(func_def_72, type, member_variable: variable > set_variable > $o).
% 3.18/1.82 thf(func_def_73, type, ua: set_variable).
% 3.18/1.82 thf(func_def_74, type, va: set_variable).
% 3.18/1.82 thf(func_def_75, type, sigma: produc1418842292n_game).
% 3.18/1.82 thf(func_def_76, type, theta: trm).
% 3.18/1.82 thf(func_def_77, type, p: char).
% 3.18/1.82 thf(func_def_78, type, vv: set_variable > set_variable > variable).
% 3.18/1.82 thf(func_def_79, type, vva: set_variable > set_variable > variable).
% 3.18/1.82 thf(func_def_96, type, sK0: char > set_variable > produc1418842292n_game > fml).
% 3.18/1.82 thf(func_def_97, type, sK1: char > produc1418842292n_game > set_variable > trm).
% 3.18/1.82 thf(func_def_98, type, sK2: char > set_variable > produc1418842292n_game > trm).
% 3.18/1.82 thf(func_def_99, type, sK3: (char > option_trm > $o) > trm).
% 3.18/1.82 thf(func_def_100, type, sK4: (char > option_trm > $o) > char).
% 3.18/1.82 thf(func_def_101, type, sK5: (char > option_trm > $o) > char).
% 3.18/1.82 thf(func_def_102, type, sK6: set_variable > produc1418842292n_game > char > trm).
% 3.18/1.82 thf(f1158,plain,(
% 3.18/1.82 $false),
% 3.18/1.82 inference(avatar_sat_refutation,[status(thm)],[f1136,f1153,f1157])).
% 3.18/1.82 thf(f1157,plain,(
% 3.18/1.82 ~spl7_2),
% 3.18/1.82 inference(avatar_contradiction_clause,[status(thm)],[f1156])).
% 3.18/1.82 thf(f1156,plain,(
% 3.18/1.82 $false | ~spl7_2),
% 3.18/1.82 inference(subsumption_resolution,[status(thm)],[f1155,f1154])).
% 3.18/1.82 thf(f1154,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ ua @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))))),
% 3.18/1.82 inference(forward_demodulation,[status(thm)],[f1061,f971])).
% 3.18/1.82 thf(f971,plain,(
% 3.18/1.82 ((uSubst516392818stappt @ sigma @ va @ theta) = (uSubst516392818stappt @ sigma @ ua @ theta))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f9])).
% 3.18/1.82 thf(f9,axiom,(
% 3.18/1.82 ((uSubst516392818stappt @ sigma @ va @ theta) = (uSubst516392818stappt @ sigma @ ua @ theta))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_8_f7)).
% 3.18/1.82 thf(f1061,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))))),
% 3.18/1.82 inference(beta_eta_normalization,[status(thm)],[f1020])).
% 3.18/1.82 thf(f1020,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va) @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))),
% 3.18/1.82 inference(definition_unfolding,[status(thm)],[f942,f937,f1009,f953,f981,f944])).
% 3.18/1.82 thf(f944,plain,(
% 3.18/1.82 (produc1420172399on_fml = (^[Y0 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y1 : produc799602994n_game]: ((^[Y2 : char]: (produc347802313on_fml @ (^[Y3 : char > option_fml]: ((^[Y4 : char > option_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f394])).
% 3.18/1.82 thf(f394,plain,(
% 3.18/1.82 (produc1420172399on_fml = (^[Y0 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y1 : produc799602994n_game]: ((^[Y2 : char]: (produc347802313on_fml @ (^[Y3 : char > option_fml]: ((^[Y4 : char > option_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f393])).
% 3.18/1.82 thf(f393,plain,(
% 3.18/1.82 (produc1420172399on_fml = (^[X0 : (char > option_fml) > (char > option_game) > char > option_fml, X1 : produc799602994n_game, X2 : char] : (produc347802313on_fml @ (^[X3 : char > option_fml, X4 : char > option_game] : (X0 @ X3 @ X4 @ X2)) @ X1)))),
% 3.18/1.82 inference(rectify,[status(thm)],[f14])).
% 3.18/1.82 thf(f14,axiom,(
% 3.18/1.82 (produc1420172399on_fml = (^[X16 : (char > option_fml) > (char > option_game) > char > option_fml, X17 : produc799602994n_game, X18 : char] : (produc347802313on_fml @ (^[X19 : char > option_fml, X20 : char > option_game] : (X16 @ X19 @ X20 @ X18)) @ X17)))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_13_case__prod__app)).
% 3.18/1.82 thf(f981,plain,(
% 3.18/1.82 (produc1615133358on_fml = (^[Y0 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y1 : produc62062515n_game]: ((^[Y2 : char]: (produc154833544on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc799602994n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f700])).
% 3.18/1.82 thf(f700,plain,(
% 3.18/1.82 (produc1615133358on_fml = (^[Y0 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y1 : produc62062515n_game]: ((^[Y2 : char]: (produc154833544on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc799602994n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f699])).
% 3.18/1.82 thf(f699,plain,(
% 3.18/1.82 (produc1615133358on_fml = (^[X0 : (char > option_trm) > produc799602994n_game > char > option_fml, X1 : produc62062515n_game, X2 : char] : (produc154833544on_fml @ (^[X3 : char > option_trm, X4 : produc799602994n_game] : (X0 @ X3 @ X4 @ X2)) @ X1)))),
% 3.18/1.82 inference(rectify,[status(thm)],[f12])).
% 3.18/1.82 thf(f12,axiom,(
% 3.18/1.82 (produc1615133358on_fml = (^[X16 : (char > option_trm) > produc799602994n_game > char > option_fml, X17 : produc62062515n_game, X18 : char] : (produc154833544on_fml @ (^[X19 : char > option_trm, X20 : produc799602994n_game] : (X16 @ X19 @ X20 @ X18)) @ X17)))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_11_case__prod__app)).
% 3.18/1.82 thf(f953,plain,(
% 3.18/1.82 (produc1250175341on_fml = (^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f610])).
% 3.18/1.82 thf(f610,plain,(
% 3.18/1.82 (produc1250175341on_fml = (^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f609])).
% 3.18/1.82 thf(f609,plain,(
% 3.18/1.82 (produc1250175341on_fml = (^[X0 : (char > option_trm) > produc62062515n_game > char > option_fml, X1 : produc1418842292n_game, X2 : char] : (produc1499310791on_fml @ (^[X3 : char > option_trm, X4 : produc62062515n_game] : (X0 @ X3 @ X4 @ X2)) @ X1)))),
% 3.18/1.82 inference(rectify,[status(thm)],[f10])).
% 3.18/1.82 thf(f10,axiom,(
% 3.18/1.82 (produc1250175341on_fml = (^[X16 : (char > option_trm) > produc62062515n_game > char > option_fml, X17 : produc1418842292n_game, X18 : char] : (produc1499310791on_fml @ (^[X19 : char > option_trm, X20 : produc62062515n_game] : (X16 @ X19 @ X20 @ X18)) @ X17)))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_9_case__prod__app)).
% 3.18/1.82 thf(f1009,plain,(
% 3.18/1.82 (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.18/1.82 inference(definition_unfolding,[status(thm)],[f943,f953,f981,f944])).
% 3.18/1.82 thf(f943,plain,(
% 3.18/1.82 (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f903])).
% 3.18/1.82 thf(f903,plain,(
% 3.18/1.82 (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) & (none_fml != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))),
% 3.18/1.82 inference(ennf_transformation,[status(thm)],[f364])).
% 3.18/1.82 thf(f364,plain,(
% 3.18/1.82 ~((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none_fml = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f363])).
% 3.18/1.82 thf(f363,plain,(
% 3.18/1.82 ~(((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : char > option_trm] : (produc1615133358on_fml @ (^[X1 : char > option_trm] : (produc1420172399on_fml @ (^[X2 : char > option_fml, X3 : char > option_game] : (X2)))))) @ sigma @ p))) @ va) = bot_bot_set_variable) => (none_fml = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p)))))),
% 3.18/1.82 inference(rectify,[status(thm)],[f3])).
% 3.18/1.82 thf(f3,axiom,(
% 3.18/1.82 ~(((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))) @ va) = bot_bot_set_variable) => (none_fml = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p)))))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062)).
% 3.18/1.82 thf(f937,plain,(
% 3.18/1.82 (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f897])).
% 3.18/1.82 thf(f897,plain,(
% 3.18/1.82 (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) & (none_fml != (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(ennf_transformation,[status(thm)],[f478])).
% 3.18/1.82 thf(f478,plain,(
% 3.18/1.82 ~((none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f477])).
% 3.18/1.82 thf(f477,plain,(
% 3.18/1.82 ~((none_fml = (produc1250175341on_fml @ (^[X0 : char > option_trm] : (produc1615133358on_fml @ (^[X1 : char > option_trm] : (produc1420172399on_fml @ (^[X2 : char > option_fml, X3 : char > option_game] : (X2)))))) @ sigma @ p)) | (none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))),
% 3.18/1.82 inference(rectify,[status(thm)],[f359])).
% 3.18/1.82 thf(f359,negated_conjecture,(
% 3.18/1.82 ~((none_fml = (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p)) | (none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))),
% 3.18/1.82 inference(negated_conjecture,[status(cth)],[f358])).
% 3.18/1.82 thf(f358,conjecture,(
% 3.18/1.82 (none_fml = (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p)) | (none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',conj_0)).
% 3.18/1.82 thf(f942,plain,(
% 3.18/1.82 (none_fml != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f903])).
% 3.18/1.82 thf(f1155,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ ua @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma)))) | ~spl7_2),
% 3.18/1.82 inference(forward_demodulation,[status(thm)],[f1135,f971])).
% 3.18/1.82 thf(f1135,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma)))) | ~spl7_2),
% 3.18/1.82 inference(avatar_component_clause,[status(thm)],[f1133])).
% 3.18/1.82 thf(f1133,definition,(
% 3.18/1.82 spl7_2 <=> ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))))),
% 3.18/1.82 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 3.18/1.82 thf(f1153,plain,(
% 3.18/1.82 ~spl7_1),
% 3.18/1.82 inference(avatar_split_clause,[status(thm)],[f1088,f1129])).
% 3.18/1.82 thf(f1129,definition,(
% 3.18/1.82 spl7_1 <=> ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))),
% 3.18/1.82 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 3.18/1.82 thf(f1088,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) != (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))),
% 3.18/1.82 inference(beta_eta_normalization,[status(thm)],[f1016])).
% 3.18/1.82 thf(f1016,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) != ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(definition_unfolding,[status(thm)],[f936,f937,f953,f981,f944])).
% 3.18/1.82 thf(f936,plain,(
% 3.18/1.82 (none_fml != (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f897])).
% 3.18/1.82 thf(f1136,plain,(
% 3.18/1.82 spl7_1 | spl7_2),
% 3.18/1.82 inference(avatar_split_clause,[status(thm)],[f1122,f1133,f1129])).
% 3.18/1.82 thf(f1122,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))) @ va) @ (the_fml @ (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma)))) | ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (produc1499310791on_fml @ (^[Y0 : char > option_trm]: (produc154833544on_fml @ (^[Y1 : char > option_trm]: (produc347802313on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2 @ p)))))))) @ sigma))),
% 3.18/1.82 inference(beta_eta_normalization,[status(thm)],[f1121])).
% 3.18/1.82 thf(f1121,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va) @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))) | ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(trivial_inequality_removal,[status(thm)],[f1046])).
% 3.18/1.82 thf(f1046,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)) | ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ (inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va) @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))) | ((inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va) != (inf_inf_set_variable @ (static_FVF @ (the_fml @ ((^[Y0 : (char > option_trm) > produc62062515n_game > char > option_fml]: ((^[Y1 : produc1418842292n_game]: ((^[Y2 : char]: (produc1499310791on_fml @ (^[Y3 : char > option_trm]: ((^[Y4 : produc62062515n_game]: (Y0 @ Y3 @ Y4 @ Y2)))) @ Y1)))))) @ (^[Y0 : char > option_trm]: ((^[Y1 : (char > option_trm) > produc799602994n_game > char > option_fml]: ((^[Y2 : produc62062515n_game]: ((^[Y3 : char]: (produc154833544on_fml @ (^[Y4 : char > option_trm]: ((^[Y5 : produc799602994n_game]: (Y1 @ Y4 @ Y5 @ Y3)))) @ Y2)))))) @ (^[Y1 : char > option_trm]: ((^[Y2 : (char > option_fml) > (char > option_game) > char > option_fml]: ((^[Y3 : produc799602994n_game]: ((^[Y4 : char]: (produc347802313on_fml @ (^[Y5 : char > option_fml]: ((^[Y6 : char > option_game]: (Y2 @ Y5 @ Y6 @ Y4)))) @ Y3)))))) @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 3.18/1.82 inference(definition_unfolding,[status(thm)],[f989,f1009,f953,f981,f944,f1009,f953,f981,f944,f937,f953,f981,f944])).
% 3.18/1.82 thf(f989,plain,(
% 3.18/1.82 ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(cnf_transformation,[status(thm)],[f894])).
% 3.18/1.82 thf(f894,plain,(
% 3.18/1.82 ((((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) & ((none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)))) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(ennf_transformation,[status(thm)],[f412])).
% 3.18/1.82 thf(f412,plain,(
% 3.18/1.82 ~(((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) => ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))) & ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))) => (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 3.18/1.82 inference(fool_elimination,[status(thm)],[f411])).
% 3.18/1.82 thf(f411,plain,(
% 3.18/1.82 ~(((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : char > option_trm] : (produc1615133358on_fml @ (^[X1 : char > option_trm] : (produc1420172399on_fml @ (^[X2 : char > option_fml, X3 : char > option_game] : (X2)))))) @ sigma @ p))) @ va)) => ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))))) & (((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ sigma @ p))) @ va) != bot_bot_set_variable) => (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))) => (none_fml = (produc1250175341on_fml @ (^[X12 : char > option_trm] : (produc1615133358on_fml @ (^[X13 : char > option_trm] : (produc1420172399on_fml @ (^[X14 : char > option_fml, X15 : char > option_game] : (X14)))))) @ sigma @ p))),
% 3.18/1.82 inference(rectify,[status(thm)],[f4])).
% 3.18/1.82 thf(f4,axiom,(
% 3.18/1.82 ~(((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))) @ va)) => ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)) = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))))) & (((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))) @ va) != bot_bot_set_variable) => (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))) => (none_fml = (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))),
% 3.18/1.82 file('/export/starexec/sandbox/tmp/tmp.xGkovyoVUm/DTF2THF_7804.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062)).
% 3.18/1.82 % SZS output end Proof for DTF2THF_7804
% 3.18/1.82 % (8025)------------------------------
% 3.18/1.82 % (8025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.82 % (8025)Termination reason: Refutation
% 3.18/1.82
% 3.18/1.82 % (8025)Memory used [KB]: 7291
% 3.18/1.82 % (8025)Time elapsed: 0.047 s
% 3.18/1.82 % (8025)Instructions burned: 146 (million)
% 3.18/1.82 % (8025)------------------------------
% 3.18/1.82 % (8025)------------------------------
% 3.18/1.82 % (7995)Success in time 0.217 s
%------------------------------------------------------------------------------