%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP202^1 : 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 : n026.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 08:56:23 AM UTC 2026
% Result : Theorem 3.09s 1.75s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 115 ( 95 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 803 ( 42 ~; 29 |; 9 &; 695 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 31 ( 30 usr)
% Number of type conns : 304 ( 304 >; 0 *; 0 +; 0 <<)
% Number of symbols : 129 ( 127 usr; 17 con; 0-8 aty)
% Number of variables : 313 ( 304 ^; 9 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
option_trm: $tType ).
thf(type_def_7,type,
char: $tType ).
thf(type_def_8,type,
option_fml: $tType ).
thf(type_def_9,type,
option_game: $tType ).
thf(type_def_10,type,
produc799602994n_game: $tType ).
thf(type_def_11,type,
produc62062515n_game: $tType ).
thf(type_def_12,type,
set_variable: $tType ).
thf(type_def_13,type,
trm: $tType ).
thf(type_def_14,type,
variable: $tType ).
thf(type_def_15,type,
set_Pr79606376n_game: $tType ).
thf(type_def_16,type,
set_Pr739694057n_game: $tType ).
thf(type_def_17,type,
set_Pr720454634n_game: $tType ).
thf(type_def_18,type,
set_Pr1235432374le_trm: $tType ).
thf(type_def_19,type,
set_Pr943832262on_trm: $tType ).
thf(type_def_20,type,
set_char: $tType ).
thf(type_def_21,type,
fml: $tType ).
thf(type_def_22,type,
game: $tType ).
thf(type_def_23,type,
produc1418842292n_game: $tType ).
thf(type_def_24,type,
denotational_interp: $tType ).
thf(type_def_25,type,
produc833882726rp_trm: $tType ).
thf(type_def_26,type,
produc46605351on_fml: $tType ).
thf(type_def_27,type,
produc1739631244on_fml: $tType ).
thf(type_def_28,type,
produc1016592119n_game: $tType ).
thf(type_def_29,type,
produc1072747943on_trm: $tType ).
thf(type_def_30,type,
produc1367888000le_trm: $tType ).
thf(type_def_31,type,
produc1699626005le_trm: $tType ).
thf(type_def_32,type,
produc464795408on_trm: $tType ).
thf(type_def_33,type,
produc1408538418on_fml: $tType ).
thf(type_def_34,type,
produc1024976764on_trm: $tType ).
thf(type_def_35,type,
real: $tType ).
thf(func_def_0,type,
produc1699626005le_trm: $tType ).
thf(func_def_1,type,
set_Pr720454634n_game: $tType ).
thf(func_def_2,type,
produc1418842292n_game: $tType ).
thf(func_def_3,type,
set_Pr739694057n_game: $tType ).
thf(func_def_4,type,
produc62062515n_game: $tType ).
thf(func_def_5,type,
set_Pr79606376n_game: $tType ).
thf(func_def_6,type,
produc799602994n_game: $tType ).
thf(func_def_7,type,
produc1016592119n_game: $tType ).
thf(func_def_8,type,
produc1739631244on_fml: $tType ).
thf(func_def_9,type,
produc1072747943on_trm: $tType ).
thf(func_def_10,type,
produc46605351on_fml: $tType ).
thf(func_def_11,type,
set_Pr943832262on_trm: $tType ).
thf(func_def_12,type,
set_Pr1235432374le_trm: $tType ).
thf(func_def_13,type,
produc1024976764on_trm: $tType ).
thf(func_def_14,type,
produc1408538418on_fml: $tType ).
thf(func_def_15,type,
produc464795408on_trm: $tType ).
thf(func_def_16,type,
produc833882726rp_trm: $tType ).
thf(func_def_17,type,
produc1367888000le_trm: $tType ).
thf(func_def_18,type,
option_game: $tType ).
thf(func_def_19,type,
option_trm: $tType ).
thf(func_def_20,type,
option_fml: $tType ).
thf(func_def_21,type,
denotational_interp: $tType ).
thf(func_def_22,type,
set_variable: $tType ).
thf(func_def_23,type,
set_char: $tType ).
thf(func_def_24,type,
variable: $tType ).
thf(func_def_25,type,
game: $tType ).
thf(func_def_26,type,
char: $tType ).
thf(func_def_27,type,
trm: $tType ).
thf(func_def_28,type,
fml: $tType ).
thf(func_def_29,type,
real: $tType ).
thf(func_def_30,type,
if_option_trm: $o > option_trm > option_trm > option_trm ).
thf(func_def_31,type,
inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
thf(func_def_32,type,
inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
thf(func_def_33,type,
inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
thf(func_def_34,type,
inf_in185389155_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > set_variable > trm > $o ).
thf(func_def_35,type,
inf_in605351507_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > char > option_trm > $o ).
thf(func_def_36,type,
inf_inf_char_o: ( char > $o ) > ( char > $o ) > char > $o ).
thf(func_def_37,type,
inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
thf(func_def_38,type,
inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game ).
thf(func_def_39,type,
inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game ).
thf(func_def_40,type,
inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game ).
thf(func_def_41,type,
inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm ).
thf(func_def_42,type,
inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm ).
thf(func_def_43,type,
inf_inf_set_char: set_char > set_char > set_char ).
thf(func_def_44,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_45,type,
combine_options_fml: ( fml > fml > fml ) > option_fml > option_fml > option_fml ).
thf(func_def_46,type,
combine_options_game: ( game > game > game ) > option_game > option_game > option_game ).
thf(func_def_47,type,
combine_options_trm: ( trm > trm > trm ) > option_trm > option_trm > option_trm ).
thf(func_def_48,type,
none_fml: option_fml ).
thf(func_def_49,type,
none_game: option_game ).
thf(func_def_50,type,
none_trm: option_trm ).
thf(func_def_51,type,
some_fml: fml > option_fml ).
thf(func_def_52,type,
some_game: game > option_game ).
thf(func_def_53,type,
some_trm: trm > option_trm ).
thf(func_def_54,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_55,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_56,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_57,type,
case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
thf(func_def_58,type,
case_o696458451e_game: option_game > ( game > option_game ) > option_game > option_game ).
thf(func_def_59,type,
case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
thf(func_def_60,type,
the_fml: option_fml > fml ).
thf(func_def_61,type,
the_game: option_game > game ).
thf(func_def_62,type,
the_trm: option_trm > trm ).
thf(func_def_63,type,
bot_bo1895715589game_o: ( char > option_fml ) > ( char > option_game ) > $o ).
thf(func_def_64,type,
bot_bo1417568964game_o: ( char > option_trm ) > produc799602994n_game > $o ).
thf(func_def_65,type,
bot_bot_char_o: char > $o ).
thf(func_def_66,type,
bot_bot_variable_o: variable > $o ).
thf(func_def_67,type,
bot_bo456479484n_game: set_Pr79606376n_game ).
thf(func_def_68,type,
bot_bo1302831229n_game: set_Pr739694057n_game ).
thf(func_def_69,type,
bot_bot_set_char: set_char ).
thf(func_def_70,type,
bot_bot_set_variable: set_variable ).
thf(func_def_71,type,
produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
thf(func_def_72,type,
produc1048060077n_game: ( char > option_trm ) > produc799602994n_game > produc62062515n_game ).
thf(func_def_73,type,
produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
thf(func_def_74,type,
produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
thf(func_def_75,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(func_def_76,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_77,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_78,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(func_def_79,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(func_def_80,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(func_def_81,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(func_def_82,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(func_def_83,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(func_def_84,type,
produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_85,type,
produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_86,type,
produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_87,type,
produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_88,type,
produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_89,type,
produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_90,type,
produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_91,type,
produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
thf(func_def_92,type,
produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
thf(func_def_93,type,
produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
thf(func_def_94,type,
produc629249376t_char: ( ( char > option_fml ) > ( char > option_game ) > set_char ) > produc799602994n_game > set_char ).
thf(func_def_95,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_96,type,
produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_97,type,
produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
thf(func_def_98,type,
produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
thf(func_def_99,type,
produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
thf(func_def_100,type,
produc1554403041t_char: ( ( char > option_trm ) > produc799602994n_game > set_char ) > produc62062515n_game > set_char ).
thf(func_def_101,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_102,type,
produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
thf(func_def_103,type,
produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
thf(func_def_104,type,
produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
thf(func_def_105,type,
produc1002100706t_char: ( ( char > option_trm ) > produc62062515n_game > set_char ) > produc1418842292n_game > set_char ).
thf(func_def_106,type,
produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
thf(func_def_107,type,
produc836445798t_char: ( set_variable > trm > set_char ) > produc1367888000le_trm > set_char ).
thf(func_def_108,type,
produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
thf(func_def_109,type,
produc33263478t_char: ( char > option_trm > set_char ) > produc464795408on_trm > set_char ).
thf(func_def_110,type,
collect_char: ( char > $o ) > set_char ).
thf(func_def_111,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_112,type,
is_empty_variable: set_variable > $o ).
thf(func_def_113,type,
static_FVF: fml > set_variable ).
thf(func_def_114,type,
static_FVT: trm > set_variable ).
thf(func_def_115,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(func_def_116,type,
geq: trm > trm > fml ).
thf(func_def_117,type,
pred: char > trm > fml ).
thf(func_def_118,type,
const: char > trm ).
thf(func_def_119,type,
differential: trm > trm ).
thf(func_def_120,type,
func: char > trm > trm ).
thf(func_def_121,type,
number: real > trm ).
thf(func_def_122,type,
plus: trm > trm > trm ).
thf(func_def_123,type,
times: trm > trm > trm ).
thf(func_def_124,type,
var: variable > trm ).
thf(func_def_125,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(func_def_126,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_127,type,
uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_128,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(func_def_129,type,
uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_130,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_131,type,
uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_132,type,
uSubst_Mirabelle_dot: trm ).
thf(func_def_133,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(func_def_134,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_135,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_136,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_137,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(func_def_138,type,
accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
thf(func_def_139,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(func_def_140,type,
member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
thf(func_def_141,type,
member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
thf(func_def_142,type,
member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o ).
thf(func_def_143,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_144,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_145,type,
member_char: char > set_char > $o ).
thf(func_def_146,type,
member_variable: variable > set_variable > $o ).
thf(func_def_147,type,
u: set_variable ).
thf(func_def_148,type,
v: set_variable ).
thf(func_def_149,type,
sigma: produc1418842292n_game ).
thf(func_def_150,type,
f: char ).
thf(func_def_165,type,
sK0: produc1418842292n_game > char > set_variable > trm ).
thf(func_def_166,type,
sK1: produc1418842292n_game > char > set_variable > trm ).
thf(f884,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f858,f871,f873,f879,f883]) ).
thf(f883,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f882]) ).
thf(f882,plain,
( $false
| ~ spl2_3
| ~ spl2_6 ),
inference(subsumption_resolution,[status(thm)],[f881,f859]) ).
thf(f859,plain,
( ( uSubst1559070963pconst @ sigma @ v @ f )
!= ( uSubst1559070963pconst @ sigma @ u @ f ) ),
inference(forward_demodulation,[status(thm)],[f839,f829]) ).
thf(f829,plain,
! [X2: produc1418842292n_game,X0: char,X1: set_variable] :
( ( uSubst1559070963pconst @ X2 @ X1 @ X0 )
= ( uSubst516392818stappt @ X2 @ X1 @ ( const @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f798]) ).
thf(f798,plain,
! [X0: char,X1: set_variable,X2: produc1418842292n_game] :
( ( uSubst1559070963pconst @ X2 @ X1 @ X0 )
= ( uSubst516392818stappt @ X2 @ X1 @ ( const @ X0 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X14: char,X13: set_variable,X12: produc1418842292n_game] :
( ( uSubst516392818stappt @ X12 @ X13 @ ( const @ X14 ) )
= ( uSubst1559070963pconst @ X12 @ X13 @ X14 ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_7_usubstappt_Osimps_I3_J) ).
thf(f839,plain,
( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
!= ( uSubst1559070963pconst @ sigma @ v @ f ) ),
inference(cnf_transformation,[status(thm)],[f807]) ).
thf(f807,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
& ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
!= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ),
inference(ennf_transformation,[status(thm)],[f589]) ).
thf(f589,plain,
~ ( ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) )
| ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ),
inference(fool_elimination,[status(thm)],[f588]) ).
thf(f588,plain,
~ ( ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) )
| ( ( produc866613687on_trm
@ ^ [X0: char > option_trm] :
( produc1231571704on_trm
@ ^ [X1: char > option_trm] :
( produc1036610745on_trm
@ ^ [X2: char > option_fml,X3: char > option_game] : X0 ) )
@ sigma
@ f )
= none_trm ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) )
| ( ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f )
= none_trm ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
( ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) )
| ( ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f )
= none_trm ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',conj_0) ).
thf(f881,plain,
( ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( uSubst1559070963pconst @ sigma @ u @ f ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(forward_demodulation,[status(thm)],[f878,f857]) ).
thf(f857,plain,
( ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f855]) ).
thf(f855,definition,
( spl2_3
<=> ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f878,plain,
( ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f876]) ).
thf(f876,definition,
( spl2_6
<=> ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f879,plain,
( ~ spl2_5
| spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f874,f876,f866]) ).
thf(f866,definition,
( spl2_5
<=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f874,plain,
( ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
inference(subsumption_resolution,[status(thm)],[f822,f840]) ).
thf(f840,plain,
( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ),
inference(cnf_transformation,[status(thm)],[f807]) ).
thf(f822,plain,
( ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
inference(cnf_transformation,[status(thm)],[f810]) ).
thf(f810,plain,
( ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) )
| ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) )
& ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) )
| ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) ) )
| ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ),
inference(ennf_transformation,[status(thm)],[f378]) ).
thf(f378,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
=> ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) )
=> ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) )
& ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f377]) ).
thf(f377,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X0: char > option_trm] :
( produc1231571704on_trm
@ ^ [X1: char > option_trm] :
( produc1036610745on_trm
@ ^ [X2: char > option_fml,X3: char > option_game] : X0 ) )
@ sigma
@ f ) )
=> ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X4: char > option_trm] :
( produc1231571704on_trm
@ ^ [X5: char > option_trm] :
( produc1036610745on_trm
@ ^ [X6: char > option_fml,X7: char > option_game] : X4 ) )
@ sigma
@ f ) ) )
@ v ) )
=> ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X8: char > option_trm] :
( produc1231571704on_trm
@ ^ [X9: char > option_trm] :
( produc1036610745on_trm
@ ^ [X10: char > option_fml,X11: char > option_game] : X8 ) )
@ sigma
@ f ) ) ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X12: char > option_trm] :
( produc1231571704on_trm
@ ^ [X13: char > option_trm] :
( produc1036610745on_trm
@ ^ [X14: char > option_fml,X15: char > option_game] : X12 ) )
@ sigma
@ f ) ) )
@ v )
!= bot_bot_set_variable )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) )
=> ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ v ) )
=> ( ( uSubst1559070963pconst @ sigma @ v @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ v )
!= bot_bot_set_variable )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062) ).
thf(f873,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f872,f848]) ).
thf(f848,definition,
( spl2_2
<=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f872,plain,
( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ),
inference(subsumption_resolution,[status(thm)],[f836,f840]) ).
thf(f836,plain,
( ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
inference(cnf_transformation,[status(thm)],[f802]) ).
thf(f802,plain,
( ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
inference(ennf_transformation,[status(thm)],[f368]) ).
thf(f368,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
inference(fool_elimination,[status(thm)],[f367]) ).
thf(f367,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X0: char > option_trm] :
( produc1231571704on_trm
@ ^ [X1: char > option_trm] :
( produc1036610745on_trm
@ ^ [X2: char > option_fml,X3: char > option_game] : X0 ) )
@ sigma
@ f ) )
=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X4: char > option_trm] :
( produc1231571704on_trm
@ ^ [X5: char > option_trm] :
( produc1036610745on_trm
@ ^ [X6: char > option_fml,X7: char > option_game] : X4 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) )
=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_3_f3) ).
thf(f871,plain,
spl2_5,
inference(avatar_split_clause,[status(thm)],[f870,f866]) ).
thf(f870,plain,
( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ),
inference(subsumption_resolution,[status(thm)],[f818,f840]) ).
thf(f818,plain,
( ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
inference(cnf_transformation,[status(thm)],[f801]) ).
thf(f801,plain,
( ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
inference(ennf_transformation,[status(thm)],[f643]) ).
thf(f643,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ v ) ) ),
inference(fool_elimination,[status(thm)],[f642]) ).
thf(f642,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X0: char > option_trm] :
( produc1231571704on_trm
@ ^ [X1: char > option_trm] :
( produc1036610745on_trm
@ ^ [X2: char > option_fml,X3: char > option_game] : X0 ) )
@ sigma
@ f ) )
=> ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X4: char > option_trm] :
( produc1231571704on_trm
@ ^ [X5: char > option_trm] :
( produc1036610745on_trm
@ ^ [X6: char > option_fml,X7: char > option_game] : X4 ) )
@ sigma
@ f ) ) )
@ v )
= bot_bot_set_variable ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) )
=> ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ v )
= bot_bot_set_variable ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).
thf(f858,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f853,f855,f848]) ).
thf(f853,plain,
( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) )
| ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f819,f840]) ).
thf(f819,plain,
( ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ),
inference(cnf_transformation,[status(thm)],[f800]) ).
thf(f800,plain,
( ( none_trm
= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
| ( ( ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) )
& ( ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) )
| ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f795]) ).
thf(f795,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) )
=> ( ( ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) )
=> ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) ) ) )
& ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [Y0: char > option_trm] :
( produc1231571704on_trm
@ ^ [Y1: char > option_trm] :
( produc1036610745on_trm
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y0 ) )
@ sigma
@ f ) ) )
@ u ) )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f794]) ).
thf(f794,plain,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X0: char > option_trm] :
( produc1231571704on_trm
@ ^ [X1: char > option_trm] :
( produc1036610745on_trm
@ ^ [X2: char > option_fml,X3: char > option_game] : X0 ) )
@ sigma
@ f ) )
=> ( ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X4: char > option_trm] :
( produc1231571704on_trm
@ ^ [X5: char > option_trm] :
( produc1036610745on_trm
@ ^ [X6: char > option_fml,X7: char > option_game] : X4 ) )
@ sigma
@ f ) ) )
@ u )
!= bot_bot_set_variable )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X8: char > option_trm] :
( produc1231571704on_trm
@ ^ [X9: char > option_trm] :
( produc1036610745on_trm
@ ^ [X10: char > option_fml,X11: char > option_game] : X8 ) )
@ sigma
@ f ) ) )
@ u )
= bot_bot_set_variable )
=> ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X12: char > option_trm] :
( produc1231571704on_trm
@ ^ [X13: char > option_trm] :
( produc1036610745on_trm
@ ^ [X14: char > option_fml,X15: char > option_game] : X12 ) )
@ sigma
@ f ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( ( none_trm
!= ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) )
=> ( ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ u )
!= bot_bot_set_variable )
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
& ( ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) )
@ u )
= bot_bot_set_variable )
=> ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X3: char > option_trm] :
( produc1231571704on_trm
@ ^ [X4: char > option_trm] :
( produc1036610745on_trm
@ ^ [X5: char > option_fml,X6: char > option_game] : X3 ) )
@ sigma
@ f ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP202^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:55 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP202^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer USubst problem prob_411__6333658_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : USubst/prob_411__6333658_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 507 ( 231 unt; 151 typ; 0 def)
% 0.31/0.46 % Number of atoms : 935 ( 675 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 31 ( 2 avg)
% 0.31/0.46 % Number of connectives : 3457 ( 227 ~; 12 |; 39 &;2745 @)
% 0.31/0.46 % ( 0 <=>; 434 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 26 ( 5 avg)
% 0.31/0.46 % Number of types : 31 ( 30 usr)
% 0.31/0.46 % Number of type conns : 970 ( 970 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 124 ( 121 usr; 14 con; 0-8 aty)
% 0.31/0.46 % Number of variables : 1377 ( 319 ^;1039 !; 19 ?;1377 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:11.864
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (30)
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.31/0.46 produc1699626005le_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__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_J,type,
% 0.31/0.46 set_Pr720454634n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc1418842292n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__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,
% 0.31/0.46 set_Pr739694057n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc62062515n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__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,
% 0.31/0.46 set_Pr79606376n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc799602994n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.31/0.46 produc1016592119n_game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.31/0.46 produc1739631244on_fml: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.31/0.46 produc1072747943on_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.31/0.46 produc46605351on_fml: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.31/0.46 set_Pr943832262on_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.31/0.46 set_Pr1235432374le_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.31/0.46 produc1024976764on_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.31/0.46 produc1408538418on_fml: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.31/0.46 produc464795408on_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp_Mt__Syntax__Otrm_J,type,
% 0.31/0.46 produc833882726rp_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.31/0.46 produc1367888000le_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.31/0.46 option_game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.31/0.46 option_trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.31/0.46 option_fml: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.31/0.46 denotational_interp: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.31/0.46 set_variable: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.46 set_char: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Syntax__Ovariable,type,
% 0.31/0.46 variable: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Syntax__Ogame,type,
% 0.31/0.46 game: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__String__Ochar,type,
% 0.31/0.46 char: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Syntax__Otrm,type,
% 0.31/0.46 trm: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Syntax__Ofml,type,
% 0.31/0.46 fml: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Real__Oreal,type,
% 0.31/0.46 real: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (121)
% 0.31/0.46 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.31/0.46 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 0.31/0.46 inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 0.31/0.46 inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 0.31/0.46 inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 0.31/0.46 inf_in185389155_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > set_variable > trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 0.31/0.47 inf_in605351507_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > char > option_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__String__Ochar_M_Eo_J,type,
% 0.31/0.47 inf_inf_char_o: ( char > $o ) > ( char > $o ) > char > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.31/0.47 inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,
% 0.31/0.47 inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,
% 0.31/0.47 inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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_J,type,
% 0.31/0.47 inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.31/0.47 inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.31/0.47 inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 inf_inf_set_char: set_char > set_char > set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.31/0.47 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ocombine__options_001t__Syntax__Ofml,type,
% 0.31/0.47 combine_options_fml: ( fml > fml > fml ) > option_fml > option_fml > option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ocombine__options_001t__Syntax__Ogame,type,
% 0.31/0.47 combine_options_game: ( game > game > game ) > option_game > option_game > option_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ocombine__options_001t__Syntax__Otrm,type,
% 0.31/0.47 combine_options_trm: ( trm > trm > trm ) > option_trm > option_trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 0.31/0.47 none_fml: option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.31/0.47 none_game: option_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 0.31/0.47 none_trm: option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 0.31/0.47 some_fml: fml > option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 0.31/0.47 some_game: game > option_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 0.31/0.47 some_trm: trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 0.31/0.47 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 0.31/0.47 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 0.31/0.47 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Ofml,type,
% 0.31/0.47 case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Syntax__Ogame,type,
% 0.31/0.47 case_o696458451e_game: option_game > ( game > option_game ) > option_game > option_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Syntax__Otrm,type,
% 0.31/0.47 case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 0.31/0.47 the_fml: option_fml > fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.31/0.47 the_game: option_game > game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 0.31/0.47 the_trm: option_trm > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 0.31/0.47 bot_bo1895715589game_o: ( char > option_fml ) > ( char > option_game ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 0.31/0.47 bot_bo1417568964game_o: ( char > option_trm ) > produc799602994n_game > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__String__Ochar_M_Eo_J,type,
% 0.31/0.47 bot_bot_char_o: char > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.31/0.47 bot_bot_variable_o: variable > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
% 0.31/0.47 bot_bo456479484n_game: set_Pr79606376n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
% 0.31/0.47 bot_bo1302831229n_game: set_Pr739694057n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 bot_bot_set_char: set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.31/0.47 bot_bot_set_variable: set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_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,type,
% 0.31/0.47 produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_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,type,
% 0.31/0.47 produc1048060077n_game: ( char > option_trm ) > produc799602994n_game > produc62062515n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_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,type,
% 0.31/0.47 produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp_001t__Syntax__Otrm,type,
% 0.31/0.47 produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.31/0.47 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.31/0.47 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.31/0.47 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.31/0.47 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_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__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_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.31/0.47 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.31/0.47 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.31/0.47 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.31/0.47 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.31/0.47 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 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_Eo,type,
% 0.31/0.47 produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 0.31/0.47
% 0.31/0.47 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__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 produc629249376t_char: ( ( char > option_fml ) > ( char > option_game ) > set_char ) > produc799602994n_game > set_char ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 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_Eo,type,
% 0.31/0.47 produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 0.31/0.47
% 0.31/0.47 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__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 produc1554403041t_char: ( ( char > option_trm ) > produc799602994n_game > set_char ) > produc62062515n_game > set_char ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 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_Eo,type,
% 0.31/0.47 produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 0.31/0.47
% 0.31/0.47 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__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 produc1002100706t_char: ( ( char > option_trm ) > produc62062515n_game > set_char ) > produc1418842292n_game > set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001_Eo,type,
% 0.31/0.47 produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001t__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 produc836445798t_char: ( set_variable > trm > set_char ) > produc1367888000le_trm > set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001_Eo,type,
% 0.31/0.47 produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Set__Oset_It__String__Ochar_J,type,
% 0.31/0.47 produc33263478t_char: ( char > option_trm > set_char ) > produc464795408on_trm > set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__String__Ochar,type,
% 0.31/0.47 collect_char: ( char > $o ) > set_char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.31/0.47 collect_variable: ( variable > $o ) > set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 0.31/0.47 is_empty_variable: set_variable > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Static__Semantics_OFVF,type,
% 0.31/0.47 static_FVF: fml > set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Static__Semantics_OFVT,type,
% 0.31/0.47 static_FVT: trm > set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_String_Ochar_OChar,type,
% 0.31/0.47 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.31/0.47 geq: trm > trm > fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Ofml_OPred,type,
% 0.31/0.47 pred: char > trm > fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.31/0.47 const: char > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.31/0.47 differential: trm > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.31/0.47 func: char > trm > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.31/0.47 number: real > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.31/0.47 plus: trm > trm > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.31/0.47 times: trm > trm > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.31/0.47 var: variable > trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 0.31/0.47 uSubst716837505ntialo: option_trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 0.31/0.47 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo__rel,type,
% 0.31/0.47 uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 0.31/0.47 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso__rel,type,
% 0.31/0.47 uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 0.31/0.47 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso__rel,type,
% 0.31/0.47 uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odot,type,
% 0.31/0.47 uSubst_Mirabelle_dot: trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 0.31/0.47 uSubst1408967625substt: trm > produc1418842292n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 0.31/0.47 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 0.31/0.47 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.31/0.47 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 0.31/0.47 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.31/0.47 accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.31/0.47 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_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,type,
% 0.31/0.47 member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_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,type,
% 0.31/0.47 member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_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__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,
% 0.31/0.47 member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.31/0.47 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.31/0.47 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__String__Ochar,type,
% 0.31/0.47 member_char: char > set_char > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.31/0.47 member_variable: variable > set_variable > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_U,type,
% 0.31/0.47 u: set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_V,type,
% 0.31/0.47 v: set_variable ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v__092_060sigma_062,type,
% 0.31/0.47 sigma: produc1418842292n_game ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_f____,type,
% 0.31/0.47 f: char ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (352)
% 0.31/0.47 thf(fact_0_f2,axiom,
% 0.31/0.47 ! [Z: option_trm,F: trm > option_trm,Za: option_trm] :
% 0.31/0.47 ( ( ( Za = none_trm )
% 0.31/0.47 => ( ( case_o487727941rm_trm @ Z @ F @ Za )
% 0.31/0.47 = Z ) )
% 0.31/0.47 & ( ( Za != none_trm )
% 0.31/0.47 => ( ( case_o487727941rm_trm @ Z @ F @ Za )
% 0.31/0.47 = ( F @ ( the_trm @ Za ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % f2
% 0.31/0.47 thf(fact_1_Const_Oprems_I1_J,axiom,
% 0.31/0.47 ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 0.31/0.47 != none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Const.prems(1)
% 0.31/0.47 thf(fact_2_Const_Oprems_I2_J,axiom,
% 0.31/0.47 ( ( uSubst516392818stappt @ sigma @ v @ ( const @ f ) )
% 0.31/0.47 != none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Const.prems(2)
% 0.31/0.47 thf(fact_3_f3,axiom,
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ u )
% 0.31/0.47 = bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % f3
% 0.31/0.47 thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ v )
% 0.31/0.47 = bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> FVT (the (SConst \<sigma> f)) \<inter> V = {}\<close>
% 0.31/0.47 thf(fact_5_usappconst__def,axiom,
% 0.31/0.47 ( uSubst1559070963pconst
% 0.31/0.47 = ( ^ [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 0.31/0.47 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F2 ) )
% 0.31/0.47 @ ^ [R: trm] :
% 0.31/0.47 ( if_option_trm
% 0.31/0.47 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 @ ( some_trm @ R )
% 0.31/0.47 @ none_trm )
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma
% 0.31/0.47 @ F2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usappconst_def
% 0.31/0.47 thf(fact_6_f1,axiom,
% 0.31/0.47 ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 0.31/0.47 = ( case_o487727941rm_trm @ ( some_trm @ ( const @ f ) )
% 0.31/0.47 @ ^ [T: trm] :
% 0.31/0.47 ( if_option_trm
% 0.31/0.47 @ ( ( inf_inf_set_variable @ ( static_FVT @ T ) @ u )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 @ ( some_trm @ T )
% 0.31/0.47 @ none_trm )
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % f1
% 0.31/0.47 thf(fact_7_usubstappt_Osimps_I3_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.31/0.47 = ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(3)
% 0.31/0.47 thf(fact_8_undeft__None,axiom,
% 0.31/0.47 none_trm = none_trm ).
% 0.31/0.47
% 0.31/0.47 % undeft_None
% 0.31/0.47 thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,axiom,
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ v )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( ( some_trm
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) )
% 0.31/0.47 & ( ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ v )
% 0.31/0.47 != bot_bot_set_variable )
% 0.31/0.47 => ( none_trm
% 0.31/0.47 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> (if FVT (the (SConst \<sigma> f)) \<inter> V = {} then Aterm (the (SConst \<sigma> f)) else undeft) = usappconst \<sigma> V f\<close>
% 0.31/0.47 thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,axiom,
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ u )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( ( some_trm
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 = ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
% 0.31/0.47 & ( ( ( inf_inf_set_variable
% 0.31/0.47 @ ( static_FVT
% 0.31/0.47 @ ( the_trm
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ sigma
% 0.31/0.47 @ f ) ) )
% 0.31/0.47 @ u )
% 0.31/0.47 != bot_bot_set_variable )
% 0.31/0.47 => ( none_trm
% 0.31/0.47 = ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>SConst \<sigma> f \<noteq> undeft \<longrightarrow> (if FVT (the (SConst \<sigma> f)) \<inter> U = {} then Aterm (the (SConst \<sigma> f)) else undeft) = usappconst \<sigma> U f\<close>
% 0.31/0.47 thf(fact_11_trm_Oinject_I3_J,axiom,
% 0.31/0.47 ! [X3: char,Y3: char] :
% 0.31/0.47 ( ( ( const @ X3 )
% 0.31/0.47 = ( const @ Y3 ) )
% 0.31/0.47 = ( X3 = Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(3)
% 0.31/0.47 thf(fact_12_case__prod__app,axiom,
% 0.31/0.47 ( produc1250175341on_fml
% 0.31/0.47 = ( ^ [F2: ( char > option_trm ) > produc62062515n_game > char > option_fml,X: produc1418842292n_game,Y: char] :
% 0.31/0.47 ( produc1499310791on_fml
% 0.31/0.47 @ ^ [L: char > option_trm,R: produc62062515n_game] : ( F2 @ L @ R @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_app
% 0.31/0.47 thf(fact_13_case__prod__app,axiom,
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_trm,X: produc62062515n_game,Y: char] :
% 0.31/0.47 ( produc692578258on_trm
% 0.31/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_app
% 0.31/0.47 thf(fact_14_case__prod__app,axiom,
% 0.31/0.47 ( produc1615133358on_fml
% 0.31/0.47 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 0.31/0.47 ( produc154833544on_fml
% 0.31/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_app
% 0.31/0.47 thf(fact_15_case__prod__app,axiom,
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 0.31/0.47 ( produc885547027on_trm
% 0.31/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_app
% 0.31/0.47 thf(fact_16_case__prod__app,axiom,
% 0.31/0.47 ( produc1420172399on_fml
% 0.31/0.47 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 0.31/0.47 ( produc347802313on_fml
% 0.31/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_app
% 0.31/0.47 thf(fact_17_usubstappt__const,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R2 ) )
% 0.31/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.31/0.47 = ( some_trm @ R2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_const
% 0.31/0.47 thf(fact_18_usubstappt__const__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 | ? [R3: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R3 ) )
% 0.31/0.47 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_const_conv
% 0.31/0.47 thf(fact_19_usappconst__simp,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R2 ) )
% 0.31/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 )
% 0.31/0.47 = ( some_trm @ R2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usappconst_simp
% 0.31/0.47 thf(fact_20_usappconst__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 0.31/0.47 ( ( ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 | ? [R3: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [F0: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R3 ) )
% 0.31/0.47 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usappconst_conv
% 0.31/0.47 thf(fact_21_ODEo_Oinduct,axiom,
% 0.31/0.47 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.31/0.47 ( ! [X2: char,Theta: trm] : ( P @ X2 @ ( some_trm @ Theta ) )
% 0.31/0.47 => ( ! [X2: char] : ( P @ X2 @ none_trm )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ODEo.induct
% 0.31/0.47 thf(fact_22_undeft__equiv,axiom,
% 0.31/0.47 ! [Theta2: option_trm] :
% 0.31/0.47 ( ( Theta2 != none_trm )
% 0.31/0.47 = ( ? [T: trm] :
% 0.31/0.47 ( Theta2
% 0.31/0.47 = ( some_trm @ T ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % undeft_equiv
% 0.31/0.47 thf(fact_23_Timeso_Oinduct,axiom,
% 0.31/0.47 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.31/0.47 ( ! [Theta: trm,Eta: trm] : ( P @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.31/0.47 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 0.31/0.47 => ( ! [V: trm] : ( P @ ( some_trm @ V ) @ none_trm )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso.induct
% 0.31/0.47 thf(fact_24_Assigno_Oinduct,axiom,
% 0.31/0.47 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.31/0.47 ( ! [X2: variable,Theta: trm] : ( P @ X2 @ ( some_trm @ Theta ) )
% 0.31/0.47 => ( ! [X2: variable] : ( P @ X2 @ none_trm )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Assigno.induct
% 0.31/0.47 thf(fact_25_Aterm__Some,axiom,
% 0.31/0.47 some_trm = some_trm ).
% 0.31/0.47
% 0.31/0.47 % Aterm_Some
% 0.31/0.47 thf(fact_26_Differentialo_Oinduct,axiom,
% 0.31/0.47 ! [P: option_trm > $o,A0: option_trm] :
% 0.31/0.47 ( ! [Theta: trm] : ( P @ ( some_trm @ Theta ) )
% 0.31/0.47 => ( ( P @ none_trm )
% 0.31/0.47 => ( P @ A0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo.induct
% 0.31/0.47 thf(fact_27_Differentialo_Ocases,axiom,
% 0.31/0.47 ! [X4: option_trm] :
% 0.31/0.47 ( ! [Theta: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( some_trm @ Theta ) )
% 0.31/0.47 => ( X4 = none_trm ) ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo.cases
% 0.31/0.47 thf(fact_28_option_Ocollapse,axiom,
% 0.31/0.47 ! [Option: option_trm] :
% 0.31/0.47 ( ( Option != none_trm )
% 0.31/0.47 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_29_option_Ocollapse,axiom,
% 0.31/0.47 ! [Option: option_fml] :
% 0.31/0.47 ( ( Option != none_fml )
% 0.31/0.47 => ( ( some_fml @ ( the_fml @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_30_option_Ocollapse,axiom,
% 0.31/0.47 ! [Option: option_game] :
% 0.31/0.47 ( ( Option != none_game )
% 0.31/0.47 => ( ( some_game @ ( the_game @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_31_not__Some__eq,axiom,
% 0.31/0.47 ! [X4: option_trm] :
% 0.31/0.47 ( ( ! [Y: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( some_trm @ Y ) ) )
% 0.31/0.47 = ( X4 = none_trm ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_Some_eq
% 0.31/0.47 thf(fact_32_not__Some__eq,axiom,
% 0.31/0.47 ! [X4: option_fml] :
% 0.31/0.47 ( ( ! [Y: fml] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( some_fml @ Y ) ) )
% 0.31/0.47 = ( X4 = none_fml ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_Some_eq
% 0.31/0.47 thf(fact_33_not__Some__eq,axiom,
% 0.31/0.47 ! [X4: option_game] :
% 0.31/0.47 ( ( ! [Y: game] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( some_game @ Y ) ) )
% 0.31/0.47 = ( X4 = none_game ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_Some_eq
% 0.31/0.47 thf(fact_34_not__None__eq,axiom,
% 0.31/0.47 ! [X4: option_trm] :
% 0.31/0.47 ( ( X4 != none_trm )
% 0.31/0.47 = ( ? [Y: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 = ( some_trm @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_None_eq
% 0.31/0.47 thf(fact_35_not__None__eq,axiom,
% 0.31/0.47 ! [X4: option_fml] :
% 0.31/0.47 ( ( X4 != none_fml )
% 0.31/0.47 = ( ? [Y: fml] :
% 0.31/0.47 ( X4
% 0.31/0.47 = ( some_fml @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_None_eq
% 0.31/0.47 thf(fact_36_not__None__eq,axiom,
% 0.31/0.47 ! [X4: option_game] :
% 0.31/0.47 ( ( X4 != none_game )
% 0.31/0.47 = ( ? [Y: game] :
% 0.31/0.47 ( X4
% 0.31/0.47 = ( some_game @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_None_eq
% 0.31/0.47 thf(fact_37_inf__bot__left,axiom,
% 0.31/0.47 ! [X4: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X4 )
% 0.31/0.47 = bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % inf_bot_left
% 0.31/0.47 thf(fact_38_inf__bot__right,axiom,
% 0.31/0.47 ! [X4: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ bot_bot_set_variable )
% 0.31/0.47 = bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % inf_bot_right
% 0.31/0.47 thf(fact_39_usubstappt__func2,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable,Theta2: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R2 ) )
% 0.31/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 0.31/0.47 != bot_bot_set_variable )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.31/0.47 = none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_func2
% 0.31/0.47 thf(fact_40_option_Osplit__sel__asm,axiom,
% 0.31/0.47 ! [P: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.31/0.47 ( ( P @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.31/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.31/0.47 & ~ ( P @ F1 ) )
% 0.31/0.47 | ( ( Option
% 0.31/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.31/0.47 & ~ ( P @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.split_sel_asm
% 0.31/0.47 thf(fact_41_option_Osplit__sel,axiom,
% 0.31/0.47 ! [P: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.31/0.47 ( ( P @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.31/0.47 = ( ( ( Option = none_trm )
% 0.31/0.47 => ( P @ F1 ) )
% 0.31/0.47 & ( ( Option
% 0.31/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.31/0.47 => ( P @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.split_sel
% 0.31/0.47 thf(fact_42_usubstappt__func__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.47 != none_trm )
% 0.31/0.47 & ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 | ? [R3: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R3 ) )
% 0.31/0.47 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_func_conv
% 0.31/0.47 thf(fact_43_option_Ocase__eq__if,axiom,
% 0.31/0.47 ( case_o487727941rm_trm
% 0.31/0.47 = ( ^ [F12: option_trm,F23: trm > option_trm,Option2: option_trm] : ( if_option_trm @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.case_eq_if
% 0.31/0.47 thf(fact_44_inf__right__idem,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Y2 )
% 0.31/0.47 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_right_idem
% 0.31/0.47 thf(fact_45_inf_Oright__idem,axiom,
% 0.31/0.47 ! [A: set_variable,B: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ B )
% 0.31/0.47 = ( inf_inf_set_variable @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf.right_idem
% 0.31/0.47 thf(fact_46_inf__left__idem,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ X4 @ Y2 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_left_idem
% 0.31/0.47 thf(fact_47_inf_Oleft__idem,axiom,
% 0.31/0.47 ! [A: set_variable,B: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B ) )
% 0.31/0.47 = ( inf_inf_set_variable @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf.left_idem
% 0.31/0.47 thf(fact_48_inf__idem,axiom,
% 0.31/0.47 ! [X4: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ X4 )
% 0.31/0.47 = X4 ) ).
% 0.31/0.47
% 0.31/0.47 % inf_idem
% 0.31/0.47 thf(fact_49_inf_Oidem,axiom,
% 0.31/0.47 ! [A: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % inf.idem
% 0.31/0.47 thf(fact_50_option_Oinject,axiom,
% 0.31/0.47 ! [X22: trm,Y22: trm] :
% 0.31/0.47 ( ( ( some_trm @ X22 )
% 0.31/0.47 = ( some_trm @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_51_option_Oinject,axiom,
% 0.31/0.47 ! [X22: fml,Y22: fml] :
% 0.31/0.47 ( ( ( some_fml @ X22 )
% 0.31/0.47 = ( some_fml @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_52_option_Oinject,axiom,
% 0.31/0.47 ! [X22: game,Y22: game] :
% 0.31/0.47 ( ( ( some_game @ X22 )
% 0.31/0.47 = ( some_game @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_53_trm_Oinject_I4_J,axiom,
% 0.31/0.47 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.31/0.47 ( ( ( func @ X41 @ X42 )
% 0.31/0.47 = ( func @ Y41 @ Y42 ) )
% 0.31/0.47 = ( ( X41 = Y41 )
% 0.31/0.47 & ( X42 = Y42 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(4)
% 0.31/0.47 thf(fact_54_option_Odisc__eq__case_I2_J,axiom,
% 0.31/0.47 ! [Option: option_trm] :
% 0.31/0.47 ( ( Option != none_trm )
% 0.31/0.47 = ( case_option_o_trm @ $false
% 0.31/0.47 @ ^ [Uu: trm] : $true
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(2)
% 0.31/0.47 thf(fact_55_option_Odisc__eq__case_I2_J,axiom,
% 0.31/0.47 ! [Option: option_fml] :
% 0.31/0.47 ( ( Option != none_fml )
% 0.31/0.47 = ( case_option_o_fml @ $false
% 0.31/0.47 @ ^ [Uu: fml] : $true
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(2)
% 0.31/0.47 thf(fact_56_option_Odisc__eq__case_I2_J,axiom,
% 0.31/0.47 ! [Option: option_game] :
% 0.31/0.47 ( ( Option != none_game )
% 0.31/0.47 = ( case_option_o_game @ $false
% 0.31/0.47 @ ^ [Uu: game] : $true
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(2)
% 0.31/0.47 thf(fact_57_option_Odisc__eq__case_I1_J,axiom,
% 0.31/0.47 ! [Option: option_trm] :
% 0.31/0.47 ( ( Option = none_trm )
% 0.31/0.47 = ( case_option_o_trm @ $true
% 0.31/0.47 @ ^ [Uu: trm] : $false
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(1)
% 0.31/0.47 thf(fact_58_option_Odisc__eq__case_I1_J,axiom,
% 0.31/0.47 ! [Option: option_fml] :
% 0.31/0.47 ( ( Option = none_fml )
% 0.31/0.47 = ( case_option_o_fml @ $true
% 0.31/0.47 @ ^ [Uu: fml] : $false
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(1)
% 0.31/0.47 thf(fact_59_option_Odisc__eq__case_I1_J,axiom,
% 0.31/0.47 ! [Option: option_game] :
% 0.31/0.47 ( ( Option = none_game )
% 0.31/0.47 = ( case_option_o_game @ $true
% 0.31/0.47 @ ^ [Uu: game] : $false
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.disc_eq_case(1)
% 0.31/0.47 thf(fact_60_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: variable,P: variable > $o] :
% 0.31/0.47 ( ( member_variable @ A @ ( collect_variable @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_61_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: char,P: char > $o] :
% 0.31/0.47 ( ( member_char @ A @ ( collect_char @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_62_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : ( member_variable @ X @ A2 ) )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_63_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A2: set_char] :
% 0.31/0.47 ( ( collect_char
% 0.31/0.47 @ ^ [X: char] : ( member_char @ X @ A2 ) )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_64_Collect__cong,axiom,
% 0.31/0.47 ! [P: variable > $o,Q: variable > $o] :
% 0.31/0.47 ( ! [X2: variable] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 = ( Q @ X2 ) )
% 0.31/0.47 => ( ( collect_variable @ P )
% 0.31/0.47 = ( collect_variable @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_65_Collect__cong,axiom,
% 0.31/0.47 ! [P: char > $o,Q: char > $o] :
% 0.31/0.47 ( ! [X2: char] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 = ( Q @ X2 ) )
% 0.31/0.47 => ( ( collect_char @ P )
% 0.31/0.47 = ( collect_char @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_66_trm_Odistinct_I23_J,axiom,
% 0.31/0.47 ! [X3: char,X41: char,X42: trm] :
% 0.31/0.47 ( ( const @ X3 )
% 0.31/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(23)
% 0.31/0.47 thf(fact_67_case__optionE,axiom,
% 0.31/0.47 ! [P: $o,Q: trm > $o,X4: option_trm] :
% 0.31/0.47 ( ( case_option_o_trm @ P @ Q @ X4 )
% 0.31/0.47 => ( ( ( X4 = none_trm )
% 0.31/0.47 => ~ P )
% 0.31/0.47 => ~ ! [Y4: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ Y4 ) )
% 0.31/0.47 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_optionE
% 0.31/0.47 thf(fact_68_case__optionE,axiom,
% 0.31/0.47 ! [P: $o,Q: fml > $o,X4: option_fml] :
% 0.31/0.47 ( ( case_option_o_fml @ P @ Q @ X4 )
% 0.31/0.47 => ( ( ( X4 = none_fml )
% 0.31/0.47 => ~ P )
% 0.31/0.47 => ~ ! [Y4: fml] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_fml @ Y4 ) )
% 0.31/0.47 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_optionE
% 0.31/0.47 thf(fact_69_case__optionE,axiom,
% 0.31/0.47 ! [P: $o,Q: game > $o,X4: option_game] :
% 0.31/0.47 ( ( case_option_o_game @ P @ Q @ X4 )
% 0.31/0.47 => ( ( ( X4 = none_game )
% 0.31/0.47 => ~ P )
% 0.31/0.47 => ~ ! [Y4: game] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_game @ Y4 ) )
% 0.31/0.47 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_optionE
% 0.31/0.47 thf(fact_70_inf__left__commute,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X4 @ Z2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_left_commute
% 0.31/0.47 thf(fact_71_inf_Oleft__commute,axiom,
% 0.31/0.47 ! [B: set_variable,A: set_variable,C: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ B @ ( inf_inf_set_variable @ A @ C ) )
% 0.31/0.47 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf.left_commute
% 0.31/0.47 thf(fact_72_inf__commute,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_commute
% 0.31/0.47 thf(fact_73_inf_Ocommute,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [A3: set_variable,B2: set_variable] : ( inf_inf_set_variable @ B2 @ A3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf.commute
% 0.31/0.47 thf(fact_74_inf__assoc,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Z2 )
% 0.31/0.47 = ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_assoc
% 0.31/0.47 thf(fact_75_inf_Oassoc,axiom,
% 0.31/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ C )
% 0.31/0.47 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf.assoc
% 0.31/0.47 thf(fact_76_boolean__algebra__cancel_Oinf2,axiom,
% 0.31/0.47 ! [B3: set_variable,K: set_variable,B: set_variable,A: set_variable] :
% 0.31/0.47 ( ( B3
% 0.31/0.47 = ( inf_inf_set_variable @ K @ B ) )
% 0.31/0.47 => ( ( inf_inf_set_variable @ A @ B3 )
% 0.31/0.47 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % boolean_algebra_cancel.inf2
% 0.31/0.47 thf(fact_77_boolean__algebra__cancel_Oinf1,axiom,
% 0.31/0.47 ! [A2: set_variable,K: set_variable,A: set_variable,B: set_variable] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( inf_inf_set_variable @ K @ A ) )
% 0.31/0.47 => ( ( inf_inf_set_variable @ A2 @ B )
% 0.31/0.47 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % boolean_algebra_cancel.inf1
% 0.31/0.47 thf(fact_78_inf__sup__aci_I1_J,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_sup_aci(1)
% 0.31/0.47 thf(fact_79_inf__sup__aci_I2_J,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Z2 )
% 0.31/0.47 = ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_sup_aci(2)
% 0.31/0.47 thf(fact_80_inf__sup__aci_I3_J,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X4 @ Z2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_sup_aci(3)
% 0.31/0.47 thf(fact_81_inf__sup__aci_I4_J,axiom,
% 0.31/0.47 ! [X4: set_variable,Y2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ X4 @ Y2 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_sup_aci(4)
% 0.31/0.47 thf(fact_82_option_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.31/0.47 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.31/0.47 = ( case_o487727941rm_trm @ ( H @ F1 )
% 0.31/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.31/0.47 @ Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.case_distrib
% 0.31/0.47 thf(fact_83_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X22: trm] :
% 0.31/0.47 ( none_trm
% 0.31/0.47 != ( some_trm @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_84_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X22: fml] :
% 0.31/0.47 ( none_fml
% 0.31/0.47 != ( some_fml @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_85_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X22: game] :
% 0.31/0.47 ( none_game
% 0.31/0.47 != ( some_game @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_86_option_OdiscI,axiom,
% 0.31/0.47 ! [Option: option_trm,X22: trm] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some_trm @ X22 ) )
% 0.31/0.47 => ( Option != none_trm ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_87_option_OdiscI,axiom,
% 0.31/0.47 ! [Option: option_fml,X22: fml] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some_fml @ X22 ) )
% 0.31/0.47 => ( Option != none_fml ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_88_option_OdiscI,axiom,
% 0.31/0.47 ! [Option: option_game,X22: game] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some_game @ X22 ) )
% 0.31/0.47 => ( Option != none_game ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_89_option_Oexhaust,axiom,
% 0.31/0.47 ! [Y2: option_trm] :
% 0.31/0.47 ( ( Y2 != none_trm )
% 0.31/0.47 => ~ ! [X23: trm] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( some_trm @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_90_option_Oexhaust,axiom,
% 0.31/0.47 ! [Y2: option_fml] :
% 0.31/0.47 ( ( Y2 != none_fml )
% 0.31/0.47 => ~ ! [X23: fml] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( some_fml @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_91_option_Oexhaust,axiom,
% 0.31/0.47 ! [Y2: option_game] :
% 0.31/0.47 ( ( Y2 != none_game )
% 0.31/0.47 => ~ ! [X23: game] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( some_game @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_92_option_Oinducts,axiom,
% 0.31/0.47 ! [P: option_trm > $o,Option: option_trm] :
% 0.31/0.47 ( ( P @ none_trm )
% 0.31/0.47 => ( ! [X2: trm] : ( P @ ( some_trm @ X2 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_93_option_Oinducts,axiom,
% 0.31/0.47 ! [P: option_fml > $o,Option: option_fml] :
% 0.31/0.47 ( ( P @ none_fml )
% 0.31/0.47 => ( ! [X2: fml] : ( P @ ( some_fml @ X2 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_94_option_Oinducts,axiom,
% 0.31/0.47 ! [P: option_game > $o,Option: option_game] :
% 0.31/0.47 ( ( P @ none_game )
% 0.31/0.47 => ( ! [X2: game] : ( P @ ( some_game @ X2 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_95_split__option__ex,axiom,
% 0.31/0.47 ( ( ^ [P2: option_trm > $o] :
% 0.31/0.47 ? [X5: option_trm] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_trm > $o] :
% 0.31/0.47 ( ( P3 @ none_trm )
% 0.31/0.47 | ? [X: trm] : ( P3 @ ( some_trm @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_96_split__option__ex,axiom,
% 0.31/0.47 ( ( ^ [P2: option_fml > $o] :
% 0.31/0.47 ? [X5: option_fml] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_fml > $o] :
% 0.31/0.47 ( ( P3 @ none_fml )
% 0.31/0.47 | ? [X: fml] : ( P3 @ ( some_fml @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_97_split__option__ex,axiom,
% 0.31/0.47 ( ( ^ [P2: option_game > $o] :
% 0.31/0.47 ? [X5: option_game] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_game > $o] :
% 0.31/0.47 ( ( P3 @ none_game )
% 0.31/0.47 | ? [X: game] : ( P3 @ ( some_game @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_98_split__option__all,axiom,
% 0.31/0.47 ( ( ^ [P2: option_trm > $o] :
% 0.31/0.47 ! [X5: option_trm] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_trm > $o] :
% 0.31/0.47 ( ( P3 @ none_trm )
% 0.31/0.47 & ! [X: trm] : ( P3 @ ( some_trm @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_99_split__option__all,axiom,
% 0.31/0.47 ( ( ^ [P2: option_fml > $o] :
% 0.31/0.47 ! [X5: option_fml] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_fml > $o] :
% 0.31/0.47 ( ( P3 @ none_fml )
% 0.31/0.47 & ! [X: fml] : ( P3 @ ( some_fml @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_100_split__option__all,axiom,
% 0.31/0.47 ( ( ^ [P2: option_game > $o] :
% 0.31/0.47 ! [X5: option_game] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_game > $o] :
% 0.31/0.47 ( ( P3 @ none_game )
% 0.31/0.47 & ! [X: game] : ( P3 @ ( some_game @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_101_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_trm,P: option_trm > option_trm > $o,Y2: option_trm] :
% 0.31/0.47 ( ( ( X4 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: trm,B4: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_trm @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_102_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_trm,P: option_trm > option_fml > $o,Y2: option_fml] :
% 0.31/0.47 ( ( ( X4 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: trm,B4: fml] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_fml @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_103_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_trm,P: option_trm > option_game > $o,Y2: option_game] :
% 0.31/0.47 ( ( ( X4 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: trm,B4: game] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_game @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_104_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_fml,P: option_fml > option_trm > $o,Y2: option_trm] :
% 0.31/0.47 ( ( ( X4 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: fml,B4: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_fml @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_trm @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_105_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_fml,P: option_fml > option_fml > $o,Y2: option_fml] :
% 0.31/0.47 ( ( ( X4 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: fml,B4: fml] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_fml @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_fml @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_106_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_fml,P: option_fml > option_game > $o,Y2: option_game] :
% 0.31/0.47 ( ( ( X4 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: fml,B4: game] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_fml @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_game @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_107_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_game,P: option_game > option_trm > $o,Y2: option_trm] :
% 0.31/0.47 ( ( ( X4 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_trm )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: game,B4: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_game @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_trm @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_108_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_game,P: option_game > option_fml > $o,Y2: option_fml] :
% 0.31/0.47 ( ( ( X4 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_fml )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: game,B4: fml] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_game @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_fml @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_109_combine__options__cases,axiom,
% 0.31/0.47 ! [X4: option_game,P: option_game > option_game > $o,Y2: option_game] :
% 0.31/0.47 ( ( ( X4 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ( ( Y2 = none_game )
% 0.31/0.47 => ( P @ X4 @ Y2 ) )
% 0.31/0.47 => ( ! [A4: game,B4: game] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_game @ A4 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_game @ B4 ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) )
% 0.31/0.47 => ( P @ X4 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_110_option_Osimps_I4_J,axiom,
% 0.31/0.47 ! [F1: option_trm,F22: trm > option_trm] :
% 0.31/0.47 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 0.31/0.47 = F1 ) ).
% 0.31/0.47
% 0.31/0.47 % option.simps(4)
% 0.31/0.47 thf(fact_111_option_Osimps_I5_J,axiom,
% 0.31/0.47 ! [F1: option_trm,F22: trm > option_trm,X22: trm] :
% 0.31/0.47 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 0.31/0.47 = ( F22 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.simps(5)
% 0.31/0.47 thf(fact_112_option_Oexpand,axiom,
% 0.31/0.47 ! [Option: option_trm,Option3: option_trm] :
% 0.31/0.47 ( ( ( Option = none_trm )
% 0.31/0.47 = ( Option3 = none_trm ) )
% 0.31/0.47 => ( ( ( Option != none_trm )
% 0.31/0.47 => ( ( Option3 != none_trm )
% 0.31/0.47 => ( ( the_trm @ Option )
% 0.31/0.47 = ( the_trm @ Option3 ) ) ) )
% 0.31/0.47 => ( Option = Option3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_113_option_Oexpand,axiom,
% 0.31/0.47 ! [Option: option_fml,Option3: option_fml] :
% 0.31/0.47 ( ( ( Option = none_fml )
% 0.31/0.47 = ( Option3 = none_fml ) )
% 0.31/0.47 => ( ( ( Option != none_fml )
% 0.31/0.47 => ( ( Option3 != none_fml )
% 0.31/0.47 => ( ( the_fml @ Option )
% 0.31/0.47 = ( the_fml @ Option3 ) ) ) )
% 0.31/0.47 => ( Option = Option3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_114_option_Oexpand,axiom,
% 0.31/0.47 ! [Option: option_game,Option3: option_game] :
% 0.31/0.47 ( ( ( Option = none_game )
% 0.31/0.47 = ( Option3 = none_game ) )
% 0.31/0.47 => ( ( ( Option != none_game )
% 0.31/0.47 => ( ( Option3 != none_game )
% 0.31/0.47 => ( ( the_game @ Option )
% 0.31/0.47 = ( the_game @ Option3 ) ) ) )
% 0.31/0.47 => ( Option = Option3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_115_option_Osel,axiom,
% 0.31/0.47 ! [X22: trm] :
% 0.31/0.47 ( ( the_trm @ ( some_trm @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_116_option_Osel,axiom,
% 0.31/0.47 ! [X22: fml] :
% 0.31/0.47 ( ( the_fml @ ( some_fml @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_117_option_Osel,axiom,
% 0.31/0.47 ! [X22: game] :
% 0.31/0.47 ( ( the_game @ ( some_game @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_118_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Option: option_trm] :
% 0.31/0.47 ( ( Option != none_trm )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_119_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Option: option_fml] :
% 0.31/0.47 ( ( Option != none_fml )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_120_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Option: option_game] :
% 0.31/0.47 ( ( Option != none_game )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_121_usubstappt__func,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable,Theta2: trm,Sigma_theta: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 )
% 0.31/0.47 = ( some_trm @ R2 ) )
% 0.31/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.47 = ( some_trm @ Sigma_theta ) )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.31/0.47 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_func
% 0.31/0.47 thf(fact_122_usubstappt_Osimps_I4_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.31/0.47 = ( case_o487727941rm_trm @ none_trm
% 0.31/0.47 @ ^ [Sigma_theta2: trm] :
% 0.31/0.47 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta2 ) )
% 0.31/0.47 @ ^ [R: trm] :
% 0.31/0.47 ( if_option_trm
% 0.31/0.47 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 0.31/0.47 @ none_trm )
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma2
% 0.31/0.47 @ F3 ) )
% 0.31/0.47 @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(4)
% 0.31/0.47 thf(fact_123_Int__iff,axiom,
% 0.31/0.47 ! [C: char,A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 0.31/0.47 = ( ( member_char @ C @ A2 )
% 0.31/0.47 & ( member_char @ C @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_iff
% 0.31/0.47 thf(fact_124_Int__iff,axiom,
% 0.31/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.31/0.47 = ( ( member_variable @ C @ A2 )
% 0.31/0.47 & ( member_variable @ C @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_iff
% 0.31/0.47 thf(fact_125_IntI,axiom,
% 0.31/0.47 ! [C: char,A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( member_char @ C @ A2 )
% 0.31/0.47 => ( ( member_char @ C @ B3 )
% 0.31/0.47 => ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntI
% 0.31/0.47 thf(fact_126_IntI,axiom,
% 0.31/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( member_variable @ C @ A2 )
% 0.31/0.47 => ( ( member_variable @ C @ B3 )
% 0.31/0.47 => ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntI
% 0.31/0.47 thf(fact_127_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: char > $o] :
% 0.31/0.47 ( ( bot_bot_set_char
% 0.31/0.47 = ( collect_char @ P ) )
% 0.31/0.47 = ( ! [X: char] :
% 0.31/0.47 ~ ( P @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_128_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: variable > $o] :
% 0.31/0.47 ( ( bot_bot_set_variable
% 0.31/0.47 = ( collect_variable @ P ) )
% 0.31/0.47 = ( ! [X: variable] :
% 0.31/0.47 ~ ( P @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_129_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: char > $o] :
% 0.31/0.47 ( ( ( collect_char @ P )
% 0.31/0.47 = bot_bot_set_char )
% 0.31/0.47 = ( ! [X: char] :
% 0.31/0.47 ~ ( P @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_130_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: variable > $o] :
% 0.31/0.47 ( ( ( collect_variable @ P )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 = ( ! [X: variable] :
% 0.31/0.47 ~ ( P @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_131_all__not__in__conv,axiom,
% 0.31/0.47 ! [A2: set_char] :
% 0.31/0.47 ( ( ! [X: char] :
% 0.31/0.47 ~ ( member_char @ X @ A2 ) )
% 0.31/0.47 = ( A2 = bot_bot_set_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_132_all__not__in__conv,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ( ! [X: variable] :
% 0.31/0.47 ~ ( member_variable @ X @ A2 ) )
% 0.31/0.47 = ( A2 = bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_133_empty__iff,axiom,
% 0.31/0.47 ! [C: char] :
% 0.31/0.47 ~ ( member_char @ C @ bot_bot_set_char ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_134_empty__iff,axiom,
% 0.31/0.47 ! [C: variable] :
% 0.31/0.47 ~ ( member_variable @ C @ bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_135_emptyE,axiom,
% 0.31/0.47 ! [A: char] :
% 0.31/0.47 ~ ( member_char @ A @ bot_bot_set_char ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_136_emptyE,axiom,
% 0.31/0.47 ! [A: variable] :
% 0.31/0.47 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_137_equals0D,axiom,
% 0.31/0.47 ! [A2: set_char,A: char] :
% 0.31/0.47 ( ( A2 = bot_bot_set_char )
% 0.31/0.47 => ~ ( member_char @ A @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_138_equals0D,axiom,
% 0.31/0.47 ! [A2: set_variable,A: variable] :
% 0.31/0.47 ( ( A2 = bot_bot_set_variable )
% 0.31/0.47 => ~ ( member_variable @ A @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_139_equals0I,axiom,
% 0.31/0.47 ! [A2: set_char] :
% 0.31/0.47 ( ! [Y4: char] :
% 0.31/0.47 ~ ( member_char @ Y4 @ A2 )
% 0.31/0.47 => ( A2 = bot_bot_set_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_140_equals0I,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ! [Y4: variable] :
% 0.31/0.47 ~ ( member_variable @ Y4 @ A2 )
% 0.31/0.47 => ( A2 = bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_141_ex__in__conv,axiom,
% 0.31/0.47 ! [A2: set_char] :
% 0.31/0.47 ( ( ? [X: char] : ( member_char @ X @ A2 ) )
% 0.31/0.47 = ( A2 != bot_bot_set_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_142_ex__in__conv,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ( ? [X: variable] : ( member_variable @ X @ A2 ) )
% 0.31/0.47 = ( A2 != bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_143_bot__set__def,axiom,
% 0.31/0.47 ( bot_bot_set_char
% 0.31/0.47 = ( collect_char @ bot_bot_char_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_144_bot__set__def,axiom,
% 0.31/0.47 ( bot_bot_set_variable
% 0.31/0.47 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_145_IntE,axiom,
% 0.31/0.47 ! [C: char,A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 0.31/0.47 => ~ ( ( member_char @ C @ A2 )
% 0.31/0.47 => ~ ( member_char @ C @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntE
% 0.31/0.47 thf(fact_146_IntE,axiom,
% 0.31/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.31/0.47 => ~ ( ( member_variable @ C @ A2 )
% 0.31/0.47 => ~ ( member_variable @ C @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntE
% 0.31/0.47 thf(fact_147_IntD1,axiom,
% 0.31/0.47 ! [C: char,A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 0.31/0.47 => ( member_char @ C @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntD1
% 0.31/0.47 thf(fact_148_IntD1,axiom,
% 0.31/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.31/0.47 => ( member_variable @ C @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntD1
% 0.31/0.47 thf(fact_149_IntD2,axiom,
% 0.31/0.47 ! [C: char,A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 0.31/0.47 => ( member_char @ C @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntD2
% 0.31/0.47 thf(fact_150_IntD2,axiom,
% 0.31/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.31/0.47 => ( member_variable @ C @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % IntD2
% 0.31/0.47 thf(fact_151_Int__assoc,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 0.31/0.47 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_assoc
% 0.31/0.47 thf(fact_152_Int__absorb,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A2 @ A2 )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % Int_absorb
% 0.31/0.47 thf(fact_153_Int__commute,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_commute
% 0.31/0.47 thf(fact_154_Int__left__absorb,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_left_absorb
% 0.31/0.47 thf(fact_155_Int__left__commute,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 0.31/0.47 = ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_left_commute
% 0.31/0.47 thf(fact_156_empty__def,axiom,
% 0.31/0.47 ( bot_bot_set_char
% 0.31/0.47 = ( collect_char
% 0.31/0.47 @ ^ [X: char] : $false ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_def
% 0.31/0.47 thf(fact_157_empty__def,axiom,
% 0.31/0.47 ( bot_bot_set_variable
% 0.31/0.47 = ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $false ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_def
% 0.31/0.47 thf(fact_158_Collect__conj__eq,axiom,
% 0.31/0.47 ! [P: char > $o,Q: char > $o] :
% 0.31/0.47 ( ( collect_char
% 0.31/0.47 @ ^ [X: char] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) )
% 0.31/0.47 = ( inf_inf_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_conj_eq
% 0.31/0.47 thf(fact_159_Collect__conj__eq,axiom,
% 0.31/0.47 ! [P: variable > $o,Q: variable > $o] :
% 0.31/0.47 ( ( collect_variable
% 0.31/0.47 @ ^ [X: variable] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) )
% 0.31/0.47 = ( inf_inf_set_variable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_conj_eq
% 0.31/0.47 thf(fact_160_Int__Collect,axiom,
% 0.31/0.47 ! [X4: char,A2: set_char,P: char > $o] :
% 0.31/0.47 ( ( member_char @ X4 @ ( inf_inf_set_char @ A2 @ ( collect_char @ P ) ) )
% 0.31/0.47 = ( ( member_char @ X4 @ A2 )
% 0.31/0.47 & ( P @ X4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_Collect
% 0.31/0.47 thf(fact_161_Int__Collect,axiom,
% 0.31/0.47 ! [X4: variable,A2: set_variable,P: variable > $o] :
% 0.31/0.47 ( ( member_variable @ X4 @ ( inf_inf_set_variable @ A2 @ ( collect_variable @ P ) ) )
% 0.31/0.47 = ( ( member_variable @ X4 @ A2 )
% 0.31/0.47 & ( P @ X4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_Collect
% 0.31/0.47 thf(fact_162_Int__def,axiom,
% 0.31/0.47 ( inf_inf_set_char
% 0.31/0.47 = ( ^ [A5: set_char,B5: set_char] :
% 0.31/0.47 ( collect_char
% 0.31/0.47 @ ^ [X: char] :
% 0.31/0.47 ( ( member_char @ X @ A5 )
% 0.31/0.47 & ( member_char @ X @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_def
% 0.31/0.47 thf(fact_163_Int__def,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.31/0.47 ( collect_variable
% 0.31/0.47 @ ^ [X: variable] :
% 0.31/0.47 ( ( member_variable @ X @ A5 )
% 0.31/0.47 & ( member_variable @ X @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_def
% 0.31/0.47 thf(fact_164_inf__set__def,axiom,
% 0.31/0.47 ( inf_inf_set_char
% 0.31/0.47 = ( ^ [A5: set_char,B5: set_char] :
% 0.31/0.47 ( collect_char
% 0.31/0.47 @ ( inf_inf_char_o
% 0.31/0.47 @ ^ [X: char] : ( member_char @ X @ A5 )
% 0.31/0.47 @ ^ [X: char] : ( member_char @ X @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_set_def
% 0.31/0.47 thf(fact_165_inf__set__def,axiom,
% 0.31/0.47 ( inf_inf_set_variable
% 0.31/0.47 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.31/0.47 ( collect_variable
% 0.31/0.47 @ ( inf_inf_variable_o
% 0.31/0.47 @ ^ [X: variable] : ( member_variable @ X @ A5 )
% 0.31/0.47 @ ^ [X: variable] : ( member_variable @ X @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_set_def
% 0.31/0.47 thf(fact_166_Int__emptyI,axiom,
% 0.31/0.47 ! [A2: set_char,B3: set_char] :
% 0.31/0.47 ( ! [X2: char] :
% 0.31/0.47 ( ( member_char @ X2 @ A2 )
% 0.31/0.47 => ~ ( member_char @ X2 @ B3 ) )
% 0.31/0.47 => ( ( inf_inf_set_char @ A2 @ B3 )
% 0.31/0.47 = bot_bot_set_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_emptyI
% 0.31/0.47 thf(fact_167_Int__emptyI,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ! [X2: variable] :
% 0.31/0.47 ( ( member_variable @ X2 @ A2 )
% 0.31/0.47 => ~ ( member_variable @ X2 @ B3 ) )
% 0.31/0.47 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.31/0.47 = bot_bot_set_variable ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_emptyI
% 0.31/0.47 thf(fact_168_disjoint__iff,axiom,
% 0.31/0.47 ! [A2: set_char,B3: set_char] :
% 0.31/0.47 ( ( ( inf_inf_set_char @ A2 @ B3 )
% 0.31/0.47 = bot_bot_set_char )
% 0.31/0.47 = ( ! [X: char] :
% 0.31/0.47 ( ( member_char @ X @ A2 )
% 0.31/0.47 => ~ ( member_char @ X @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % disjoint_iff
% 0.31/0.47 thf(fact_169_disjoint__iff,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 = ( ! [X: variable] :
% 0.31/0.47 ( ( member_variable @ X @ A2 )
% 0.31/0.47 => ~ ( member_variable @ X @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % disjoint_iff
% 0.31/0.47 thf(fact_170_Int__empty__left,axiom,
% 0.31/0.47 ! [B3: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B3 )
% 0.31/0.47 = bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % Int_empty_left
% 0.31/0.47 thf(fact_171_Int__empty__right,axiom,
% 0.31/0.47 ! [A2: set_variable] :
% 0.31/0.47 ( ( inf_inf_set_variable @ A2 @ bot_bot_set_variable )
% 0.31/0.47 = bot_bot_set_variable ) ).
% 0.31/0.47
% 0.31/0.47 % Int_empty_right
% 0.31/0.47 thf(fact_172_disjoint__iff__not__equal,axiom,
% 0.31/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.31/0.47 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 = ( ! [X: variable] :
% 0.31/0.47 ( ( member_variable @ X @ A2 )
% 0.31/0.47 => ! [Y: variable] :
% 0.31/0.47 ( ( member_variable @ Y @ B3 )
% 0.31/0.47 => ( X != Y ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % disjoint_iff_not_equal
% 0.31/0.47 thf(fact_173_disjE__realizer2,axiom,
% 0.31/0.47 ! [P: $o,Q: trm > $o,X4: option_trm,R4: option_trm > $o,F3: option_trm,G: trm > option_trm] :
% 0.31/0.47 ( ( case_option_o_trm @ P @ Q @ X4 )
% 0.31/0.47 => ( ( P
% 0.31/0.47 => ( R4 @ F3 ) )
% 0.31/0.47 => ( ! [Q2: trm] :
% 0.31/0.47 ( ( Q @ Q2 )
% 0.31/0.47 => ( R4 @ ( G @ Q2 ) ) )
% 0.31/0.47 => ( R4 @ ( case_o487727941rm_trm @ F3 @ G @ X4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % disjE_realizer2
% 0.31/0.47 thf(fact_174_Set_Ois__empty__def,axiom,
% 0.31/0.47 ( is_empty_variable
% 0.31/0.47 = ( ^ [A5: set_variable] : ( A5 = bot_bot_set_variable ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.is_empty_def
% 0.31/0.47 thf(fact_175_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,Prod: produc1418842292n_game] :
% 0.31/0.47 ( ( H @ ( produc1250175341on_fml @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1250175341on_fml
% 0.31/0.47 @ ^ [X1: char > option_trm,X24: produc62062515n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_176_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_trm ) > char > option_trm,F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,Prod: produc62062515n_game] :
% 0.31/0.47 ( ( H @ ( produc1231571704on_trm @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1231571704on_trm
% 0.31/0.47 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_177_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_trm ) > char > option_fml,F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,Prod: produc62062515n_game] :
% 0.31/0.47 ( ( H @ ( produc1231571704on_trm @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1615133358on_fml
% 0.31/0.47 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_178_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_fml ) > char > option_trm,F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,Prod: produc62062515n_game] :
% 0.31/0.47 ( ( H @ ( produc1615133358on_fml @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1231571704on_trm
% 0.31/0.47 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_179_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,Prod: produc62062515n_game] :
% 0.31/0.47 ( ( H @ ( produc1615133358on_fml @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1615133358on_fml
% 0.31/0.47 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_180_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_trm ) > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.31/0.47 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1036610745on_trm
% 0.31/0.47 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_181_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_trm ) > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.31/0.47 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1420172399on_fml
% 0.31/0.47 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_182_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_fml ) > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.31/0.47 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1036610745on_trm
% 0.31/0.47 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_183_prod_Ocase__distrib,axiom,
% 0.31/0.47 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.31/0.47 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 0.31/0.47 = ( produc1420172399on_fml
% 0.31/0.47 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 0.31/0.47 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.case_distrib
% 0.31/0.47 thf(fact_184_inf__Int__eq,axiom,
% 0.31/0.47 ! [R4: set_char,S: set_char] :
% 0.31/0.47 ( ( inf_inf_char_o
% 0.31/0.47 @ ^ [X: char] : ( member_char @ X @ R4 )
% 0.31/0.47 @ ^ [X: char] : ( member_char @ X @ S ) )
% 0.31/0.47 = ( ^ [X: char] : ( member_char @ X @ ( inf_inf_set_char @ R4 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_Int_eq
% 0.31/0.47 thf(fact_185_inf__Int__eq,axiom,
% 0.31/0.47 ! [R4: set_variable,S: set_variable] :
% 0.31/0.47 ( ( inf_inf_variable_o
% 0.31/0.47 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 0.31/0.47 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 0.31/0.47 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_Int_eq
% 0.31/0.47 thf(fact_186_Timeso_Osimps_I3_J,axiom,
% 0.31/0.47 ! [V2: trm] :
% 0.31/0.47 ( ( uSubst918876924Timeso @ ( some_trm @ V2 ) @ none_trm )
% 0.31/0.47 = none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso.simps(3)
% 0.31/0.47 thf(fact_187_Pluso_Osimps_I3_J,axiom,
% 0.31/0.47 ! [V2: trm] :
% 0.31/0.47 ( ( uSubst141955042_Pluso @ ( some_trm @ V2 ) @ none_trm )
% 0.31/0.47 = none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Pluso.simps(3)
% 0.31/0.47 thf(fact_188_Pluso_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Eta2: option_trm] :
% 0.31/0.47 ( ( uSubst141955042_Pluso @ none_trm @ Eta2 )
% 0.31/0.47 = none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Pluso.simps(2)
% 0.31/0.47 thf(fact_189_Timeso_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Eta2: option_trm] :
% 0.31/0.47 ( ( uSubst918876924Timeso @ none_trm @ Eta2 )
% 0.31/0.47 = none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso.simps(2)
% 0.31/0.47 thf(fact_190_Pluso__undef,axiom,
% 0.31/0.47 ! [Theta2: option_trm,Eta2: option_trm] :
% 0.31/0.47 ( ( ( uSubst141955042_Pluso @ Theta2 @ Eta2 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 = ( ( Theta2 = none_trm )
% 0.31/0.47 | ( Eta2 = none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pluso_undef
% 0.31/0.47 thf(fact_191_Timeso__undef,axiom,
% 0.31/0.47 ! [Theta2: option_trm,Eta2: option_trm] :
% 0.31/0.47 ( ( ( uSubst918876924Timeso @ Theta2 @ Eta2 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 = ( ( Theta2 = none_trm )
% 0.31/0.47 | ( Eta2 = none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso_undef
% 0.31/0.47 thf(fact_192_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bot_char_o
% 0.31/0.47 = ( ^ [X: char] : ( member_char @ X @ bot_bot_set_char ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_193_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bot_variable_o
% 0.31/0.47 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_194_Collect__empty__eq__bot,axiom,
% 0.31/0.47 ! [P: char > $o] :
% 0.31/0.47 ( ( ( collect_char @ P )
% 0.31/0.47 = bot_bot_set_char )
% 0.31/0.47 = ( P = bot_bot_char_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq_bot
% 0.31/0.47 thf(fact_195_Collect__empty__eq__bot,axiom,
% 0.31/0.47 ! [P: variable > $o] :
% 0.31/0.47 ( ( ( collect_variable @ P )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 = ( P = bot_bot_variable_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq_bot
% 0.31/0.47 thf(fact_196_internal__case__prod__def,axiom,
% 0.31/0.47 produc1278328899on_fml = produc1250175341on_fml ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_def
% 0.31/0.47 thf(fact_197_internal__case__prod__def,axiom,
% 0.31/0.47 produc2141841102on_trm = produc1231571704on_trm ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_def
% 0.31/0.47 thf(fact_198_internal__case__prod__def,axiom,
% 0.31/0.47 produc377919108on_fml = produc1615133358on_fml ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_def
% 0.31/0.47 thf(fact_199_internal__case__prod__def,axiom,
% 0.31/0.47 produc1214549391on_trm = produc1036610745on_trm ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_def
% 0.31/0.47 thf(fact_200_internal__case__prod__def,axiom,
% 0.31/0.47 produc1598111045on_fml = produc1420172399on_fml ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_def
% 0.31/0.47 thf(fact_201_Pluso_Oelims,axiom,
% 0.31/0.47 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.31/0.47 ( ( ( uSubst141955042_Pluso @ X4 @ Xa )
% 0.31/0.47 = Y2 )
% 0.31/0.47 => ( ! [Theta: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ Theta ) )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( some_trm @ Eta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( some_trm @ ( plus @ Theta @ Eta ) ) ) ) )
% 0.31/0.47 => ( ( ( X4 = none_trm )
% 0.31/0.47 => ( Y2 != none_trm ) )
% 0.31/0.47 => ~ ( ? [V: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 = ( some_trm @ V ) )
% 0.31/0.47 => ( ( Xa = none_trm )
% 0.31/0.47 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pluso.elims
% 0.31/0.47 thf(fact_202_Timeso_Oelims,axiom,
% 0.31/0.47 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.31/0.47 ( ( ( uSubst918876924Timeso @ X4 @ Xa )
% 0.31/0.47 = Y2 )
% 0.31/0.47 => ( ! [Theta: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ Theta ) )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( some_trm @ Eta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( some_trm @ ( times @ Theta @ Eta ) ) ) ) )
% 0.31/0.47 => ( ( ( X4 = none_trm )
% 0.31/0.47 => ( Y2 != none_trm ) )
% 0.31/0.47 => ~ ( ? [V: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 = ( some_trm @ V ) )
% 0.31/0.47 => ( ( Xa = none_trm )
% 0.31/0.47 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso.elims
% 0.31/0.47 thf(fact_203_trm_Oinject_I5_J,axiom,
% 0.31/0.47 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.31/0.47 ( ( ( plus @ X51 @ X52 )
% 0.31/0.47 = ( plus @ Y51 @ Y52 ) )
% 0.31/0.47 = ( ( X51 = Y51 )
% 0.31/0.47 & ( X52 = Y52 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(5)
% 0.31/0.47 thf(fact_204_trm_Oinject_I6_J,axiom,
% 0.31/0.47 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.31/0.47 ( ( ( times @ X61 @ X62 )
% 0.31/0.47 = ( times @ Y61 @ Y62 ) )
% 0.31/0.47 = ( ( X61 = Y61 )
% 0.31/0.47 & ( X62 = Y62 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(6)
% 0.31/0.47 thf(fact_205_trm_Odistinct_I37_J,axiom,
% 0.31/0.47 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.31/0.47 ( ( plus @ X51 @ X52 )
% 0.31/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(37)
% 0.31/0.47 thf(fact_206_trm_Odistinct_I25_J,axiom,
% 0.31/0.47 ! [X3: char,X51: trm,X52: trm] :
% 0.31/0.47 ( ( const @ X3 )
% 0.31/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(25)
% 0.31/0.47 thf(fact_207_trm_Odistinct_I27_J,axiom,
% 0.31/0.47 ! [X3: char,X61: trm,X62: trm] :
% 0.31/0.47 ( ( const @ X3 )
% 0.31/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(27)
% 0.31/0.47 thf(fact_208_trm_Odistinct_I31_J,axiom,
% 0.31/0.47 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.31/0.47 ( ( func @ X41 @ X42 )
% 0.31/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(31)
% 0.31/0.47 thf(fact_209_trm_Odistinct_I33_J,axiom,
% 0.31/0.47 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.31/0.47 ( ( func @ X41 @ X42 )
% 0.31/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(33)
% 0.31/0.47 thf(fact_210_usubstappt__times__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.47 != none_trm )
% 0.31/0.47 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 0.31/0.47 != none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_times_conv
% 0.31/0.47 thf(fact_211_usubstappt__plus__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.47 != none_trm )
% 0.31/0.47 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 0.31/0.47 != none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_plus_conv
% 0.31/0.47 thf(fact_212_Timeso_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( uSubst918876924Timeso @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.31/0.47 = ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Timeso.simps(1)
% 0.31/0.47 thf(fact_213_Pluso_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( uSubst141955042_Pluso @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.31/0.47 = ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pluso.simps(1)
% 0.31/0.47 thf(fact_214_usubstappt_Osimps_I6_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.31/0.47 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(6)
% 0.31/0.47 thf(fact_215_usubstappt_Osimps_I5_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.31/0.47 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(5)
% 0.31/0.47 thf(fact_216_usubstappt_Oelims,axiom,
% 0.31/0.47 ! [X4: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ X4 @ Xa @ Xb )
% 0.31/0.47 = Y2 )
% 0.31/0.47 => ( ! [X2: variable] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( var @ X2 ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( some_trm @ ( var @ X2 ) ) ) )
% 0.31/0.47 => ( ! [R3: real] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( number @ R3 ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( some_trm @ ( number @ R3 ) ) ) )
% 0.31/0.47 => ( ! [F5: char] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( const @ F5 ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( uSubst1559070963pconst @ X4 @ Xa @ F5 ) ) )
% 0.31/0.47 => ( ! [F5: char,Theta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( func @ F5 @ Theta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( case_o487727941rm_trm @ none_trm
% 0.31/0.47 @ ^ [Sigma_theta2: trm] :
% 0.31/0.47 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta2 ) )
% 0.31/0.47 @ ^ [R: trm] :
% 0.31/0.47 ( if_option_trm
% 0.31/0.47 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 0.31/0.47 @ none_trm )
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ X4
% 0.31/0.47 @ F5 ) )
% 0.31/0.47 @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) ) ) )
% 0.31/0.47 => ( ! [Theta: trm,Eta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( plus @ Theta @ Eta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) ) )
% 0.31/0.47 => ( ! [Theta: trm,Eta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( times @ Theta @ Eta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) ) )
% 0.31/0.47 => ~ ! [Theta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( differential @ Theta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( uSubst716837505ntialo
% 0.31/0.47 @ ( uSubst516392818stappt @ X4
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.elims
% 0.31/0.47 thf(fact_217_usubstappt__induct,axiom,
% 0.31/0.47 ! [P: produc1418842292n_game > set_variable > trm > $o,A0: produc1418842292n_game,A1: set_variable,A22: trm] :
% 0.31/0.47 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] : ( P @ Sigma3 @ U3 @ ( var @ X2 ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] : ( P @ Sigma3 @ U3 @ ( number @ R3 ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] : ( P @ Sigma3 @ U3 @ ( const @ F5 ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 0.31/0.47 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.47 => ( ! [X25: trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta )
% 0.31/0.47 = ( some_trm @ X25 ) )
% 0.31/0.47 => ! [X2a: trm] :
% 0.31/0.47 ( ( ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ Sigma3
% 0.31/0.47 @ F5 )
% 0.31/0.47 = ( some_trm @ X2a ) )
% 0.31/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 => ( P @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 0.31/0.47 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 0.31/0.47 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( P @ Sigma3 @ U3 @ Eta )
% 0.31/0.47 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 0.31/0.47 ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( P @ Sigma3 @ U3 @ Eta )
% 0.31/0.47 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.31/0.47 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 0.31/0.47 ( ( P @ Sigma3
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta )
% 0.31/0.47 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_induct
% 0.31/0.47 thf(fact_218_Geqo_Osimps_I3_J,axiom,
% 0.31/0.47 ! [V2: trm] :
% 0.31/0.47 ( ( uSubst152838031e_Geqo @ ( some_trm @ V2 ) @ none_trm )
% 0.31/0.47 = none_fml ) ).
% 0.31/0.47
% 0.31/0.47 % Geqo.simps(3)
% 0.31/0.47 thf(fact_219_combine__options__def,axiom,
% 0.31/0.47 ( combine_options_fml
% 0.31/0.47 = ( ^ [F2: fml > fml > fml,X: option_fml,Y: option_fml] :
% 0.31/0.47 ( case_o209804997ml_fml @ Y
% 0.31/0.47 @ ^ [Z3: fml] :
% 0.31/0.47 ( case_o209804997ml_fml @ ( some_fml @ Z3 )
% 0.31/0.47 @ ^ [Aa: fml] : ( some_fml @ ( F2 @ Z3 @ Aa ) )
% 0.31/0.47 @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_def
% 0.31/0.47 thf(fact_220_combine__options__def,axiom,
% 0.31/0.47 ( combine_options_game
% 0.31/0.47 = ( ^ [F2: game > game > game,X: option_game,Y: option_game] :
% 0.31/0.47 ( case_o696458451e_game @ Y
% 0.31/0.47 @ ^ [Z3: game] :
% 0.31/0.47 ( case_o696458451e_game @ ( some_game @ Z3 )
% 0.31/0.47 @ ^ [Aa: game] : ( some_game @ ( F2 @ Z3 @ Aa ) )
% 0.31/0.47 @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_def
% 0.31/0.47 thf(fact_221_combine__options__def,axiom,
% 0.31/0.47 ( combine_options_trm
% 0.31/0.47 = ( ^ [F2: trm > trm > trm,X: option_trm,Y: option_trm] :
% 0.31/0.47 ( case_o487727941rm_trm @ Y
% 0.31/0.47 @ ^ [Z3: trm] :
% 0.31/0.47 ( case_o487727941rm_trm @ ( some_trm @ Z3 )
% 0.31/0.47 @ ^ [Aa: trm] : ( some_trm @ ( F2 @ Z3 @ Aa ) )
% 0.31/0.47 @ Y )
% 0.31/0.47 @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_def
% 0.31/0.47 thf(fact_222_trm_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X22: real,Y22: real] :
% 0.31/0.47 ( ( ( number @ X22 )
% 0.31/0.47 = ( number @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(2)
% 0.31/0.47 thf(fact_223_trm_Oinject_I1_J,axiom,
% 0.31/0.47 ! [X12: variable,Y1: variable] :
% 0.31/0.47 ( ( ( var @ X12 )
% 0.31/0.47 = ( var @ Y1 ) )
% 0.31/0.47 = ( X12 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(1)
% 0.31/0.47 thf(fact_224_trm_Oinject_I7_J,axiom,
% 0.31/0.47 ! [X7: trm,Y7: trm] :
% 0.31/0.47 ( ( ( differential @ X7 )
% 0.31/0.47 = ( differential @ Y7 ) )
% 0.31/0.47 = ( X7 = Y7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.inject(7)
% 0.31/0.47 thf(fact_225_combine__options__simps_I2_J,axiom,
% 0.31/0.47 ! [F3: trm > trm > trm,X4: option_trm] :
% 0.31/0.47 ( ( combine_options_trm @ F3 @ X4 @ none_trm )
% 0.31/0.47 = X4 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(2)
% 0.31/0.47 thf(fact_226_combine__options__simps_I2_J,axiom,
% 0.31/0.47 ! [F3: fml > fml > fml,X4: option_fml] :
% 0.31/0.47 ( ( combine_options_fml @ F3 @ X4 @ none_fml )
% 0.31/0.47 = X4 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(2)
% 0.31/0.47 thf(fact_227_combine__options__simps_I2_J,axiom,
% 0.31/0.47 ! [F3: game > game > game,X4: option_game] :
% 0.31/0.47 ( ( combine_options_game @ F3 @ X4 @ none_game )
% 0.31/0.47 = X4 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(2)
% 0.31/0.47 thf(fact_228_combine__options__simps_I1_J,axiom,
% 0.31/0.47 ! [F3: trm > trm > trm,Y2: option_trm] :
% 0.31/0.47 ( ( combine_options_trm @ F3 @ none_trm @ Y2 )
% 0.31/0.47 = Y2 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(1)
% 0.31/0.47 thf(fact_229_combine__options__simps_I1_J,axiom,
% 0.31/0.47 ! [F3: fml > fml > fml,Y2: option_fml] :
% 0.31/0.47 ( ( combine_options_fml @ F3 @ none_fml @ Y2 )
% 0.31/0.47 = Y2 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(1)
% 0.31/0.47 thf(fact_230_combine__options__simps_I1_J,axiom,
% 0.31/0.47 ! [F3: game > game > game,Y2: option_game] :
% 0.31/0.47 ( ( combine_options_game @ F3 @ none_game @ Y2 )
% 0.31/0.47 = Y2 ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(1)
% 0.31/0.47 thf(fact_231_combine__options__simps_I3_J,axiom,
% 0.31/0.47 ! [F3: trm > trm > trm,A: trm,B: trm] :
% 0.31/0.47 ( ( combine_options_trm @ F3 @ ( some_trm @ A ) @ ( some_trm @ B ) )
% 0.31/0.47 = ( some_trm @ ( F3 @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(3)
% 0.31/0.47 thf(fact_232_combine__options__simps_I3_J,axiom,
% 0.31/0.47 ! [F3: fml > fml > fml,A: fml,B: fml] :
% 0.31/0.47 ( ( combine_options_fml @ F3 @ ( some_fml @ A ) @ ( some_fml @ B ) )
% 0.31/0.47 = ( some_fml @ ( F3 @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(3)
% 0.31/0.47 thf(fact_233_combine__options__simps_I3_J,axiom,
% 0.31/0.47 ! [F3: game > game > game,A: game,B: game] :
% 0.31/0.47 ( ( combine_options_game @ F3 @ ( some_game @ A ) @ ( some_game @ B ) )
% 0.31/0.47 = ( some_game @ ( F3 @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_simps(3)
% 0.31/0.47 thf(fact_234_Differentialo_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Theta2: trm] :
% 0.31/0.47 ( ( uSubst716837505ntialo @ ( some_trm @ Theta2 ) )
% 0.31/0.47 = ( some_trm @ ( differential @ Theta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo.simps(1)
% 0.31/0.47 thf(fact_235_trm_Odistinct_I21_J,axiom,
% 0.31/0.47 ! [X22: real,X7: trm] :
% 0.31/0.47 ( ( number @ X22 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(21)
% 0.31/0.47 thf(fact_236_trm_Odistinct_I11_J,axiom,
% 0.31/0.47 ! [X12: variable,X7: trm] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(11)
% 0.31/0.47 thf(fact_237_trm_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X12: variable,X22: real] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( number @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(1)
% 0.31/0.47 thf(fact_238_usubstappt_Osimps_I7_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.31/0.47 = ( uSubst716837505ntialo
% 0.31/0.47 @ ( uSubst516392818stappt @ Sigma2
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(7)
% 0.31/0.47 thf(fact_239_trm_Odistinct_I13_J,axiom,
% 0.31/0.47 ! [X22: real,X3: char] :
% 0.31/0.47 ( ( number @ X22 )
% 0.31/0.47 != ( const @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(13)
% 0.31/0.47 thf(fact_240_trm_Odistinct_I15_J,axiom,
% 0.31/0.47 ! [X22: real,X41: char,X42: trm] :
% 0.31/0.47 ( ( number @ X22 )
% 0.31/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(15)
% 0.31/0.47 thf(fact_241_trm_Odistinct_I19_J,axiom,
% 0.31/0.47 ! [X22: real,X61: trm,X62: trm] :
% 0.31/0.47 ( ( number @ X22 )
% 0.31/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(19)
% 0.31/0.47 thf(fact_242_trm_Odistinct_I17_J,axiom,
% 0.31/0.47 ! [X22: real,X51: trm,X52: trm] :
% 0.31/0.47 ( ( number @ X22 )
% 0.31/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(17)
% 0.31/0.47 thf(fact_243_Differentialo_Oelims,axiom,
% 0.31/0.47 ! [X4: option_trm,Y2: option_trm] :
% 0.31/0.47 ( ( ( uSubst716837505ntialo @ X4 )
% 0.31/0.47 = Y2 )
% 0.31/0.47 => ( ! [Theta: trm] :
% 0.31/0.47 ( ( X4
% 0.31/0.47 = ( some_trm @ Theta ) )
% 0.31/0.47 => ( Y2
% 0.31/0.47 != ( some_trm @ ( differential @ Theta ) ) ) )
% 0.31/0.47 => ~ ( ( X4 = none_trm )
% 0.31/0.47 => ( Y2 != none_trm ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo.elims
% 0.31/0.47 thf(fact_244_trm_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [X12: variable,X3: char] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( const @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(3)
% 0.31/0.47 thf(fact_245_trm_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [X12: variable,X41: char,X42: trm] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( func @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(5)
% 0.31/0.47 thf(fact_246_trm_Odistinct_I9_J,axiom,
% 0.31/0.47 ! [X12: variable,X61: trm,X62: trm] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( times @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(9)
% 0.31/0.47 thf(fact_247_trm_Odistinct_I7_J,axiom,
% 0.31/0.47 ! [X12: variable,X51: trm,X52: trm] :
% 0.31/0.47 ( ( var @ X12 )
% 0.31/0.47 != ( plus @ X51 @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(7)
% 0.31/0.47 thf(fact_248_trm_Odistinct_I29_J,axiom,
% 0.31/0.47 ! [X3: char,X7: trm] :
% 0.31/0.47 ( ( const @ X3 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(29)
% 0.31/0.47 thf(fact_249_trm_Odistinct_I35_J,axiom,
% 0.31/0.47 ! [X41: char,X42: trm,X7: trm] :
% 0.31/0.47 ( ( func @ X41 @ X42 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(35)
% 0.31/0.47 thf(fact_250_trm_Odistinct_I41_J,axiom,
% 0.31/0.47 ! [X61: trm,X62: trm,X7: trm] :
% 0.31/0.47 ( ( times @ X61 @ X62 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(41)
% 0.31/0.47 thf(fact_251_trm_Odistinct_I39_J,axiom,
% 0.31/0.47 ! [X51: trm,X52: trm,X7: trm] :
% 0.31/0.47 ( ( plus @ X51 @ X52 )
% 0.31/0.47 != ( differential @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.distinct(39)
% 0.31/0.47 thf(fact_252_trm_Oexhaust,axiom,
% 0.31/0.47 ! [Y2: trm] :
% 0.31/0.47 ( ! [X13: variable] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( var @ X13 ) )
% 0.31/0.47 => ( ! [X23: real] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( number @ X23 ) )
% 0.31/0.47 => ( ! [X32: char] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( const @ X32 ) )
% 0.31/0.47 => ( ! [X412: char,X422: trm] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( func @ X412 @ X422 ) )
% 0.31/0.47 => ( ! [X512: trm,X522: trm] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( plus @ X512 @ X522 ) )
% 0.31/0.47 => ( ! [X612: trm,X622: trm] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( times @ X612 @ X622 ) )
% 0.31/0.47 => ~ ! [X72: trm] :
% 0.31/0.47 ( Y2
% 0.31/0.47 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.exhaust
% 0.31/0.47 thf(fact_253_trm_Oinduct,axiom,
% 0.31/0.47 ! [P: trm > $o,Trm: trm] :
% 0.31/0.47 ( ! [X2: variable] : ( P @ ( var @ X2 ) )
% 0.31/0.47 => ( ! [X2: real] : ( P @ ( number @ X2 ) )
% 0.31/0.47 => ( ! [X2: char] : ( P @ ( const @ X2 ) )
% 0.31/0.47 => ( ! [X1a: char,X2a2: trm] :
% 0.31/0.47 ( ( P @ X2a2 )
% 0.31/0.47 => ( P @ ( func @ X1a @ X2a2 ) ) )
% 0.31/0.47 => ( ! [X1a: trm,X2a2: trm] :
% 0.31/0.47 ( ( P @ X1a )
% 0.31/0.47 => ( ( P @ X2a2 )
% 0.31/0.47 => ( P @ ( plus @ X1a @ X2a2 ) ) ) )
% 0.31/0.47 => ( ! [X1a: trm,X2a2: trm] :
% 0.31/0.47 ( ( P @ X1a )
% 0.31/0.47 => ( ( P @ X2a2 )
% 0.31/0.47 => ( P @ ( times @ X1a @ X2a2 ) ) ) )
% 0.31/0.47 => ( ! [X2: trm] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( differential @ X2 ) ) )
% 0.31/0.47 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trm.induct
% 0.31/0.47 thf(fact_254_Geqo_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Eta2: option_trm] :
% 0.31/0.47 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 0.31/0.47 = none_fml ) ).
% 0.31/0.47
% 0.31/0.47 % Geqo.simps(2)
% 0.31/0.47 thf(fact_255_Geqo__undef,axiom,
% 0.31/0.47 ! [Theta2: option_trm,Eta2: option_trm] :
% 0.31/0.47 ( ( ( uSubst152838031e_Geqo @ Theta2 @ Eta2 )
% 0.31/0.47 = none_fml )
% 0.31/0.47 = ( ( Theta2 = none_trm )
% 0.31/0.47 | ( Eta2 = none_trm ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Geqo_undef
% 0.31/0.47 thf(fact_256_Differentialo_Osimps_I2_J,axiom,
% 0.31/0.47 ( ( uSubst716837505ntialo @ none_trm )
% 0.31/0.47 = none_trm ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo.simps(2)
% 0.31/0.47 thf(fact_257_Differentialo__undef,axiom,
% 0.31/0.47 ! [Theta2: option_trm] :
% 0.31/0.47 ( ( ( uSubst716837505ntialo @ Theta2 )
% 0.31/0.47 = none_trm )
% 0.31/0.47 = ( Theta2 = none_trm ) ) ).
% 0.31/0.47
% 0.31/0.47 % Differentialo_undef
% 0.31/0.47 thf(fact_258_usubstappt_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,R2: real] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 0.31/0.47 = ( some_trm @ ( number @ R2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(2)
% 0.31/0.47 thf(fact_259_usubstappt_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,X4: variable] :
% 0.31/0.47 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 0.31/0.47 = ( some_trm @ ( var @ X4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.simps(1)
% 0.31/0.47 thf(fact_260_usubstappt__differential__conv,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.31/0.47 != none_trm )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta2 )
% 0.31/0.47 != none_trm ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt_differential_conv
% 0.31/0.47 thf(fact_261_usubstappt_Opelims,axiom,
% 0.31/0.47 ! [X4: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 0.31/0.47 ( ( ( uSubst516392818stappt @ X4 @ Xa @ Xb )
% 0.31/0.47 = Y2 )
% 0.31/0.47 => ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ Xb ) ) )
% 0.31/0.47 => ( ! [X2: variable] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( var @ X2 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_trm @ ( var @ X2 ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( var @ X2 ) ) ) ) ) )
% 0.31/0.47 => ( ! [R3: real] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( number @ R3 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( some_trm @ ( number @ R3 ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 0.31/0.47 => ( ! [F5: char] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( const @ F5 ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( uSubst1559070963pconst @ X4 @ Xa @ F5 ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 0.31/0.47 => ( ! [F5: char,Theta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( func @ F5 @ Theta ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( case_o487727941rm_trm @ none_trm
% 0.31/0.47 @ ^ [Sigma_theta2: trm] :
% 0.31/0.47 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta2 ) )
% 0.31/0.47 @ ^ [R: trm] :
% 0.31/0.47 ( if_option_trm
% 0.31/0.47 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 0.31/0.47 = bot_bot_set_variable )
% 0.31/0.47 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 0.31/0.47 @ none_trm )
% 0.31/0.47 @ ( produc866613687on_trm
% 0.31/0.47 @ ^ [Uu: char > option_trm] :
% 0.31/0.47 ( produc1231571704on_trm
% 0.31/0.47 @ ^ [F4: char > option_trm] :
% 0.31/0.47 ( produc1036610745on_trm
% 0.31/0.47 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.31/0.47 @ X4
% 0.31/0.47 @ F5 ) )
% 0.31/0.47 @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( func @ F5 @ Theta ) ) ) ) ) )
% 0.31/0.47 => ( ! [Theta: trm,Eta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( plus @ Theta @ Eta ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( plus @ Theta @ Eta ) ) ) ) ) )
% 0.31/0.47 => ( ! [Theta: trm,Eta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( times @ Theta @ Eta ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( times @ Theta @ Eta ) ) ) ) ) )
% 0.31/0.47 => ~ ! [Theta: trm] :
% 0.31/0.47 ( ( Xb
% 0.31/0.47 = ( differential @ Theta ) )
% 0.31/0.47 => ( ( Y2
% 0.31/0.47 = ( uSubst716837505ntialo
% 0.31/0.47 @ ( uSubst516392818stappt @ X4
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta ) ) )
% 0.31/0.47 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.pelims
% 0.31/0.47 thf(fact_262_term__sem_Ocases,axiom,
% 0.31/0.47 ! [X4: produc833882726rp_trm] :
% 0.31/0.47 ( ! [I: denotational_interp,X2: variable] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( var @ X2 ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,R3: real] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( number @ R3 ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,F5: char] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( const @ F5 ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( func @ F5 @ Theta ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( plus @ Theta @ Eta ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( times @ Theta @ Eta ) ) )
% 0.31/0.47 => ~ ! [I: denotational_interp,Theta: trm] :
% 0.31/0.47 ( X4
% 0.31/0.47 != ( produc1132922070rp_trm @ I @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % term_sem.cases
% 0.31/0.47 thf(fact_263_term__sem_Oinduct,axiom,
% 0.31/0.47 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.31/0.47 ( ! [I: denotational_interp,X2: variable] : ( P @ I @ ( var @ X2 ) )
% 0.31/0.47 => ( ! [I: denotational_interp,R3: real] : ( P @ I @ ( number @ R3 ) )
% 0.31/0.47 => ( ! [I: denotational_interp,F5: char] : ( P @ I @ ( const @ F5 ) )
% 0.31/0.47 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 0.31/0.47 ( ( P @ I @ Theta )
% 0.31/0.47 => ( P @ I @ ( func @ F5 @ Theta ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,Theta: trm] :
% 0.31/0.47 ( ( P @ I @ Theta )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( P @ I @ Eta )
% 0.31/0.47 => ( P @ I @ ( plus @ Theta @ Eta ) ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,Theta: trm] :
% 0.31/0.47 ( ( P @ I @ Theta )
% 0.31/0.47 => ! [Eta: trm] :
% 0.31/0.47 ( ( P @ I @ Eta )
% 0.31/0.47 => ( P @ I @ ( times @ Theta @ Eta ) ) ) )
% 0.31/0.47 => ( ! [I: denotational_interp,Theta: trm] :
% 0.31/0.47 ( ( ? [Xa2: char] :
% 0.31/0.47 ( member_char @ Xa2
% 0.31/0.47 @ ( collect_char
% 0.31/0.47 @ ^ [Uu: char] : $true ) )
% 0.31/0.47 => ( P @ I @ Theta ) )
% 0.31/0.47 => ( P @ I @ ( differential @ Theta ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % term_sem.induct
% 0.31/0.47 thf(fact_264_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: char,B: option_trm,A6: char,B6: option_trm] :
% 0.31/0.47 ( ( ( produc1500300866on_trm @ A @ B )
% 0.31/0.47 = ( produc1500300866on_trm @ A6 @ B6 ) )
% 0.31/0.47 = ( ( A = A6 )
% 0.31/0.47 & ( B = B6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_265_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: set_variable,B: trm,A6: set_variable,B6: trm] :
% 0.31/0.47 ( ( ( produc1482344242le_trm @ A @ B )
% 0.31/0.47 = ( produc1482344242le_trm @ A6 @ B6 ) )
% 0.31/0.47 = ( ( A = A6 )
% 0.31/0.47 & ( B = B6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_266_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: char > option_trm,B: produc62062515n_game,A6: char > option_trm,B6: produc62062515n_game] :
% 0.31/0.47 ( ( ( produc1618635950n_game @ A @ B )
% 0.31/0.47 = ( produc1618635950n_game @ A6 @ B6 ) )
% 0.31/0.47 = ( ( A = A6 )
% 0.31/0.47 & ( B = B6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_267_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: char > option_trm,B: produc799602994n_game,A6: char > option_trm,B6: produc799602994n_game] :
% 0.31/0.47 ( ( ( produc1048060077n_game @ A @ B )
% 0.31/0.47 = ( produc1048060077n_game @ A6 @ B6 ) )
% 0.31/0.47 = ( ( A = A6 )
% 0.31/0.47 & ( B = B6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_268_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: char > option_fml,B: char > option_game,A6: char > option_fml,B6: char > option_game] :
% 0.31/0.47 ( ( ( produc123610156n_game @ A @ B )
% 0.31/0.47 = ( produc123610156n_game @ A6 @ B6 ) )
% 0.31/0.47 = ( ( A = A6 )
% 0.31/0.47 & ( B = B6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_269_prod_Oinject,axiom,
% 0.31/0.47 ! [X12: char,X22: option_trm,Y1: char,Y22: option_trm] :
% 0.31/0.47 ( ( ( produc1500300866on_trm @ X12 @ X22 )
% 0.31/0.47 = ( produc1500300866on_trm @ Y1 @ Y22 ) )
% 0.31/0.47 = ( ( X12 = Y1 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_270_prod_Oinject,axiom,
% 0.31/0.47 ! [X12: set_variable,X22: trm,Y1: set_variable,Y22: trm] :
% 0.31/0.47 ( ( ( produc1482344242le_trm @ X12 @ X22 )
% 0.31/0.47 = ( produc1482344242le_trm @ Y1 @ Y22 ) )
% 0.31/0.47 = ( ( X12 = Y1 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_271_prod_Oinject,axiom,
% 0.31/0.47 ! [X12: char > option_trm,X22: produc62062515n_game,Y1: char > option_trm,Y22: produc62062515n_game] :
% 0.31/0.47 ( ( ( produc1618635950n_game @ X12 @ X22 )
% 0.31/0.47 = ( produc1618635950n_game @ Y1 @ Y22 ) )
% 0.31/0.47 = ( ( X12 = Y1 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_272_prod_Oinject,axiom,
% 0.31/0.47 ! [X12: char > option_trm,X22: produc799602994n_game,Y1: char > option_trm,Y22: produc799602994n_game] :
% 0.31/0.47 ( ( ( produc1048060077n_game @ X12 @ X22 )
% 0.31/0.47 = ( produc1048060077n_game @ Y1 @ Y22 ) )
% 0.31/0.47 = ( ( X12 = Y1 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_273_prod_Oinject,axiom,
% 0.31/0.47 ! [X12: char > option_fml,X22: char > option_game,Y1: char > option_fml,Y22: char > option_game] :
% 0.31/0.47 ( ( ( produc123610156n_game @ X12 @ X22 )
% 0.31/0.47 = ( produc123610156n_game @ Y1 @ Y22 ) )
% 0.31/0.47 = ( ( X12 = Y1 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_274_case__prodI,axiom,
% 0.31/0.47 ! [F3: char > option_trm > $o,A: char,B: option_trm] :
% 0.31/0.47 ( ( F3 @ A @ B )
% 0.31/0.47 => ( produc584666985_trm_o @ F3 @ ( produc1500300866on_trm @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI
% 0.31/0.47 thf(fact_275_case__prodI,axiom,
% 0.31/0.47 ! [F3: set_variable > trm > $o,A: set_variable,B: trm] :
% 0.31/0.47 ( ( F3 @ A @ B )
% 0.31/0.47 => ( produc82209913_trm_o @ F3 @ ( produc1482344242le_trm @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI
% 0.31/0.47 thf(fact_276_case__prodI,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc62062515n_game > $o,A: char > option_trm,B: produc62062515n_game] :
% 0.31/0.47 ( ( F3 @ A @ B )
% 0.31/0.47 => ( produc1707653117game_o @ F3 @ ( produc1618635950n_game @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI
% 0.31/0.47 thf(fact_277_case__prodI,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc799602994n_game > $o,A: char > option_trm,B: produc799602994n_game] :
% 0.31/0.47 ( ( F3 @ A @ B )
% 0.31/0.47 => ( produc1868740670game_o @ F3 @ ( produc1048060077n_game @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI
% 0.31/0.47 thf(fact_278_case__prodI,axiom,
% 0.31/0.47 ! [F3: ( char > option_fml ) > ( char > option_game ) > $o,A: char > option_fml,B: char > option_game] :
% 0.31/0.47 ( ( F3 @ A @ B )
% 0.31/0.47 => ( produc159680767game_o @ F3 @ ( produc123610156n_game @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI
% 0.31/0.47 thf(fact_279_case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc464795408on_trm,C: char > option_trm > $o] :
% 0.31/0.47 ( ! [A4: char,B4: option_trm] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 0.31/0.47 => ( C @ A4 @ B4 ) )
% 0.31/0.47 => ( produc584666985_trm_o @ C @ P4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI2
% 0.31/0.47 thf(fact_280_case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc1367888000le_trm,C: set_variable > trm > $o] :
% 0.31/0.47 ( ! [A4: set_variable,B4: trm] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 0.31/0.47 => ( C @ A4 @ B4 ) )
% 0.31/0.47 => ( produc82209913_trm_o @ C @ P4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI2
% 0.31/0.47 thf(fact_281_case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc1418842292n_game,C: ( char > option_trm ) > produc62062515n_game > $o] :
% 0.31/0.47 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1618635950n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( C @ A4 @ B4 ) )
% 0.31/0.47 => ( produc1707653117game_o @ C @ P4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI2
% 0.31/0.47 thf(fact_282_case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc62062515n_game,C: ( char > option_trm ) > produc799602994n_game > $o] :
% 0.31/0.47 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1048060077n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( C @ A4 @ B4 ) )
% 0.31/0.47 => ( produc1868740670game_o @ C @ P4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI2
% 0.31/0.47 thf(fact_283_case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc799602994n_game,C: ( char > option_fml ) > ( char > option_game ) > $o] :
% 0.31/0.47 ( ! [A4: char > option_fml,B4: char > option_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc123610156n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( C @ A4 @ B4 ) )
% 0.31/0.47 => ( produc159680767game_o @ C @ P4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prodI2
% 0.31/0.47 thf(fact_284_mem__case__prodI,axiom,
% 0.31/0.47 ! [Z2: char,C: char > option_trm > set_char,A: char,B: option_trm] :
% 0.31/0.47 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc33263478t_char @ C @ ( produc1500300866on_trm @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI
% 0.31/0.47 thf(fact_285_mem__case__prodI,axiom,
% 0.31/0.47 ! [Z2: char,C: set_variable > trm > set_char,A: set_variable,B: trm] :
% 0.31/0.47 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc836445798t_char @ C @ ( produc1482344242le_trm @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI
% 0.31/0.47 thf(fact_286_mem__case__prodI,axiom,
% 0.31/0.47 ! [Z2: char,C: ( char > option_trm ) > produc62062515n_game > set_char,A: char > option_trm,B: produc62062515n_game] :
% 0.31/0.47 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc1002100706t_char @ C @ ( produc1618635950n_game @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI
% 0.31/0.47 thf(fact_287_mem__case__prodI,axiom,
% 0.31/0.47 ! [Z2: char,C: ( char > option_trm ) > produc799602994n_game > set_char,A: char > option_trm,B: produc799602994n_game] :
% 0.31/0.47 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc1554403041t_char @ C @ ( produc1048060077n_game @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI
% 0.31/0.47 thf(fact_288_mem__case__prodI,axiom,
% 0.31/0.47 ! [Z2: char,C: ( char > option_fml ) > ( char > option_game ) > set_char,A: char > option_fml,B: char > option_game] :
% 0.31/0.47 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc629249376t_char @ C @ ( produc123610156n_game @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI
% 0.31/0.47 thf(fact_289_mem__case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc464795408on_trm,Z2: char,C: char > option_trm > set_char] :
% 0.31/0.47 ( ! [A4: char,B4: option_trm] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc33263478t_char @ C @ P4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI2
% 0.31/0.47 thf(fact_290_mem__case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc1367888000le_trm,Z2: char,C: set_variable > trm > set_char] :
% 0.31/0.47 ( ! [A4: set_variable,B4: trm] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc836445798t_char @ C @ P4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI2
% 0.31/0.47 thf(fact_291_mem__case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc1418842292n_game,Z2: char,C: ( char > option_trm ) > produc62062515n_game > set_char] :
% 0.31/0.47 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1618635950n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc1002100706t_char @ C @ P4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI2
% 0.31/0.47 thf(fact_292_mem__case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc62062515n_game,Z2: char,C: ( char > option_trm ) > produc799602994n_game > set_char] :
% 0.31/0.47 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc1048060077n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc1554403041t_char @ C @ P4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI2
% 0.31/0.47 thf(fact_293_mem__case__prodI2,axiom,
% 0.31/0.47 ! [P4: produc799602994n_game,Z2: char,C: ( char > option_fml ) > ( char > option_game ) > set_char] :
% 0.31/0.47 ( ! [A4: char > option_fml,B4: char > option_game] :
% 0.31/0.47 ( ( P4
% 0.31/0.47 = ( produc123610156n_game @ A4 @ B4 ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 0.31/0.47 => ( member_char @ Z2 @ ( produc629249376t_char @ C @ P4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_case_prodI2
% 0.31/0.47 thf(fact_294_case__prod__conv,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 0.31/0.47 ( ( produc1250175341on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 0.31/0.47 = ( F3 @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_conv
% 0.31/0.47 thf(fact_295_case__prod__conv,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 0.31/0.47 ( ( produc1231571704on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.31/0.47 = ( F3 @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_conv
% 0.31/0.47 thf(fact_296_case__prod__conv,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 0.31/0.47 ( ( produc1615133358on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.31/0.47 = ( F3 @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_conv
% 0.31/0.47 thf(fact_297_case__prod__conv,axiom,
% 0.31/0.47 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,A: char > option_fml,B: char > option_game] :
% 0.31/0.47 ( ( produc1036610745on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.31/0.47 = ( F3 @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_conv
% 0.31/0.47 thf(fact_298_case__prod__conv,axiom,
% 0.31/0.47 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,A: char > option_fml,B: char > option_game] :
% 0.31/0.47 ( ( produc1420172399on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.31/0.47 = ( F3 @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_conv
% 0.31/0.47 thf(fact_299_usubstappt_Opsimps_I7_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 0.31/0.47 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( differential @ Theta2 ) ) ) )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 0.31/0.47 = ( uSubst716837505ntialo
% 0.31/0.47 @ ( uSubst516392818stappt @ Sigma2
% 0.31/0.47 @ ( collect_variable
% 0.31/0.47 @ ^ [X: variable] : $true )
% 0.31/0.47 @ Theta2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.psimps(7)
% 0.31/0.47 thf(fact_300_usubstappt_Opsimps_I1_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,X4: variable] :
% 0.31/0.47 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( var @ X4 ) ) ) )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 0.31/0.47 = ( some_trm @ ( var @ X4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.psimps(1)
% 0.31/0.47 thf(fact_301_usubstappt_Opsimps_I2_J,axiom,
% 0.31/0.47 ! [Sigma2: produc1418842292n_game,U2: set_variable,R2: real] :
% 0.31/0.47 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( number @ R2 ) ) ) )
% 0.31/0.47 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 0.31/0.47 = ( some_trm @ ( number @ R2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % usubstappt.psimps(2)
% 0.31/0.47 thf(fact_302_cond__case__prod__eta,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,G: produc1418842292n_game > char > option_fml] :
% 0.31/0.47 ( ! [X2: char > option_trm,Y4: produc62062515n_game] :
% 0.31/0.47 ( ( F3 @ X2 @ Y4 )
% 0.31/0.47 = ( G @ ( produc1618635950n_game @ X2 @ Y4 ) ) )
% 0.31/0.47 => ( ( produc1250175341on_fml @ F3 )
% 0.31/0.47 = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_case_prod_eta
% 0.31/0.47 thf(fact_303_cond__case__prod__eta,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,G: produc62062515n_game > char > option_trm] :
% 0.31/0.47 ( ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 0.31/0.47 ( ( F3 @ X2 @ Y4 )
% 0.31/0.47 = ( G @ ( produc1048060077n_game @ X2 @ Y4 ) ) )
% 0.31/0.47 => ( ( produc1231571704on_trm @ F3 )
% 0.31/0.47 = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_case_prod_eta
% 0.31/0.47 thf(fact_304_cond__case__prod__eta,axiom,
% 0.31/0.47 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,G: produc62062515n_game > char > option_fml] :
% 0.31/0.47 ( ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 0.31/0.47 ( ( F3 @ X2 @ Y4 )
% 0.31/0.47 = ( G @ ( produc1048060077n_game @ X2 @ Y4 ) ) )
% 0.31/0.47 => ( ( produc1615133358on_fml @ F3 )
% 0.31/0.47 = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_case_prod_eta
% 0.31/0.47 thf(fact_305_cond__case__prod__eta,axiom,
% 0.31/0.47 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,G: produc799602994n_game > char > option_trm] :
% 0.31/0.47 ( ! [X2: char > option_fml,Y4: char > option_game] :
% 0.31/0.47 ( ( F3 @ X2 @ Y4 )
% 0.31/0.47 = ( G @ ( produc123610156n_game @ X2 @ Y4 ) ) )
% 0.31/0.47 => ( ( produc1036610745on_trm @ F3 )
% 0.31/0.47 = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_case_prod_eta
% 0.31/0.47 thf(fact_306_cond__case__prod__eta,axiom,
% 0.31/0.47 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,G: produc799602994n_game > char > option_fml] :
% 0.31/0.47 ( ! [X2: char > option_fml,Y4: char > option_game] :
% 0.31/0.47 ( ( F3 @ X2 @ Y4 )
% 0.31/0.47 = ( G @ ( produc123610156n_game @ X2 @ Y4 ) ) )
% 0.31/0.47 => ( ( produc1420172399on_fml @ F3 )
% 0.31/0.47 = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_case_prod_eta
% 0.31/0.47 thf(fact_307_case__prod__eta,axiom,
% 0.31/0.47 ! [F3: produc1418842292n_game > char > option_fml] :
% 0.31/0.47 ( ( produc1250175341on_fml
% 0.31/0.47 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 0.31/0.47 = F3 ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_eta
% 0.31/0.47 thf(fact_308_case__prod__eta,axiom,
% 0.31/0.47 ! [F3: produc62062515n_game > char > option_trm] :
% 0.31/0.47 ( ( produc1231571704on_trm
% 0.31/0.47 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.31/0.47 = F3 ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_eta
% 0.31/0.47 thf(fact_309_case__prod__eta,axiom,
% 0.31/0.47 ! [F3: produc62062515n_game > char > option_fml] :
% 0.31/0.47 ( ( produc1615133358on_fml
% 0.31/0.47 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.31/0.47 = F3 ) ).
% 0.31/0.47
% 0.31/0.47 % case_prod_eta
% 0.31/0.47 thf(fact_310_case__prod__eta,axiom,
% 0.31/0.47 ! [F3: produc799602994n_game > char > option_trm] :
% 0.31/0.47 ( ( produc1036610745on_trm
% 0.31/0.47 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.31/0.48 = F3 ) ).
% 0.31/0.48
% 0.31/0.48 % case_prod_eta
% 0.31/0.48 thf(fact_311_case__prod__eta,axiom,
% 0.31/0.48 ! [F3: produc799602994n_game > char > option_fml] :
% 0.31/0.48 ( ( produc1420172399on_fml
% 0.31/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.31/0.48 = F3 ) ).
% 0.31/0.48
% 0.31/0.48 % case_prod_eta
% 0.31/0.48 thf(fact_312_case__prodE2,axiom,
% 0.31/0.48 ! [Q: ( char > option_fml ) > $o,P: ( char > option_trm ) > produc62062515n_game > char > option_fml,Z2: produc1418842292n_game] :
% 0.31/0.48 ( ( Q @ ( produc1250175341on_fml @ P @ Z2 ) )
% 0.31/0.48 => ~ ! [X2: char > option_trm,Y4: produc62062515n_game] :
% 0.31/0.48 ( ( Z2
% 0.31/0.48 = ( produc1618635950n_game @ X2 @ Y4 ) )
% 0.31/0.48 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % case_prodE2
% 0.31/0.48 thf(fact_313_case__prodE2,axiom,
% 0.31/0.48 ! [Q: ( char > option_trm ) > $o,P: ( char > option_trm ) > produc799602994n_game > char > option_trm,Z2: produc62062515n_game] :
% 0.31/0.48 ( ( Q @ ( produc1231571704on_trm @ P @ Z2 ) )
% 0.31/0.48 => ~ ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 0.31/0.48 ( ( Z2
% 0.31/0.48 = ( produc1048060077n_game @ X2 @ Y4 ) )
% 0.31/0.48 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % case_prodE2
% 0.31/0.48 thf(fact_314_case__prodE2,axiom,
% 0.31/0.48 ! [Q: ( char > option_fml ) > $o,P: ( char > option_trm ) > produc799602994n_game > char > option_fml,Z2: produc62062515n_game] :
% 0.31/0.48 ( ( Q @ ( produc1615133358on_fml @ P @ Z2 ) )
% 0.31/0.48 => ~ ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 0.31/0.48 ( ( Z2
% 0.31/0.48 = ( produc1048060077n_game @ X2 @ Y4 ) )
% 0.31/0.48 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % case_prodE2
% 0.31/0.48 thf(fact_315_case__prodE2,axiom,
% 0.31/0.48 ! [Q: ( char > option_trm ) > $o,P: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Z2: produc799602994n_game] :
% 0.31/0.48 ( ( Q @ ( produc1036610745on_trm @ P @ Z2 ) )
% 0.31/0.48 => ~ ! [X2: char > option_fml,Y4: char > option_game] :
% 0.31/0.48 ( ( Z2
% 0.31/0.48 = ( produc123610156n_game @ X2 @ Y4 ) )
% 0.31/0.48 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % case_prodE2
% 0.31/0.48 thf(fact_316_case__prodE2,axiom,
% 0.31/0.48 ! [Q: ( char > option_fml ) > $o,P: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Z2: produc799602994n_game] :
% 0.31/0.48 ( ( Q @ ( produc1420172399on_fml @ P @ Z2 ) )
% 0.31/0.48 => ~ ! [X2: char > option_fml,Y4: char > option_game] :
% 0.31/0.48 ( ( Z2
% 0.31/0.48 = ( produc123610156n_game @ X2 @ Y4 ) )
% 0.31/0.48 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % case_prodE2
% 0.31/0.48 thf(fact_317_inf__Int__eq2,axiom,
% 0.31/0.48 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.31/0.48 ( ( inf_in605351507_trm_o
% 0.31/0.48 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 )
% 0.31/0.48 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) )
% 0.31/0.48 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ ( inf_in1243659096on_trm @ R4 @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_Int_eq2
% 0.31/0.48 thf(fact_318_inf__Int__eq2,axiom,
% 0.31/0.48 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.31/0.48 ( ( inf_in185389155_trm_o
% 0.31/0.48 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 )
% 0.31/0.48 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) )
% 0.31/0.48 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ ( inf_in906025800le_trm @ R4 @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_Int_eq2
% 0.31/0.48 thf(fact_319_inf__Int__eq2,axiom,
% 0.31/0.48 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 0.31/0.48 ( ( inf_in1920662529game_o
% 0.31/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 )
% 0.31/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) )
% 0.31/0.48 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ ( inf_in360367996n_game @ R4 @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_Int_eq2
% 0.31/0.48 thf(fact_320_inf__Int__eq2,axiom,
% 0.31/0.48 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 0.31/0.48 ( ( inf_in1072207554game_o
% 0.31/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 )
% 0.31/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) )
% 0.31/0.48 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ ( inf_in69689467n_game @ R4 @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_Int_eq2
% 0.31/0.48 thf(fact_321_inf__Int__eq2,axiom,
% 0.31/0.48 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 0.31/0.48 ( ( inf_in243546115game_o
% 0.31/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 )
% 0.31/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) )
% 0.31/0.48 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ ( inf_in1391117306n_game @ R4 @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_Int_eq2
% 0.31/0.48 thf(fact_322_bot__empty__eq2,axiom,
% 0.31/0.48 ( bot_bo1417568964game_o
% 0.31/0.48 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ bot_bo1302831229n_game ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq2
% 0.31/0.48 thf(fact_323_bot__empty__eq2,axiom,
% 0.31/0.48 ( bot_bo1895715589game_o
% 0.31/0.48 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ bot_bo456479484n_game ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq2
% 0.31/0.48 thf(fact_324_usubstappt_Opsimps_I3_J,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( const @ F3 ) ) ) )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 0.31/0.48 = ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.psimps(3)
% 0.31/0.48 thf(fact_325_usubstappt_Opsimps_I6_J,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 0.31/0.48 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.psimps(6)
% 0.31/0.48 thf(fact_326_usubstappt_Opsimps_I5_J,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 0.31/0.48 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.psimps(5)
% 0.31/0.48 thf(fact_327_usubstappt_Opsimps_I4_J,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.31/0.48 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 0.31/0.48 = ( case_o487727941rm_trm @ none_trm
% 0.31/0.48 @ ^ [Sigma_theta2: trm] :
% 0.31/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta2 ) )
% 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 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ 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 @ Sigma2
% 0.31/0.48 @ F3 ) )
% 0.31/0.48 @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.psimps(4)
% 0.31/0.48 thf(fact_328_usubstappt_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1699626005le_trm] :
% 0.31/0.48 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X2 ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.31/0.48 => ~ ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.cases
% 0.31/0.48 thf(fact_329_usubstappt_Opinduct,axiom,
% 0.31/0.48 ! [A0: produc1418842292n_game,A1: set_variable,A22: trm,P: produc1418842292n_game > set_variable > trm > $o] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A0 @ ( produc1482344242le_trm @ A1 @ A22 ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X2 ) ) ) )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( var @ X2 ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 0.31/0.48 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.48 => ( ! [X25: trm] :
% 0.31/0.48 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta )
% 0.31/0.48 = ( some_trm @ X25 ) )
% 0.31/0.48 => ! [X2a: 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 @ Sigma3
% 0.31/0.48 @ F5 )
% 0.31/0.48 = ( some_trm @ X2a ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 => ( P @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 0.31/0.48 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.48 => ( ( P @ Sigma3 @ U3 @ Eta )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 0.31/0.48 => ( ( P @ Sigma3 @ U3 @ Theta )
% 0.31/0.48 => ( ( P @ Sigma3 @ U3 @ Eta )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) ) )
% 0.31/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 0.31/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta ) ) ) )
% 0.31/0.48 => ( ( P @ Sigma3
% 0.31/0.48 @ ( collect_variable
% 0.31/0.48 @ ^ [X: variable] : $true )
% 0.31/0.48 @ Theta )
% 0.31/0.48 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) ) )
% 0.31/0.48 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappt.pinduct
% 0.31/0.48 thf(fact_330_Geqo_Oelims,axiom,
% 0.31/0.48 ! [X4: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.31/0.48 ( ( ( uSubst152838031e_Geqo @ X4 @ Xa )
% 0.31/0.48 = Y2 )
% 0.31/0.48 => ( ! [Theta: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ Theta ) )
% 0.31/0.48 => ! [Eta: trm] :
% 0.31/0.48 ( ( Xa
% 0.31/0.48 = ( some_trm @ Eta ) )
% 0.31/0.48 => ( Y2
% 0.31/0.48 != ( some_fml @ ( geq @ Theta @ Eta ) ) ) ) )
% 0.31/0.48 => ( ( ( X4 = none_trm )
% 0.31/0.48 => ( Y2 != none_fml ) )
% 0.31/0.48 => ~ ( ? [V: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 = ( some_trm @ V ) )
% 0.31/0.48 => ( ( Xa = none_trm )
% 0.31/0.48 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Geqo.elims
% 0.31/0.48 thf(fact_331_fml_Oinject_I2_J,axiom,
% 0.31/0.48 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 0.31/0.48 ( ( ( geq @ X21 @ X222 )
% 0.31/0.48 = ( geq @ Y21 @ Y222 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y222 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % fml.inject(2)
% 0.31/0.48 thf(fact_332_Diamondo_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1739631244on_fml] :
% 0.31/0.48 ( ! [Alpha: game,Phi: fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) ) )
% 0.31/0.48 => ( ! [Phi: option_fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2124676926on_fml @ none_game @ Phi ) )
% 0.31/0.48 => ~ ! [V: game] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc2124676926on_fml @ ( some_game @ V ) @ none_fml ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Diamondo.cases
% 0.31/0.48 thf(fact_333_Existso_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1408538418on_fml] :
% 0.31/0.48 ( ! [X2: variable,Phi: fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1205977188on_fml @ X2 @ ( some_fml @ Phi ) ) )
% 0.31/0.48 => ~ ! [X2: variable] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1205977188on_fml @ X2 @ none_fml ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Existso.cases
% 0.31/0.48 thf(fact_334_Ando_Ocases,axiom,
% 0.31/0.48 ! [X4: produc46605351on_fml] :
% 0.31/0.48 ( ! [Phi: fml,Psi: fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc909629463on_fml @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) ) )
% 0.31/0.48 => ( ! [Psi: option_fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 0.31/0.48 => ~ ! [V: fml] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc909629463on_fml @ ( some_fml @ V ) @ none_fml ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Ando.cases
% 0.31/0.48 thf(fact_335_ODEo_Ocases,axiom,
% 0.31/0.48 ! [X4: produc464795408on_trm] :
% 0.31/0.48 ( ! [X2: char,Theta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1500300866on_trm @ X2 @ ( some_trm @ Theta ) ) )
% 0.31/0.48 => ~ ! [X2: char] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1500300866on_trm @ X2 @ none_trm ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ODEo.cases
% 0.31/0.48 thf(fact_336_Assigno_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1024976764on_trm] :
% 0.31/0.48 ( ! [X2: variable,Theta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1743721902on_trm @ X2 @ ( some_trm @ Theta ) ) )
% 0.31/0.48 => ~ ! [X2: variable] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1743721902on_trm @ X2 @ none_trm ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Assigno.cases
% 0.31/0.48 thf(fact_337_Timeso_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1072747943on_trm] :
% 0.31/0.48 ( ! [Theta: trm,Eta: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) )
% 0.31/0.48 => ( ! [Eta: option_trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc709594775on_trm @ none_trm @ Eta ) )
% 0.31/0.48 => ~ ! [V: trm] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Timeso.cases
% 0.31/0.48 thf(fact_338_Geqo_Osimps_I1_J,axiom,
% 0.31/0.48 ! [Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.31/0.48 = ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Geqo.simps(1)
% 0.31/0.48 thf(fact_339_usubstappf__geqr,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.31/0.48 != none_fml )
% 0.31/0.48 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.31/0.48 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf_geqr
% 0.31/0.48 thf(fact_340_usubstappf__geq,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.48 != none_trm )
% 0.31/0.48 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 0.31/0.48 != none_trm )
% 0.31/0.48 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.31/0.48 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf_geq
% 0.31/0.48 thf(fact_341_Composeo_Ocases,axiom,
% 0.31/0.48 ! [X4: produc1016592119n_game] :
% 0.31/0.48 ( ! [Alpha: game,Beta: game] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 0.31/0.48 => ( ! [Alpha: option_game] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 0.31/0.48 => ~ ! [V: game] :
% 0.31/0.48 ( X4
% 0.31/0.48 != ( produc1111617711n_game @ none_game @ ( some_game @ V ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Composeo.cases
% 0.31/0.48 thf(fact_342_usubstappf_Osimps_I2_J,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.31/0.48 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf.simps(2)
% 0.31/0.48 thf(fact_343_usubstappf__geq__conv,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 0.31/0.48 ( ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 0.31/0.48 != none_fml )
% 0.31/0.48 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.48 != none_trm )
% 0.31/0.48 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 0.31/0.48 != none_trm ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf_geq_conv
% 0.31/0.48 thf(fact_344_dotsubstt__def,axiom,
% 0.31/0.48 ( uSubst1408967625substt
% 0.31/0.48 = ( ^ [Theta3: trm] :
% 0.31/0.48 ( produc1618635950n_game
% 0.31/0.48 @ ^ [F2: char] :
% 0.31/0.48 ( if_option_trm
% 0.31/0.48 @ ( F2
% 0.31/0.48 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 0.31/0.48 @ ( some_trm @ Theta3 )
% 0.31/0.48 @ none_trm )
% 0.31/0.48 @ ( produc1048060077n_game
% 0.31/0.48 @ ^ [Uu: char] : none_trm
% 0.31/0.48 @ ( produc123610156n_game
% 0.31/0.48 @ ^ [Uu: char] : none_fml
% 0.31/0.48 @ ^ [Uu: char] : none_game ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % dotsubstt_def
% 0.31/0.48 thf(fact_345_Geqo_Opelims,axiom,
% 0.31/0.48 ! [X4: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.31/0.48 ( ( ( uSubst152838031e_Geqo @ X4 @ Xa )
% 0.31/0.48 = Y2 )
% 0.31/0.48 => ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 0.31/0.48 => ( ! [Theta: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ Theta ) )
% 0.31/0.48 => ! [Eta: trm] :
% 0.31/0.48 ( ( Xa
% 0.31/0.48 = ( some_trm @ Eta ) )
% 0.31/0.48 => ( ( Y2
% 0.31/0.48 = ( some_fml @ ( geq @ Theta @ Eta ) ) )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 0.31/0.48 => ( ( ( X4 = none_trm )
% 0.31/0.48 => ( ( Y2 = none_fml )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.31/0.48 => ~ ! [V: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ V ) )
% 0.31/0.48 => ( ( Xa = none_trm )
% 0.31/0.48 => ( ( Y2 = none_fml )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Geqo.pelims
% 0.31/0.48 thf(fact_346_Timeso_Opelims,axiom,
% 0.31/0.48 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.31/0.48 ( ( ( uSubst918876924Timeso @ X4 @ Xa )
% 0.31/0.48 = Y2 )
% 0.31/0.48 => ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 0.31/0.48 => ( ! [Theta: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ Theta ) )
% 0.31/0.48 => ! [Eta: trm] :
% 0.31/0.48 ( ( Xa
% 0.31/0.48 = ( some_trm @ Eta ) )
% 0.31/0.48 => ( ( Y2
% 0.31/0.48 = ( some_trm @ ( times @ Theta @ Eta ) ) )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 0.31/0.48 => ( ( ( X4 = none_trm )
% 0.31/0.48 => ( ( Y2 = none_trm )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.31/0.48 => ~ ! [V: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ V ) )
% 0.31/0.48 => ( ( Xa = none_trm )
% 0.31/0.48 => ( ( Y2 = none_trm )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Timeso.pelims
% 0.31/0.48 thf(fact_347_Pluso_Opelims,axiom,
% 0.31/0.48 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.31/0.48 ( ( ( uSubst141955042_Pluso @ X4 @ Xa )
% 0.31/0.48 = Y2 )
% 0.31/0.48 => ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 0.31/0.48 => ( ! [Theta: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ Theta ) )
% 0.31/0.48 => ! [Eta: trm] :
% 0.31/0.48 ( ( Xa
% 0.31/0.48 = ( some_trm @ Eta ) )
% 0.31/0.48 => ( ( Y2
% 0.31/0.48 = ( some_trm @ ( plus @ Theta @ Eta ) ) )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 0.31/0.48 => ( ( ( X4 = none_trm )
% 0.31/0.48 => ( ( Y2 = none_trm )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.31/0.48 => ~ ! [V: trm] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( some_trm @ V ) )
% 0.31/0.48 => ( ( Xa = none_trm )
% 0.31/0.48 => ( ( Y2 = none_trm )
% 0.31/0.48 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Pluso.pelims
% 0.31/0.48 thf(fact_348_dot__def,axiom,
% 0.31/0.48 ( uSubst_Mirabelle_dot
% 0.31/0.48 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % dot_def
% 0.31/0.48 thf(fact_349_usubstappf__pred,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,P4: char,R2: fml,U2: set_variable,Theta2: trm,Sigma_theta: trm] :
% 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 @ ^ [P3: char > option_fml,Uw: char > option_game] : P3 ) )
% 0.31/0.48 @ Sigma2
% 0.31/0.48 @ P4 )
% 0.31/0.48 = ( some_fml @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U2 )
% 0.31/0.48 = bot_bot_set_variable )
% 0.31/0.48 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 0.31/0.48 = ( some_trm @ Sigma_theta ) )
% 0.31/0.48 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 0.31/0.48 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf_pred
% 0.31/0.48 thf(fact_350_fml_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X11: char,X122: trm,Y11: char,Y12: trm] :
% 0.31/0.48 ( ( ( pred @ X11 @ X122 )
% 0.31/0.48 = ( pred @ Y11 @ Y12 ) )
% 0.31/0.48 = ( ( X11 = Y11 )
% 0.31/0.48 & ( X122 = Y12 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % fml.inject(1)
% 0.31/0.48 thf(fact_351_usubstappf__pred2,axiom,
% 0.31/0.48 ! [Sigma2: produc1418842292n_game,P4: char,R2: fml,U2: set_variable,Theta2: trm] :
% 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 @ ^ [P3: char > option_fml,Uw: char > option_game] : P3 ) )
% 0.31/0.48 @ Sigma2
% 0.31/0.48 @ P4 )
% 0.31/0.48 = ( some_fml @ R2 ) )
% 0.31/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U2 )
% 0.31/0.48 != bot_bot_set_variable )
% 0.31/0.48 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 0.31/0.48 = none_fml ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % usubstappf_pred2
% 0.31/0.48
% 0.31/0.48 % Helper facts (3)
% 0.31/0.48 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.31/0.48 ! [P: $o] :
% 0.31/0.48 ( ( P = $true )
% 0.31/0.48 | ( P = $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 ! [X4: option_trm,Y2: option_trm] :
% 0.31/0.48 ( ( if_option_trm @ $false @ X4 @ Y2 )
% 0.31/0.48 = Y2 ) ).
% 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 ! [X4: option_trm,Y2: option_trm] :
% 0.31/0.48 ( ( if_option_trm @ $true @ X4 @ Y2 )
% 0.31/0.48 = X4 ) ).
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 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 @ f )
% 0.31/0.48 = none_trm )
% 0.31/0.48 | ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 0.31/0.48 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.81/1.58 ---- Embedded in THF ---
% 2.81/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.81/1.58 %%% Generated on Tue Feb 24 08:29:56 EST 2026
% 2.81/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.81/1.58 %%% Logic specification used:
% 2.81/1.58 %%% thf(spec, logic, $$dhol).
% 2.81/1.58
% 2.81/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2DTF9609.p
% See solution above
% 2.81/1.58 ------------------------
% 3.05/1.62 ---- Cleaned THF ---
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 3.05/1.62 produc1699626005le_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__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_J,type,
% 3.05/1.62 set_Pr720454634n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1418842292n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__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,
% 3.05/1.62 set_Pr739694057n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc62062515n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__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,
% 3.05/1.62 set_Pr79606376n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc799602994n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 3.05/1.62 produc1016592119n_game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.05/1.62 produc1739631244on_fml: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.05/1.62 produc1072747943on_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.05/1.62 produc46605351on_fml: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 3.05/1.62 set_Pr943832262on_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 3.05/1.62 set_Pr1235432374le_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.05/1.62 produc1024976764on_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 3.05/1.62 produc1408538418on_fml: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.05/1.62 produc464795408on_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp_Mt__Syntax__Otrm_J,type,
% 3.05/1.62 produc833882726rp_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 3.05/1.62 produc1367888000le_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 3.05/1.62 option_game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.05/1.62 option_trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.05/1.62 option_fml: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 3.05/1.62 denotational_interp: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.05/1.62 set_variable: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 set_char: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Syntax__Ovariable,type,
% 3.05/1.62 variable: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Syntax__Ogame,type,
% 3.05/1.62 game: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__String__Ochar,type,
% 3.05/1.62 char: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Syntax__Otrm,type,
% 3.05/1.62 trm: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Syntax__Ofml,type,
% 3.05/1.62 fml: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Real__Oreal,type,
% 3.05/1.62 real: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.05/1.62 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 3.05/1.62 inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 3.05/1.62 inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 3.05/1.62 inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 3.05/1.62 inf_in185389155_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > set_variable > trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 3.05/1.62 inf_in605351507_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > char > option_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__String__Ochar_M_Eo_J,type,
% 3.05/1.62 inf_inf_char_o: ( char > $o ) > ( char > $o ) > char > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 3.05/1.62 inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,
% 3.05/1.62 inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,
% 3.05/1.62 inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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_J,type,
% 3.05/1.62 inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 3.05/1.62 inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 3.05/1.62 inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 inf_inf_set_char: set_char > set_char > set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.05/1.62 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ocombine__options_001t__Syntax__Ofml,type,
% 3.05/1.62 combine_options_fml: ( fml > fml > fml ) > option_fml > option_fml > option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ocombine__options_001t__Syntax__Ogame,type,
% 3.05/1.62 combine_options_game: ( game > game > game ) > option_game > option_game > option_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ocombine__options_001t__Syntax__Otrm,type,
% 3.05/1.62 combine_options_trm: ( trm > trm > trm ) > option_trm > option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 3.05/1.62 none_fml: option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 3.05/1.62 none_game: option_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 3.05/1.62 none_trm: option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 3.05/1.62 some_fml: fml > option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 3.05/1.62 some_game: game > option_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 3.05/1.62 some_trm: trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 3.05/1.62 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 3.05/1.62 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 3.05/1.62 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Ofml,type,
% 3.05/1.62 case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Syntax__Ogame,type,
% 3.05/1.62 case_o696458451e_game: option_game > ( game > option_game ) > option_game > option_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Syntax__Otrm,type,
% 3.05/1.62 case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 3.05/1.62 the_fml: option_fml > fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 3.05/1.62 the_game: option_game > game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 3.05/1.62 the_trm: option_trm > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 3.05/1.62 bot_bo1895715589game_o: ( char > option_fml ) > ( char > option_game ) > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 3.05/1.62 bot_bo1417568964game_o: ( char > option_trm ) > produc799602994n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__String__Ochar_M_Eo_J,type,
% 3.05/1.62 bot_bot_char_o: char > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 3.05/1.62 bot_bot_variable_o: variable > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
% 3.05/1.62 bot_bo456479484n_game: set_Pr79606376n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
% 3.05/1.62 bot_bo1302831229n_game: set_Pr739694057n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 bot_bot_set_char: set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 3.05/1.62 bot_bot_set_variable: set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_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,type,
% 3.05/1.62 produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_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,type,
% 3.05/1.62 produc1048060077n_game: ( char > option_trm ) > produc799602994n_game > produc62062515n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_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,type,
% 3.05/1.62 produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp_001t__Syntax__Otrm,type,
% 3.05/1.62 produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.05/1.62 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.05/1.62 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 3.05/1.62 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.05/1.62 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_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__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_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 3.05/1.62 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 3.05/1.62 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.05/1.62 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 3.05/1.62 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 3.05/1.62 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 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_Eo,type,
% 3.05/1.62 produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 3.05/1.62
% 3.05/1.62 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__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 produc629249376t_char: ( ( char > option_fml ) > ( char > option_game ) > set_char ) > produc799602994n_game > set_char ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 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_Eo,type,
% 3.05/1.62 produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 3.05/1.62
% 3.05/1.62 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__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 produc1554403041t_char: ( ( char > option_trm ) > produc799602994n_game > set_char ) > produc62062515n_game > set_char ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 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_Eo,type,
% 3.05/1.62 produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
% 3.05/1.62
% 3.05/1.62 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,
% 3.05/1.62 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 3.05/1.62
% 3.05/1.62 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__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 produc1002100706t_char: ( ( char > option_trm ) > produc62062515n_game > set_char ) > produc1418842292n_game > set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001_Eo,type,
% 3.05/1.62 produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001t__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 produc836445798t_char: ( set_variable > trm > set_char ) > produc1367888000le_trm > set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001_Eo,type,
% 3.05/1.62 produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Set__Oset_It__String__Ochar_J,type,
% 3.05/1.62 produc33263478t_char: ( char > option_trm > set_char ) > produc464795408on_trm > set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_OCollect_001t__String__Ochar,type,
% 3.05/1.62 collect_char: ( char > $o ) > set_char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 3.05/1.62 collect_variable: ( variable > $o ) > set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 3.05/1.62 is_empty_variable: set_variable > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Static__Semantics_OFVF,type,
% 3.05/1.62 static_FVF: fml > set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Static__Semantics_OFVT,type,
% 3.05/1.62 static_FVT: trm > set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_String_Ochar_OChar,type,
% 3.05/1.62 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Ofml_OGeq,type,
% 3.05/1.62 geq: trm > trm > fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Ofml_OPred,type,
% 3.05/1.62 pred: char > trm > fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_OConst,type,
% 3.05/1.62 const: char > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 3.05/1.62 differential: trm > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_OFunc,type,
% 3.05/1.62 func: char > trm > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_ONumber,type,
% 3.05/1.62 number: real > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_OPlus,type,
% 3.05/1.62 plus: trm > trm > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_OTimes,type,
% 3.05/1.62 times: trm > trm > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Syntax_Otrm_OVar,type,
% 3.05/1.62 var: variable > trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 3.05/1.62 uSubst716837505ntialo: option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 3.05/1.62 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo__rel,type,
% 3.05/1.62 uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 3.05/1.62 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso__rel,type,
% 3.05/1.62 uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 3.05/1.62 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso__rel,type,
% 3.05/1.62 uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odot,type,
% 3.05/1.62 uSubst_Mirabelle_dot: trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 3.05/1.62 uSubst1408967625substt: trm > produc1418842292n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 3.05/1.62 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 3.05/1.62 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 3.05/1.62 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 3.05/1.62 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.05/1.62 accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 3.05/1.62 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_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,type,
% 3.05/1.62 member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_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,type,
% 3.05/1.62 member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_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__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,
% 3.05/1.62 member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 3.05/1.62 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 3.05/1.62 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__String__Ochar,type,
% 3.05/1.62 member_char: char > set_char > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 3.05/1.62 member_variable: variable > set_variable > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_U,type,
% 3.05/1.62 u: set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_V,type,
% 3.05/1.62 v: set_variable ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v__092_060sigma_062,type,
% 3.05/1.62 sigma: produc1418842292n_game ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_f____,type,
% 3.05/1.62 f: char ).
% 3.05/1.62
% 3.05/1.62 thf(fact_0_f2,axiom,
% 3.05/1.62 ! [Z: option_trm,F: trm > option_trm,Za: option_trm] :
% 3.05/1.62 ( ( ( Za = none_trm )
% 3.05/1.62 => ( ( case_o487727941rm_trm @ Z @ F @ Za )
% 3.05/1.62 = Z ) )
% 3.05/1.62 & ( ( Za != none_trm )
% 3.05/1.62 => ( ( case_o487727941rm_trm @ Z @ F @ Za )
% 3.05/1.62 = ( F @ ( the_trm @ Za ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_1_Const_Oprems_I1_J,axiom,
% 3.05/1.62 ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 3.05/1.62 != none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_2_Const_Oprems_I2_J,axiom,
% 3.05/1.62 ( ( uSubst516392818stappt @ sigma @ v @ ( const @ f ) )
% 3.05/1.62 != none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_3_f3,axiom,
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ u )
% 3.05/1.62 = bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ v )
% 3.05/1.62 = bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_5_usappconst__def,axiom,
% 3.05/1.62 ( uSubst1559070963pconst
% 3.05/1.62 = ( ^ [Sigma: produc1418842292n_game,U: set_variable,F2: char] :
% 3.05/1.62 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F2 ) )
% 3.05/1.62 @ ^ [R: trm] :
% 3.05/1.62 ( if_option_trm
% 3.05/1.62 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 @ ( some_trm @ R )
% 3.05/1.62 @ none_trm )
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma
% 3.05/1.62 @ F2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_6_f1,axiom,
% 3.05/1.62 ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 3.05/1.62 = ( case_o487727941rm_trm @ ( some_trm @ ( const @ f ) )
% 3.05/1.62 @ ^ [T: trm] :
% 3.05/1.62 ( if_option_trm
% 3.05/1.62 @ ( ( inf_inf_set_variable @ ( static_FVT @ T ) @ u )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 @ ( some_trm @ T )
% 3.05/1.62 @ none_trm )
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_7_usubstappt_Osimps_I3_J,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 3.05/1.62 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 3.05/1.62 = ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_8_undeft__None,axiom,
% 3.05/1.62 none_trm = none_trm ).
% 3.05/1.62
% 3.05/1.62 thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,axiom,
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ v )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 => ( ( some_trm
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) )
% 3.05/1.62 & ( ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ v )
% 3.05/1.62 != bot_bot_set_variable )
% 3.05/1.62 => ( none_trm
% 3.05/1.62 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,axiom,
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ u )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 => ( ( some_trm
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 = ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
% 3.05/1.62 & ( ( ( inf_inf_set_variable
% 3.05/1.62 @ ( static_FVT
% 3.05/1.62 @ ( the_trm
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ sigma
% 3.05/1.62 @ f ) ) )
% 3.05/1.62 @ u )
% 3.05/1.62 != bot_bot_set_variable )
% 3.05/1.62 => ( none_trm
% 3.05/1.62 = ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_11_trm_Oinject_I3_J,axiom,
% 3.05/1.62 ! [X3: char,Y3: char] :
% 3.05/1.62 ( ( ( const @ X3 )
% 3.05/1.62 = ( const @ Y3 ) )
% 3.05/1.62 = ( X3 = Y3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_12_case__prod__app,axiom,
% 3.05/1.62 ( produc1250175341on_fml
% 3.05/1.62 = ( ^ [F2: ( char > option_trm ) > produc62062515n_game > char > option_fml,X: produc1418842292n_game,Y: char] :
% 3.05/1.62 ( produc1499310791on_fml
% 3.05/1.62 @ ^ [L: char > option_trm,R: produc62062515n_game] : ( F2 @ L @ R @ Y )
% 3.05/1.62 @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_13_case__prod__app,axiom,
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_trm,X: produc62062515n_game,Y: char] :
% 3.05/1.62 ( produc692578258on_trm
% 3.05/1.62 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 3.05/1.62 @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_14_case__prod__app,axiom,
% 3.05/1.62 ( produc1615133358on_fml
% 3.05/1.62 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 3.05/1.62 ( produc154833544on_fml
% 3.05/1.62 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 3.05/1.62 @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_15_case__prod__app,axiom,
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 3.05/1.62 ( produc885547027on_trm
% 3.05/1.62 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 3.05/1.62 @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_16_case__prod__app,axiom,
% 3.05/1.62 ( produc1420172399on_fml
% 3.05/1.62 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 3.05/1.62 ( produc347802313on_fml
% 3.05/1.62 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 3.05/1.62 @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_17_usubstappt__const,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R2 ) )
% 3.05/1.62 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 3.05/1.62 = ( some_trm @ R2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_18_usubstappt__const__conv,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 3.05/1.62 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = none_trm )
% 3.05/1.62 | ? [R3: trm] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R3 ) )
% 3.05/1.62 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_19_usappconst__simp,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R2 ) )
% 3.05/1.62 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 => ( ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 )
% 3.05/1.62 = ( some_trm @ R2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_20_usappconst__conv,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 3.05/1.62 ( ( ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = none_trm )
% 3.05/1.62 | ? [R3: trm] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [F0: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R3 ) )
% 3.05/1.62 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_21_ODEo_Oinduct,axiom,
% 3.05/1.62 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 3.05/1.62 ( ! [X2: char,Theta: trm] : ( P @ X2 @ ( some_trm @ Theta ) )
% 3.05/1.62 => ( ! [X2: char] : ( P @ X2 @ none_trm )
% 3.05/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_22_undeft__equiv,axiom,
% 3.05/1.62 ! [Theta2: option_trm] :
% 3.05/1.62 ( ( Theta2 != none_trm )
% 3.05/1.62 = ( ? [T: trm] :
% 3.05/1.62 ( Theta2
% 3.05/1.62 = ( some_trm @ T ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_23_Timeso_Oinduct,axiom,
% 3.05/1.62 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 3.05/1.62 ( ! [Theta: trm,Eta: trm] : ( P @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 3.05/1.62 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 3.05/1.62 => ( ! [V: trm] : ( P @ ( some_trm @ V ) @ none_trm )
% 3.05/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_24_Assigno_Oinduct,axiom,
% 3.05/1.62 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 3.05/1.62 ( ! [X2: variable,Theta: trm] : ( P @ X2 @ ( some_trm @ Theta ) )
% 3.05/1.62 => ( ! [X2: variable] : ( P @ X2 @ none_trm )
% 3.05/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_25_Aterm__Some,axiom,
% 3.05/1.62 some_trm = some_trm ).
% 3.05/1.62
% 3.05/1.62 thf(fact_26_Differentialo_Oinduct,axiom,
% 3.05/1.62 ! [P: option_trm > $o,A0: option_trm] :
% 3.05/1.62 ( ! [Theta: trm] : ( P @ ( some_trm @ Theta ) )
% 3.05/1.62 => ( ( P @ none_trm )
% 3.05/1.62 => ( P @ A0 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_27_Differentialo_Ocases,axiom,
% 3.05/1.62 ! [X4: option_trm] :
% 3.05/1.62 ( ! [Theta: trm] :
% 3.05/1.62 ( X4
% 3.05/1.62 != ( some_trm @ Theta ) )
% 3.05/1.62 => ( X4 = none_trm ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_28_option_Ocollapse,axiom,
% 3.05/1.62 ! [Option: option_trm] :
% 3.05/1.62 ( ( Option != none_trm )
% 3.05/1.62 => ( ( some_trm @ ( the_trm @ Option ) )
% 3.05/1.62 = Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_29_option_Ocollapse,axiom,
% 3.05/1.62 ! [Option: option_fml] :
% 3.05/1.62 ( ( Option != none_fml )
% 3.05/1.62 => ( ( some_fml @ ( the_fml @ Option ) )
% 3.05/1.62 = Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_30_option_Ocollapse,axiom,
% 3.05/1.62 ! [Option: option_game] :
% 3.05/1.62 ( ( Option != none_game )
% 3.05/1.62 => ( ( some_game @ ( the_game @ Option ) )
% 3.05/1.62 = Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_31_not__Some__eq,axiom,
% 3.05/1.62 ! [X4: option_trm] :
% 3.05/1.62 ( ( ! [Y: trm] :
% 3.05/1.62 ( X4
% 3.05/1.62 != ( some_trm @ Y ) ) )
% 3.05/1.62 = ( X4 = none_trm ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_32_not__Some__eq,axiom,
% 3.05/1.62 ! [X4: option_fml] :
% 3.05/1.62 ( ( ! [Y: fml] :
% 3.05/1.62 ( X4
% 3.05/1.62 != ( some_fml @ Y ) ) )
% 3.05/1.62 = ( X4 = none_fml ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_33_not__Some__eq,axiom,
% 3.05/1.62 ! [X4: option_game] :
% 3.05/1.62 ( ( ! [Y: game] :
% 3.05/1.62 ( X4
% 3.05/1.62 != ( some_game @ Y ) ) )
% 3.05/1.62 = ( X4 = none_game ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_34_not__None__eq,axiom,
% 3.05/1.62 ! [X4: option_trm] :
% 3.05/1.62 ( ( X4 != none_trm )
% 3.05/1.62 = ( ? [Y: trm] :
% 3.05/1.62 ( X4
% 3.05/1.62 = ( some_trm @ Y ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_35_not__None__eq,axiom,
% 3.05/1.62 ! [X4: option_fml] :
% 3.05/1.62 ( ( X4 != none_fml )
% 3.05/1.62 = ( ? [Y: fml] :
% 3.05/1.62 ( X4
% 3.05/1.62 = ( some_fml @ Y ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_36_not__None__eq,axiom,
% 3.05/1.62 ! [X4: option_game] :
% 3.05/1.62 ( ( X4 != none_game )
% 3.05/1.62 = ( ? [Y: game] :
% 3.05/1.62 ( X4
% 3.05/1.62 = ( some_game @ Y ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_37_inf__bot__left,axiom,
% 3.05/1.62 ! [X4: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X4 )
% 3.05/1.62 = bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_38_inf__bot__right,axiom,
% 3.05/1.62 ! [X4: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ bot_bot_set_variable )
% 3.05/1.62 = bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_39_usubstappt__func2,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable,Theta2: trm] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [F4: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R2 ) )
% 3.05/1.62 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 3.05/1.62 != bot_bot_set_variable )
% 3.05/1.62 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 3.05/1.62 = none_trm ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_40_option_Osplit__sel__asm,axiom,
% 3.05/1.62 ! [P: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.62 ( ( P @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.62 = ( ~ ( ( ( Option = none_trm )
% 3.05/1.62 & ~ ( P @ F1 ) )
% 3.05/1.62 | ( ( Option
% 3.05/1.62 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.62 & ~ ( P @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_41_option_Osplit__sel,axiom,
% 3.05/1.62 ! [P: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.62 ( ( P @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.62 = ( ( ( Option = none_trm )
% 3.05/1.62 => ( P @ F1 ) )
% 3.05/1.62 & ( ( Option
% 3.05/1.62 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.62 => ( P @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_42_usubstappt__func__conv,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 3.05/1.62 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 3.05/1.62 != none_trm )
% 3.05/1.62 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.62 != none_trm )
% 3.05/1.62 & ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [F4: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = none_trm )
% 3.05/1.62 | ? [R3: trm] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [F4: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R3 ) )
% 3.05/1.62 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_43_option_Ocase__eq__if,axiom,
% 3.05/1.62 ( case_o487727941rm_trm
% 3.05/1.62 = ( ^ [F12: option_trm,F23: trm > option_trm,Option2: option_trm] : ( if_option_trm @ ( Option2 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option2 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_44_inf__right__idem,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Y2 )
% 3.05/1.62 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_45_inf_Oright__idem,axiom,
% 3.05/1.62 ! [A: set_variable,B: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ B )
% 3.05/1.62 = ( inf_inf_set_variable @ A @ B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_46_inf__left__idem,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ X4 @ Y2 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_47_inf_Oleft__idem,axiom,
% 3.05/1.62 ! [A: set_variable,B: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B ) )
% 3.05/1.62 = ( inf_inf_set_variable @ A @ B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_48_inf__idem,axiom,
% 3.05/1.62 ! [X4: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ X4 )
% 3.05/1.62 = X4 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_49_inf_Oidem,axiom,
% 3.05/1.62 ! [A: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A @ A )
% 3.05/1.62 = A ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_50_option_Oinject,axiom,
% 3.05/1.62 ! [X22: trm,Y22: trm] :
% 3.05/1.62 ( ( ( some_trm @ X22 )
% 3.05/1.62 = ( some_trm @ Y22 ) )
% 3.05/1.62 = ( X22 = Y22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_51_option_Oinject,axiom,
% 3.05/1.62 ! [X22: fml,Y22: fml] :
% 3.05/1.62 ( ( ( some_fml @ X22 )
% 3.05/1.62 = ( some_fml @ Y22 ) )
% 3.05/1.62 = ( X22 = Y22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_52_option_Oinject,axiom,
% 3.05/1.62 ! [X22: game,Y22: game] :
% 3.05/1.62 ( ( ( some_game @ X22 )
% 3.05/1.62 = ( some_game @ Y22 ) )
% 3.05/1.62 = ( X22 = Y22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_53_trm_Oinject_I4_J,axiom,
% 3.05/1.62 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 3.05/1.62 ( ( ( func @ X41 @ X42 )
% 3.05/1.62 = ( func @ Y41 @ Y42 ) )
% 3.05/1.62 = ( ( X41 = Y41 )
% 3.05/1.62 & ( X42 = Y42 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_54_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.62 ! [Option: option_trm] :
% 3.05/1.62 ( ( Option != none_trm )
% 3.05/1.62 = ( case_option_o_trm @ $false
% 3.05/1.62 @ ^ [Uu: trm] : $true
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_55_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.62 ! [Option: option_fml] :
% 3.05/1.62 ( ( Option != none_fml )
% 3.05/1.62 = ( case_option_o_fml @ $false
% 3.05/1.62 @ ^ [Uu: fml] : $true
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_56_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.62 ! [Option: option_game] :
% 3.05/1.62 ( ( Option != none_game )
% 3.05/1.62 = ( case_option_o_game @ $false
% 3.05/1.62 @ ^ [Uu: game] : $true
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_57_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.62 ! [Option: option_trm] :
% 3.05/1.62 ( ( Option = none_trm )
% 3.05/1.62 = ( case_option_o_trm @ $true
% 3.05/1.62 @ ^ [Uu: trm] : $false
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_58_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.62 ! [Option: option_fml] :
% 3.05/1.62 ( ( Option = none_fml )
% 3.05/1.62 = ( case_option_o_fml @ $true
% 3.05/1.62 @ ^ [Uu: fml] : $false
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_59_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.62 ! [Option: option_game] :
% 3.05/1.62 ( ( Option = none_game )
% 3.05/1.62 = ( case_option_o_game @ $true
% 3.05/1.62 @ ^ [Uu: game] : $false
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_60_mem__Collect__eq,axiom,
% 3.05/1.62 ! [A: variable,P: variable > $o] :
% 3.05/1.62 ( ( member_variable @ A @ ( collect_variable @ P ) )
% 3.05/1.62 = ( P @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_61_mem__Collect__eq,axiom,
% 3.05/1.62 ! [A: char,P: char > $o] :
% 3.05/1.62 ( ( member_char @ A @ ( collect_char @ P ) )
% 3.05/1.62 = ( P @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_62_Collect__mem__eq,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ( collect_variable
% 3.05/1.62 @ ^ [X: variable] : ( member_variable @ X @ A2 ) )
% 3.05/1.62 = A2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_63_Collect__mem__eq,axiom,
% 3.05/1.62 ! [A2: set_char] :
% 3.05/1.62 ( ( collect_char
% 3.05/1.62 @ ^ [X: char] : ( member_char @ X @ A2 ) )
% 3.05/1.62 = A2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_64_Collect__cong,axiom,
% 3.05/1.62 ! [P: variable > $o,Q: variable > $o] :
% 3.05/1.62 ( ! [X2: variable] :
% 3.05/1.62 ( ( P @ X2 )
% 3.05/1.62 = ( Q @ X2 ) )
% 3.05/1.62 => ( ( collect_variable @ P )
% 3.05/1.62 = ( collect_variable @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_65_Collect__cong,axiom,
% 3.05/1.62 ! [P: char > $o,Q: char > $o] :
% 3.05/1.62 ( ! [X2: char] :
% 3.05/1.62 ( ( P @ X2 )
% 3.05/1.62 = ( Q @ X2 ) )
% 3.05/1.62 => ( ( collect_char @ P )
% 3.05/1.62 = ( collect_char @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_66_trm_Odistinct_I23_J,axiom,
% 3.05/1.62 ! [X3: char,X41: char,X42: trm] :
% 3.05/1.62 ( ( const @ X3 )
% 3.05/1.62 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_67_case__optionE,axiom,
% 3.05/1.62 ! [P: $o,Q: trm > $o,X4: option_trm] :
% 3.05/1.62 ( ( case_option_o_trm @ P @ Q @ X4 )
% 3.05/1.62 => ( ( ( X4 = none_trm )
% 3.05/1.62 => ~ P )
% 3.05/1.62 => ~ ! [Y4: trm] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_trm @ Y4 ) )
% 3.05/1.62 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_68_case__optionE,axiom,
% 3.05/1.62 ! [P: $o,Q: fml > $o,X4: option_fml] :
% 3.05/1.62 ( ( case_option_o_fml @ P @ Q @ X4 )
% 3.05/1.62 => ( ( ( X4 = none_fml )
% 3.05/1.62 => ~ P )
% 3.05/1.62 => ~ ! [Y4: fml] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_fml @ Y4 ) )
% 3.05/1.62 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_69_case__optionE,axiom,
% 3.05/1.62 ! [P: $o,Q: game > $o,X4: option_game] :
% 3.05/1.62 ( ( case_option_o_game @ P @ Q @ X4 )
% 3.05/1.62 => ( ( ( X4 = none_game )
% 3.05/1.62 => ~ P )
% 3.05/1.62 => ~ ! [Y4: game] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_game @ Y4 ) )
% 3.05/1.62 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_70_inf__left__commute,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X4 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_71_inf_Oleft__commute,axiom,
% 3.05/1.62 ! [B: set_variable,A: set_variable,C: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ B @ ( inf_inf_set_variable @ A @ C ) )
% 3.05/1.62 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_72_inf__commute,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_73_inf_Ocommute,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [A3: set_variable,B2: set_variable] : ( inf_inf_set_variable @ B2 @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_74_inf__assoc,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Z2 )
% 3.05/1.62 = ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_75_inf_Oassoc,axiom,
% 3.05/1.62 ! [A: set_variable,B: set_variable,C: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ C )
% 3.05/1.62 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_76_boolean__algebra__cancel_Oinf2,axiom,
% 3.05/1.62 ! [B3: set_variable,K: set_variable,B: set_variable,A: set_variable] :
% 3.05/1.62 ( ( B3
% 3.05/1.62 = ( inf_inf_set_variable @ K @ B ) )
% 3.05/1.62 => ( ( inf_inf_set_variable @ A @ B3 )
% 3.05/1.62 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_77_boolean__algebra__cancel_Oinf1,axiom,
% 3.05/1.62 ! [A2: set_variable,K: set_variable,A: set_variable,B: set_variable] :
% 3.05/1.62 ( ( A2
% 3.05/1.62 = ( inf_inf_set_variable @ K @ A ) )
% 3.05/1.62 => ( ( inf_inf_set_variable @ A2 @ B )
% 3.05/1.62 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_78_inf__sup__aci_I1_J,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_79_inf__sup__aci_I2_J,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X4 @ Y2 ) @ Z2 )
% 3.05/1.62 = ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_80_inf__sup__aci_I3_J,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X4 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_81_inf__sup__aci_I4_J,axiom,
% 3.05/1.62 ! [X4: set_variable,Y2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ X4 @ ( inf_inf_set_variable @ X4 @ Y2 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ X4 @ Y2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_82_option_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.62 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.62 = ( case_o487727941rm_trm @ ( H @ F1 )
% 3.05/1.62 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_83_option_Odistinct_I1_J,axiom,
% 3.05/1.62 ! [X22: trm] :
% 3.05/1.62 ( none_trm
% 3.05/1.62 != ( some_trm @ X22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_84_option_Odistinct_I1_J,axiom,
% 3.05/1.62 ! [X22: fml] :
% 3.05/1.62 ( none_fml
% 3.05/1.62 != ( some_fml @ X22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_85_option_Odistinct_I1_J,axiom,
% 3.05/1.62 ! [X22: game] :
% 3.05/1.62 ( none_game
% 3.05/1.62 != ( some_game @ X22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_86_option_OdiscI,axiom,
% 3.05/1.62 ! [Option: option_trm,X22: trm] :
% 3.05/1.62 ( ( Option
% 3.05/1.62 = ( some_trm @ X22 ) )
% 3.05/1.62 => ( Option != none_trm ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_87_option_OdiscI,axiom,
% 3.05/1.62 ! [Option: option_fml,X22: fml] :
% 3.05/1.62 ( ( Option
% 3.05/1.62 = ( some_fml @ X22 ) )
% 3.05/1.62 => ( Option != none_fml ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_88_option_OdiscI,axiom,
% 3.05/1.62 ! [Option: option_game,X22: game] :
% 3.05/1.62 ( ( Option
% 3.05/1.62 = ( some_game @ X22 ) )
% 3.05/1.62 => ( Option != none_game ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_89_option_Oexhaust,axiom,
% 3.05/1.62 ! [Y2: option_trm] :
% 3.05/1.62 ( ( Y2 != none_trm )
% 3.05/1.62 => ~ ! [X23: trm] :
% 3.05/1.62 ( Y2
% 3.05/1.62 != ( some_trm @ X23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_90_option_Oexhaust,axiom,
% 3.05/1.62 ! [Y2: option_fml] :
% 3.05/1.62 ( ( Y2 != none_fml )
% 3.05/1.62 => ~ ! [X23: fml] :
% 3.05/1.62 ( Y2
% 3.05/1.62 != ( some_fml @ X23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_91_option_Oexhaust,axiom,
% 3.05/1.62 ! [Y2: option_game] :
% 3.05/1.62 ( ( Y2 != none_game )
% 3.05/1.62 => ~ ! [X23: game] :
% 3.05/1.62 ( Y2
% 3.05/1.62 != ( some_game @ X23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_92_option_Oinducts,axiom,
% 3.05/1.62 ! [P: option_trm > $o,Option: option_trm] :
% 3.05/1.62 ( ( P @ none_trm )
% 3.05/1.62 => ( ! [X2: trm] : ( P @ ( some_trm @ X2 ) )
% 3.05/1.62 => ( P @ Option ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_93_option_Oinducts,axiom,
% 3.05/1.62 ! [P: option_fml > $o,Option: option_fml] :
% 3.05/1.62 ( ( P @ none_fml )
% 3.05/1.62 => ( ! [X2: fml] : ( P @ ( some_fml @ X2 ) )
% 3.05/1.62 => ( P @ Option ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_94_option_Oinducts,axiom,
% 3.05/1.62 ! [P: option_game > $o,Option: option_game] :
% 3.05/1.62 ( ( P @ none_game )
% 3.05/1.62 => ( ! [X2: game] : ( P @ ( some_game @ X2 ) )
% 3.05/1.62 => ( P @ Option ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_95_split__option__ex,axiom,
% 3.05/1.62 ( ( ^ [P2: option_trm > $o] :
% 3.05/1.62 ? [X5: option_trm] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_trm > $o] :
% 3.05/1.62 ( ( P3 @ none_trm )
% 3.05/1.62 | ? [X: trm] : ( P3 @ ( some_trm @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_96_split__option__ex,axiom,
% 3.05/1.62 ( ( ^ [P2: option_fml > $o] :
% 3.05/1.62 ? [X5: option_fml] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_fml > $o] :
% 3.05/1.62 ( ( P3 @ none_fml )
% 3.05/1.62 | ? [X: fml] : ( P3 @ ( some_fml @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_97_split__option__ex,axiom,
% 3.05/1.62 ( ( ^ [P2: option_game > $o] :
% 3.05/1.62 ? [X5: option_game] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_game > $o] :
% 3.05/1.62 ( ( P3 @ none_game )
% 3.05/1.62 | ? [X: game] : ( P3 @ ( some_game @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_98_split__option__all,axiom,
% 3.05/1.62 ( ( ^ [P2: option_trm > $o] :
% 3.05/1.62 ! [X5: option_trm] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_trm > $o] :
% 3.05/1.62 ( ( P3 @ none_trm )
% 3.05/1.62 & ! [X: trm] : ( P3 @ ( some_trm @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_99_split__option__all,axiom,
% 3.05/1.62 ( ( ^ [P2: option_fml > $o] :
% 3.05/1.62 ! [X5: option_fml] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_fml > $o] :
% 3.05/1.62 ( ( P3 @ none_fml )
% 3.05/1.62 & ! [X: fml] : ( P3 @ ( some_fml @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_100_split__option__all,axiom,
% 3.05/1.62 ( ( ^ [P2: option_game > $o] :
% 3.05/1.62 ! [X5: option_game] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_game > $o] :
% 3.05/1.62 ( ( P3 @ none_game )
% 3.05/1.62 & ! [X: game] : ( P3 @ ( some_game @ X ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_101_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_trm,P: option_trm > option_trm > $o,Y2: option_trm] :
% 3.05/1.62 ( ( ( X4 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: trm,B4: trm] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_trm @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_trm @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_102_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_trm,P: option_trm > option_fml > $o,Y2: option_fml] :
% 3.05/1.62 ( ( ( X4 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: trm,B4: fml] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_trm @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_fml @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_103_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_trm,P: option_trm > option_game > $o,Y2: option_game] :
% 3.05/1.62 ( ( ( X4 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: trm,B4: game] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_trm @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_game @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_104_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_fml,P: option_fml > option_trm > $o,Y2: option_trm] :
% 3.05/1.62 ( ( ( X4 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: fml,B4: trm] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_fml @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_trm @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_105_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_fml,P: option_fml > option_fml > $o,Y2: option_fml] :
% 3.05/1.62 ( ( ( X4 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: fml,B4: fml] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_fml @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_fml @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_106_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_fml,P: option_fml > option_game > $o,Y2: option_game] :
% 3.05/1.62 ( ( ( X4 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: fml,B4: game] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_fml @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_game @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_107_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_game,P: option_game > option_trm > $o,Y2: option_trm] :
% 3.05/1.62 ( ( ( X4 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_trm )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: game,B4: trm] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_game @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_trm @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_108_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_game,P: option_game > option_fml > $o,Y2: option_fml] :
% 3.05/1.62 ( ( ( X4 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_fml )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: game,B4: fml] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_game @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_fml @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_109_combine__options__cases,axiom,
% 3.05/1.62 ! [X4: option_game,P: option_game > option_game > $o,Y2: option_game] :
% 3.05/1.62 ( ( ( X4 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ( ( Y2 = none_game )
% 3.05/1.62 => ( P @ X4 @ Y2 ) )
% 3.05/1.62 => ( ! [A4: game,B4: game] :
% 3.05/1.62 ( ( X4
% 3.05/1.62 = ( some_game @ A4 ) )
% 3.05/1.62 => ( ( Y2
% 3.05/1.62 = ( some_game @ B4 ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) )
% 3.05/1.62 => ( P @ X4 @ Y2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_110_option_Osimps_I4_J,axiom,
% 3.05/1.62 ! [F1: option_trm,F22: trm > option_trm] :
% 3.05/1.62 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 3.05/1.62 = F1 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_111_option_Osimps_I5_J,axiom,
% 3.05/1.62 ! [F1: option_trm,F22: trm > option_trm,X22: trm] :
% 3.05/1.62 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X22 ) )
% 3.05/1.62 = ( F22 @ X22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_112_option_Oexpand,axiom,
% 3.05/1.62 ! [Option: option_trm,Option3: option_trm] :
% 3.05/1.62 ( ( ( Option = none_trm )
% 3.05/1.62 = ( Option3 = none_trm ) )
% 3.05/1.62 => ( ( ( Option != none_trm )
% 3.05/1.62 => ( ( Option3 != none_trm )
% 3.05/1.62 => ( ( the_trm @ Option )
% 3.05/1.62 = ( the_trm @ Option3 ) ) ) )
% 3.05/1.62 => ( Option = Option3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_113_option_Oexpand,axiom,
% 3.05/1.62 ! [Option: option_fml,Option3: option_fml] :
% 3.05/1.62 ( ( ( Option = none_fml )
% 3.05/1.62 = ( Option3 = none_fml ) )
% 3.05/1.62 => ( ( ( Option != none_fml )
% 3.05/1.62 => ( ( Option3 != none_fml )
% 3.05/1.62 => ( ( the_fml @ Option )
% 3.05/1.62 = ( the_fml @ Option3 ) ) ) )
% 3.05/1.62 => ( Option = Option3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_114_option_Oexpand,axiom,
% 3.05/1.62 ! [Option: option_game,Option3: option_game] :
% 3.05/1.62 ( ( ( Option = none_game )
% 3.05/1.62 = ( Option3 = none_game ) )
% 3.05/1.62 => ( ( ( Option != none_game )
% 3.05/1.62 => ( ( Option3 != none_game )
% 3.05/1.62 => ( ( the_game @ Option )
% 3.05/1.62 = ( the_game @ Option3 ) ) ) )
% 3.05/1.62 => ( Option = Option3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_115_option_Osel,axiom,
% 3.05/1.62 ! [X22: trm] :
% 3.05/1.62 ( ( the_trm @ ( some_trm @ X22 ) )
% 3.05/1.62 = X22 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_116_option_Osel,axiom,
% 3.05/1.62 ! [X22: fml] :
% 3.05/1.62 ( ( the_fml @ ( some_fml @ X22 ) )
% 3.05/1.62 = X22 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_117_option_Osel,axiom,
% 3.05/1.62 ! [X22: game] :
% 3.05/1.62 ( ( the_game @ ( some_game @ X22 ) )
% 3.05/1.62 = X22 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_118_option_Oexhaust__sel,axiom,
% 3.05/1.62 ! [Option: option_trm] :
% 3.05/1.62 ( ( Option != none_trm )
% 3.05/1.62 => ( Option
% 3.05/1.62 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_119_option_Oexhaust__sel,axiom,
% 3.05/1.62 ! [Option: option_fml] :
% 3.05/1.62 ( ( Option != none_fml )
% 3.05/1.62 => ( Option
% 3.05/1.62 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_120_option_Oexhaust__sel,axiom,
% 3.05/1.62 ! [Option: option_game] :
% 3.05/1.62 ( ( Option != none_game )
% 3.05/1.62 => ( Option
% 3.05/1.62 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_121_usubstappt__func,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,F3: char,R2: trm,U2: set_variable,Theta2: trm,Sigma_theta: trm] :
% 3.05/1.62 ( ( ( produc866613687on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [F4: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 )
% 3.05/1.62 = ( some_trm @ R2 ) )
% 3.05/1.62 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.62 = ( some_trm @ Sigma_theta ) )
% 3.05/1.62 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 3.05/1.62 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_122_usubstappt_Osimps_I4_J,axiom,
% 3.05/1.62 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 3.05/1.62 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 3.05/1.62 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.62 @ ^ [Sigma_theta2: trm] :
% 3.05/1.62 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta2 ) )
% 3.05/1.62 @ ^ [R: trm] :
% 3.05/1.62 ( if_option_trm
% 3.05/1.62 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 3.05/1.62 @ none_trm )
% 3.05/1.62 @ ( produc866613687on_trm
% 3.05/1.62 @ ^ [Uu: char > option_trm] :
% 3.05/1.62 ( produc1231571704on_trm
% 3.05/1.62 @ ^ [F4: char > option_trm] :
% 3.05/1.62 ( produc1036610745on_trm
% 3.05/1.62 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.62 @ Sigma2
% 3.05/1.62 @ F3 ) )
% 3.05/1.62 @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_123_Int__iff,axiom,
% 3.05/1.62 ! [C: char,A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 3.05/1.62 = ( ( member_char @ C @ A2 )
% 3.05/1.62 & ( member_char @ C @ B3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_124_Int__iff,axiom,
% 3.05/1.62 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.62 = ( ( member_variable @ C @ A2 )
% 3.05/1.62 & ( member_variable @ C @ B3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_125_IntI,axiom,
% 3.05/1.62 ! [C: char,A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( member_char @ C @ A2 )
% 3.05/1.62 => ( ( member_char @ C @ B3 )
% 3.05/1.62 => ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_126_IntI,axiom,
% 3.05/1.62 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( member_variable @ C @ A2 )
% 3.05/1.62 => ( ( member_variable @ C @ B3 )
% 3.05/1.62 => ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_127_empty__Collect__eq,axiom,
% 3.05/1.62 ! [P: char > $o] :
% 3.05/1.62 ( ( bot_bot_set_char
% 3.05/1.62 = ( collect_char @ P ) )
% 3.05/1.62 = ( ! [X: char] :
% 3.05/1.62 ~ ( P @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_128_empty__Collect__eq,axiom,
% 3.05/1.62 ! [P: variable > $o] :
% 3.05/1.62 ( ( bot_bot_set_variable
% 3.05/1.62 = ( collect_variable @ P ) )
% 3.05/1.62 = ( ! [X: variable] :
% 3.05/1.62 ~ ( P @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_129_Collect__empty__eq,axiom,
% 3.05/1.62 ! [P: char > $o] :
% 3.05/1.62 ( ( ( collect_char @ P )
% 3.05/1.62 = bot_bot_set_char )
% 3.05/1.62 = ( ! [X: char] :
% 3.05/1.62 ~ ( P @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_130_Collect__empty__eq,axiom,
% 3.05/1.62 ! [P: variable > $o] :
% 3.05/1.62 ( ( ( collect_variable @ P )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 = ( ! [X: variable] :
% 3.05/1.62 ~ ( P @ X ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_131_all__not__in__conv,axiom,
% 3.05/1.62 ! [A2: set_char] :
% 3.05/1.62 ( ( ! [X: char] :
% 3.05/1.62 ~ ( member_char @ X @ A2 ) )
% 3.05/1.62 = ( A2 = bot_bot_set_char ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_132_all__not__in__conv,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ( ! [X: variable] :
% 3.05/1.62 ~ ( member_variable @ X @ A2 ) )
% 3.05/1.62 = ( A2 = bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_133_empty__iff,axiom,
% 3.05/1.62 ! [C: char] :
% 3.05/1.62 ~ ( member_char @ C @ bot_bot_set_char ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_134_empty__iff,axiom,
% 3.05/1.62 ! [C: variable] :
% 3.05/1.62 ~ ( member_variable @ C @ bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_135_emptyE,axiom,
% 3.05/1.62 ! [A: char] :
% 3.05/1.62 ~ ( member_char @ A @ bot_bot_set_char ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_136_emptyE,axiom,
% 3.05/1.62 ! [A: variable] :
% 3.05/1.62 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_137_equals0D,axiom,
% 3.05/1.62 ! [A2: set_char,A: char] :
% 3.05/1.62 ( ( A2 = bot_bot_set_char )
% 3.05/1.62 => ~ ( member_char @ A @ A2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_138_equals0D,axiom,
% 3.05/1.62 ! [A2: set_variable,A: variable] :
% 3.05/1.62 ( ( A2 = bot_bot_set_variable )
% 3.05/1.62 => ~ ( member_variable @ A @ A2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_139_equals0I,axiom,
% 3.05/1.62 ! [A2: set_char] :
% 3.05/1.62 ( ! [Y4: char] :
% 3.05/1.62 ~ ( member_char @ Y4 @ A2 )
% 3.05/1.62 => ( A2 = bot_bot_set_char ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_140_equals0I,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ! [Y4: variable] :
% 3.05/1.62 ~ ( member_variable @ Y4 @ A2 )
% 3.05/1.62 => ( A2 = bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_141_ex__in__conv,axiom,
% 3.05/1.62 ! [A2: set_char] :
% 3.05/1.62 ( ( ? [X: char] : ( member_char @ X @ A2 ) )
% 3.05/1.62 = ( A2 != bot_bot_set_char ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_142_ex__in__conv,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ( ? [X: variable] : ( member_variable @ X @ A2 ) )
% 3.05/1.62 = ( A2 != bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_143_bot__set__def,axiom,
% 3.05/1.62 ( bot_bot_set_char
% 3.05/1.62 = ( collect_char @ bot_bot_char_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_144_bot__set__def,axiom,
% 3.05/1.62 ( bot_bot_set_variable
% 3.05/1.62 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_145_IntE,axiom,
% 3.05/1.62 ! [C: char,A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 3.05/1.62 => ~ ( ( member_char @ C @ A2 )
% 3.05/1.62 => ~ ( member_char @ C @ B3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_146_IntE,axiom,
% 3.05/1.62 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.62 => ~ ( ( member_variable @ C @ A2 )
% 3.05/1.62 => ~ ( member_variable @ C @ B3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_147_IntD1,axiom,
% 3.05/1.62 ! [C: char,A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 3.05/1.62 => ( member_char @ C @ A2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_148_IntD1,axiom,
% 3.05/1.62 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.62 => ( member_variable @ C @ A2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_149_IntD2,axiom,
% 3.05/1.62 ! [C: char,A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( member_char @ C @ ( inf_inf_set_char @ A2 @ B3 ) )
% 3.05/1.62 => ( member_char @ C @ B3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_150_IntD2,axiom,
% 3.05/1.62 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.62 => ( member_variable @ C @ B3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_151_Int__assoc,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 3.05/1.62 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_152_Int__absorb,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A2 @ A2 )
% 3.05/1.62 = A2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_153_Int__commute,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_154_Int__left__absorb,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_155_Int__left__commute,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 3.05/1.62 = ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_156_empty__def,axiom,
% 3.05/1.62 ( bot_bot_set_char
% 3.05/1.62 = ( collect_char
% 3.05/1.62 @ ^ [X: char] : $false ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_157_empty__def,axiom,
% 3.05/1.62 ( bot_bot_set_variable
% 3.05/1.62 = ( collect_variable
% 3.05/1.62 @ ^ [X: variable] : $false ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_158_Collect__conj__eq,axiom,
% 3.05/1.62 ! [P: char > $o,Q: char > $o] :
% 3.05/1.62 ( ( collect_char
% 3.05/1.62 @ ^ [X: char] :
% 3.05/1.62 ( ( P @ X )
% 3.05/1.62 & ( Q @ X ) ) )
% 3.05/1.62 = ( inf_inf_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_159_Collect__conj__eq,axiom,
% 3.05/1.62 ! [P: variable > $o,Q: variable > $o] :
% 3.05/1.62 ( ( collect_variable
% 3.05/1.62 @ ^ [X: variable] :
% 3.05/1.62 ( ( P @ X )
% 3.05/1.62 & ( Q @ X ) ) )
% 3.05/1.62 = ( inf_inf_set_variable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_160_Int__Collect,axiom,
% 3.05/1.62 ! [X4: char,A2: set_char,P: char > $o] :
% 3.05/1.62 ( ( member_char @ X4 @ ( inf_inf_set_char @ A2 @ ( collect_char @ P ) ) )
% 3.05/1.62 = ( ( member_char @ X4 @ A2 )
% 3.05/1.62 & ( P @ X4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_161_Int__Collect,axiom,
% 3.05/1.62 ! [X4: variable,A2: set_variable,P: variable > $o] :
% 3.05/1.62 ( ( member_variable @ X4 @ ( inf_inf_set_variable @ A2 @ ( collect_variable @ P ) ) )
% 3.05/1.62 = ( ( member_variable @ X4 @ A2 )
% 3.05/1.62 & ( P @ X4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_162_Int__def,axiom,
% 3.05/1.62 ( inf_inf_set_char
% 3.05/1.62 = ( ^ [A5: set_char,B5: set_char] :
% 3.05/1.62 ( collect_char
% 3.05/1.62 @ ^ [X: char] :
% 3.05/1.62 ( ( member_char @ X @ A5 )
% 3.05/1.62 & ( member_char @ X @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_163_Int__def,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.05/1.62 ( collect_variable
% 3.05/1.62 @ ^ [X: variable] :
% 3.05/1.62 ( ( member_variable @ X @ A5 )
% 3.05/1.62 & ( member_variable @ X @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_164_inf__set__def,axiom,
% 3.05/1.62 ( inf_inf_set_char
% 3.05/1.62 = ( ^ [A5: set_char,B5: set_char] :
% 3.05/1.62 ( collect_char
% 3.05/1.62 @ ( inf_inf_char_o
% 3.05/1.62 @ ^ [X: char] : ( member_char @ X @ A5 )
% 3.05/1.62 @ ^ [X: char] : ( member_char @ X @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_165_inf__set__def,axiom,
% 3.05/1.62 ( inf_inf_set_variable
% 3.05/1.62 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.05/1.62 ( collect_variable
% 3.05/1.62 @ ( inf_inf_variable_o
% 3.05/1.62 @ ^ [X: variable] : ( member_variable @ X @ A5 )
% 3.05/1.62 @ ^ [X: variable] : ( member_variable @ X @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_166_Int__emptyI,axiom,
% 3.05/1.62 ! [A2: set_char,B3: set_char] :
% 3.05/1.62 ( ! [X2: char] :
% 3.05/1.62 ( ( member_char @ X2 @ A2 )
% 3.05/1.62 => ~ ( member_char @ X2 @ B3 ) )
% 3.05/1.62 => ( ( inf_inf_set_char @ A2 @ B3 )
% 3.05/1.62 = bot_bot_set_char ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_167_Int__emptyI,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ! [X2: variable] :
% 3.05/1.62 ( ( member_variable @ X2 @ A2 )
% 3.05/1.62 => ~ ( member_variable @ X2 @ B3 ) )
% 3.05/1.62 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.62 = bot_bot_set_variable ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_168_disjoint__iff,axiom,
% 3.05/1.62 ! [A2: set_char,B3: set_char] :
% 3.05/1.62 ( ( ( inf_inf_set_char @ A2 @ B3 )
% 3.05/1.62 = bot_bot_set_char )
% 3.05/1.62 = ( ! [X: char] :
% 3.05/1.62 ( ( member_char @ X @ A2 )
% 3.05/1.62 => ~ ( member_char @ X @ B3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_169_disjoint__iff,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 = ( ! [X: variable] :
% 3.05/1.62 ( ( member_variable @ X @ A2 )
% 3.05/1.62 => ~ ( member_variable @ X @ B3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_170_Int__empty__left,axiom,
% 3.05/1.62 ! [B3: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B3 )
% 3.05/1.62 = bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_171_Int__empty__right,axiom,
% 3.05/1.62 ! [A2: set_variable] :
% 3.05/1.62 ( ( inf_inf_set_variable @ A2 @ bot_bot_set_variable )
% 3.05/1.62 = bot_bot_set_variable ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_172_disjoint__iff__not__equal,axiom,
% 3.05/1.62 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.62 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.62 = bot_bot_set_variable )
% 3.05/1.62 = ( ! [X: variable] :
% 3.05/1.62 ( ( member_variable @ X @ A2 )
% 3.05/1.62 => ! [Y: variable] :
% 3.05/1.62 ( ( member_variable @ Y @ B3 )
% 3.05/1.62 => ( X != Y ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_173_disjE__realizer2,axiom,
% 3.05/1.62 ! [P: $o,Q: trm > $o,X4: option_trm,R4: option_trm > $o,F3: option_trm,G: trm > option_trm] :
% 3.05/1.62 ( ( case_option_o_trm @ P @ Q @ X4 )
% 3.05/1.62 => ( ( P
% 3.05/1.62 => ( R4 @ F3 ) )
% 3.05/1.62 => ( ! [Q2: trm] :
% 3.05/1.62 ( ( Q @ Q2 )
% 3.05/1.62 => ( R4 @ ( G @ Q2 ) ) )
% 3.05/1.62 => ( R4 @ ( case_o487727941rm_trm @ F3 @ G @ X4 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_174_Set_Ois__empty__def,axiom,
% 3.05/1.62 ( is_empty_variable
% 3.05/1.62 = ( ^ [A5: set_variable] : ( A5 = bot_bot_set_variable ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_175_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,Prod: produc1418842292n_game] :
% 3.05/1.62 ( ( H @ ( produc1250175341on_fml @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1250175341on_fml
% 3.05/1.62 @ ^ [X1: char > option_trm,X24: produc62062515n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_176_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_trm ) > char > option_trm,F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,Prod: produc62062515n_game] :
% 3.05/1.62 ( ( H @ ( produc1231571704on_trm @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1231571704on_trm
% 3.05/1.62 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_177_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_trm ) > char > option_fml,F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,Prod: produc62062515n_game] :
% 3.05/1.62 ( ( H @ ( produc1231571704on_trm @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1615133358on_fml
% 3.05/1.62 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_178_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_fml ) > char > option_trm,F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,Prod: produc62062515n_game] :
% 3.05/1.62 ( ( H @ ( produc1615133358on_fml @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1231571704on_trm
% 3.05/1.62 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_179_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,Prod: produc62062515n_game] :
% 3.05/1.62 ( ( H @ ( produc1615133358on_fml @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1615133358on_fml
% 3.05/1.62 @ ^ [X1: char > option_trm,X24: produc799602994n_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_180_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_trm ) > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 3.05/1.62 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1036610745on_trm
% 3.05/1.62 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_181_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_trm ) > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 3.05/1.62 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1420172399on_fml
% 3.05/1.62 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_182_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_fml ) > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 3.05/1.62 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1036610745on_trm
% 3.05/1.62 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_183_prod_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: ( char > option_fml ) > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 3.05/1.62 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 3.05/1.62 = ( produc1420172399on_fml
% 3.05/1.62 @ ^ [X1: char > option_fml,X24: char > option_game] : ( H @ ( F3 @ X1 @ X24 ) )
% 3.05/1.62 @ Prod ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_184_inf__Int__eq,axiom,
% 3.05/1.62 ! [R4: set_char,S: set_char] :
% 3.05/1.62 ( ( inf_inf_char_o
% 3.05/1.62 @ ^ [X: char] : ( member_char @ X @ R4 )
% 3.05/1.62 @ ^ [X: char] : ( member_char @ X @ S ) )
% 3.05/1.62 = ( ^ [X: char] : ( member_char @ X @ ( inf_inf_set_char @ R4 @ S ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_185_inf__Int__eq,axiom,
% 3.05/1.62 ! [R4: set_variable,S: set_variable] :
% 3.05/1.62 ( ( inf_inf_variable_o
% 3.05/1.62 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 3.05/1.62 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 3.05/1.62 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_186_Timeso_Osimps_I3_J,axiom,
% 3.05/1.62 ! [V2: trm] :
% 3.05/1.62 ( ( uSubst918876924Timeso @ ( some_trm @ V2 ) @ none_trm )
% 3.05/1.62 = none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_187_Pluso_Osimps_I3_J,axiom,
% 3.05/1.62 ! [V2: trm] :
% 3.05/1.62 ( ( uSubst141955042_Pluso @ ( some_trm @ V2 ) @ none_trm )
% 3.05/1.62 = none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_188_Pluso_Osimps_I2_J,axiom,
% 3.05/1.62 ! [Eta2: option_trm] :
% 3.05/1.62 ( ( uSubst141955042_Pluso @ none_trm @ Eta2 )
% 3.05/1.62 = none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_189_Timeso_Osimps_I2_J,axiom,
% 3.05/1.62 ! [Eta2: option_trm] :
% 3.05/1.62 ( ( uSubst918876924Timeso @ none_trm @ Eta2 )
% 3.05/1.62 = none_trm ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_190_Pluso__undef,axiom,
% 3.05/1.62 ! [Theta2: option_trm,Eta2: option_trm] :
% 3.05/1.62 ( ( ( uSubst141955042_Pluso @ Theta2 @ Eta2 )
% 3.05/1.62 = none_trm )
% 3.05/1.62 = ( ( Theta2 = none_trm )
% 3.05/1.62 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_191_Timeso__undef,axiom,
% 3.05/1.62 ! [Theta2: option_trm,Eta2: option_trm] :
% 3.05/1.62 ( ( ( uSubst918876924Timeso @ Theta2 @ Eta2 )
% 3.05/1.63 = none_trm )
% 3.05/1.63 = ( ( Theta2 = none_trm )
% 3.05/1.63 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_192_bot__empty__eq,axiom,
% 3.05/1.63 ( bot_bot_char_o
% 3.05/1.63 = ( ^ [X: char] : ( member_char @ X @ bot_bot_set_char ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_193_bot__empty__eq,axiom,
% 3.05/1.63 ( bot_bot_variable_o
% 3.05/1.63 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_194_Collect__empty__eq__bot,axiom,
% 3.05/1.63 ! [P: char > $o] :
% 3.05/1.63 ( ( ( collect_char @ P )
% 3.05/1.63 = bot_bot_set_char )
% 3.05/1.63 = ( P = bot_bot_char_o ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_195_Collect__empty__eq__bot,axiom,
% 3.05/1.63 ! [P: variable > $o] :
% 3.05/1.63 ( ( ( collect_variable @ P )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 = ( P = bot_bot_variable_o ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_196_internal__case__prod__def,axiom,
% 3.05/1.63 produc1278328899on_fml = produc1250175341on_fml ).
% 3.05/1.63
% 3.05/1.63 thf(fact_197_internal__case__prod__def,axiom,
% 3.05/1.63 produc2141841102on_trm = produc1231571704on_trm ).
% 3.05/1.63
% 3.05/1.63 thf(fact_198_internal__case__prod__def,axiom,
% 3.05/1.63 produc377919108on_fml = produc1615133358on_fml ).
% 3.05/1.63
% 3.05/1.63 thf(fact_199_internal__case__prod__def,axiom,
% 3.05/1.63 produc1214549391on_trm = produc1036610745on_trm ).
% 3.05/1.63
% 3.05/1.63 thf(fact_200_internal__case__prod__def,axiom,
% 3.05/1.63 produc1598111045on_fml = produc1420172399on_fml ).
% 3.05/1.63
% 3.05/1.63 thf(fact_201_Pluso_Oelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst141955042_Pluso @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_trm @ ( plus @ Theta @ Eta ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( Y2 != none_trm ) )
% 3.05/1.63 => ~ ( ? [V: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_202_Timeso_Oelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst918876924Timeso @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_trm @ ( times @ Theta @ Eta ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( Y2 != none_trm ) )
% 3.05/1.63 => ~ ( ? [V: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_203_trm_Oinject_I5_J,axiom,
% 3.05/1.63 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 3.05/1.63 ( ( ( plus @ X51 @ X52 )
% 3.05/1.63 = ( plus @ Y51 @ Y52 ) )
% 3.05/1.63 = ( ( X51 = Y51 )
% 3.05/1.63 & ( X52 = Y52 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_204_trm_Oinject_I6_J,axiom,
% 3.05/1.63 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 3.05/1.63 ( ( ( times @ X61 @ X62 )
% 3.05/1.63 = ( times @ Y61 @ Y62 ) )
% 3.05/1.63 = ( ( X61 = Y61 )
% 3.05/1.63 & ( X62 = Y62 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_205_trm_Odistinct_I37_J,axiom,
% 3.05/1.63 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 3.05/1.63 ( ( plus @ X51 @ X52 )
% 3.05/1.63 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_206_trm_Odistinct_I25_J,axiom,
% 3.05/1.63 ! [X3: char,X51: trm,X52: trm] :
% 3.05/1.63 ( ( const @ X3 )
% 3.05/1.63 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_207_trm_Odistinct_I27_J,axiom,
% 3.05/1.63 ! [X3: char,X61: trm,X62: trm] :
% 3.05/1.63 ( ( const @ X3 )
% 3.05/1.63 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_208_trm_Odistinct_I31_J,axiom,
% 3.05/1.63 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 3.05/1.63 ( ( func @ X41 @ X42 )
% 3.05/1.63 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_209_trm_Odistinct_I33_J,axiom,
% 3.05/1.63 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 3.05/1.63 ( ( func @ X41 @ X42 )
% 3.05/1.63 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_210_usubstappt__times__conv,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 3.05/1.63 != none_trm )
% 3.05/1.63 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.63 != none_trm )
% 3.05/1.63 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 3.05/1.63 != none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_211_usubstappt__plus__conv,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 3.05/1.63 != none_trm )
% 3.05/1.63 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.63 != none_trm )
% 3.05/1.63 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 3.05/1.63 != none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_212_Timeso_Osimps_I1_J,axiom,
% 3.05/1.63 ! [Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst918876924Timeso @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 3.05/1.63 = ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_213_Pluso_Osimps_I1_J,axiom,
% 3.05/1.63 ! [Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst141955042_Pluso @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 3.05/1.63 = ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_214_usubstappt_Osimps_I6_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_215_usubstappt_Osimps_I5_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_216_usubstappt_Oelims,axiom,
% 3.05/1.63 ! [X4: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ X4 @ Xa @ Xb )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ! [X2: variable] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( var @ X2 ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_trm @ ( var @ X2 ) ) ) )
% 3.05/1.63 => ( ! [R3: real] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( number @ R3 ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_trm @ ( number @ R3 ) ) ) )
% 3.05/1.63 => ( ! [F5: char] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( const @ F5 ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( uSubst1559070963pconst @ X4 @ Xa @ F5 ) ) )
% 3.05/1.63 => ( ! [F5: char,Theta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( func @ F5 @ Theta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( case_o487727941rm_trm @ none_trm
% 3.05/1.63 @ ^ [Sigma_theta2: trm] :
% 3.05/1.63 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta2 ) )
% 3.05/1.63 @ ^ [R: trm] :
% 3.05/1.63 ( if_option_trm
% 3.05/1.63 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 3.05/1.63 @ none_trm )
% 3.05/1.63 @ ( produc866613687on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [F4: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.63 @ X4
% 3.05/1.63 @ F5 ) )
% 3.05/1.63 @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) ) ) )
% 3.05/1.63 => ( ! [Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( plus @ Theta @ Eta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) ) )
% 3.05/1.63 => ( ! [Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( times @ Theta @ Eta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) ) )
% 3.05/1.63 => ~ ! [Theta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( differential @ Theta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( uSubst716837505ntialo
% 3.05/1.63 @ ( uSubst516392818stappt @ X4
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta ) ) ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_217_usubstappt__induct,axiom,
% 3.05/1.63 ! [P: produc1418842292n_game > set_variable > trm > $o,A0: produc1418842292n_game,A1: set_variable,A22: trm] :
% 3.05/1.63 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] : ( P @ Sigma3 @ U3 @ ( var @ X2 ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] : ( P @ Sigma3 @ U3 @ ( number @ R3 ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] : ( P @ Sigma3 @ U3 @ ( const @ F5 ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 3.05/1.63 ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ( ! [X25: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 = ( some_trm @ X25 ) )
% 3.05/1.63 => ! [X2a: trm] :
% 3.05/1.63 ( ( ( produc866613687on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [F4: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.63 @ Sigma3
% 3.05/1.63 @ F5 )
% 3.05/1.63 = ( some_trm @ X2a ) )
% 3.05/1.63 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 => ( P @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 3.05/1.63 ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( P @ Sigma3 @ U3 @ Eta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 3.05/1.63 ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( P @ Sigma3 @ U3 @ Eta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 3.05/1.63 ( ( P @ Sigma3
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) )
% 3.05/1.63 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_218_Geqo_Osimps_I3_J,axiom,
% 3.05/1.63 ! [V2: trm] :
% 3.05/1.63 ( ( uSubst152838031e_Geqo @ ( some_trm @ V2 ) @ none_trm )
% 3.05/1.63 = none_fml ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_219_combine__options__def,axiom,
% 3.05/1.63 ( combine_options_fml
% 3.05/1.63 = ( ^ [F2: fml > fml > fml,X: option_fml,Y: option_fml] :
% 3.05/1.63 ( case_o209804997ml_fml @ Y
% 3.05/1.63 @ ^ [Z3: fml] :
% 3.05/1.63 ( case_o209804997ml_fml @ ( some_fml @ Z3 )
% 3.05/1.63 @ ^ [Aa: fml] : ( some_fml @ ( F2 @ Z3 @ Aa ) )
% 3.05/1.63 @ Y )
% 3.05/1.63 @ X ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_220_combine__options__def,axiom,
% 3.05/1.63 ( combine_options_game
% 3.05/1.63 = ( ^ [F2: game > game > game,X: option_game,Y: option_game] :
% 3.05/1.63 ( case_o696458451e_game @ Y
% 3.05/1.63 @ ^ [Z3: game] :
% 3.05/1.63 ( case_o696458451e_game @ ( some_game @ Z3 )
% 3.05/1.63 @ ^ [Aa: game] : ( some_game @ ( F2 @ Z3 @ Aa ) )
% 3.05/1.63 @ Y )
% 3.05/1.63 @ X ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_221_combine__options__def,axiom,
% 3.05/1.63 ( combine_options_trm
% 3.05/1.63 = ( ^ [F2: trm > trm > trm,X: option_trm,Y: option_trm] :
% 3.05/1.63 ( case_o487727941rm_trm @ Y
% 3.05/1.63 @ ^ [Z3: trm] :
% 3.05/1.63 ( case_o487727941rm_trm @ ( some_trm @ Z3 )
% 3.05/1.63 @ ^ [Aa: trm] : ( some_trm @ ( F2 @ Z3 @ Aa ) )
% 3.05/1.63 @ Y )
% 3.05/1.63 @ X ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_222_trm_Oinject_I2_J,axiom,
% 3.05/1.63 ! [X22: real,Y22: real] :
% 3.05/1.63 ( ( ( number @ X22 )
% 3.05/1.63 = ( number @ Y22 ) )
% 3.05/1.63 = ( X22 = Y22 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_223_trm_Oinject_I1_J,axiom,
% 3.05/1.63 ! [X12: variable,Y1: variable] :
% 3.05/1.63 ( ( ( var @ X12 )
% 3.05/1.63 = ( var @ Y1 ) )
% 3.05/1.63 = ( X12 = Y1 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_224_trm_Oinject_I7_J,axiom,
% 3.05/1.63 ! [X7: trm,Y7: trm] :
% 3.05/1.63 ( ( ( differential @ X7 )
% 3.05/1.63 = ( differential @ Y7 ) )
% 3.05/1.63 = ( X7 = Y7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_225_combine__options__simps_I2_J,axiom,
% 3.05/1.63 ! [F3: trm > trm > trm,X4: option_trm] :
% 3.05/1.63 ( ( combine_options_trm @ F3 @ X4 @ none_trm )
% 3.05/1.63 = X4 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_226_combine__options__simps_I2_J,axiom,
% 3.05/1.63 ! [F3: fml > fml > fml,X4: option_fml] :
% 3.05/1.63 ( ( combine_options_fml @ F3 @ X4 @ none_fml )
% 3.05/1.63 = X4 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_227_combine__options__simps_I2_J,axiom,
% 3.05/1.63 ! [F3: game > game > game,X4: option_game] :
% 3.05/1.63 ( ( combine_options_game @ F3 @ X4 @ none_game )
% 3.05/1.63 = X4 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_228_combine__options__simps_I1_J,axiom,
% 3.05/1.63 ! [F3: trm > trm > trm,Y2: option_trm] :
% 3.05/1.63 ( ( combine_options_trm @ F3 @ none_trm @ Y2 )
% 3.05/1.63 = Y2 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_229_combine__options__simps_I1_J,axiom,
% 3.05/1.63 ! [F3: fml > fml > fml,Y2: option_fml] :
% 3.05/1.63 ( ( combine_options_fml @ F3 @ none_fml @ Y2 )
% 3.05/1.63 = Y2 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_230_combine__options__simps_I1_J,axiom,
% 3.05/1.63 ! [F3: game > game > game,Y2: option_game] :
% 3.05/1.63 ( ( combine_options_game @ F3 @ none_game @ Y2 )
% 3.05/1.63 = Y2 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_231_combine__options__simps_I3_J,axiom,
% 3.05/1.63 ! [F3: trm > trm > trm,A: trm,B: trm] :
% 3.05/1.63 ( ( combine_options_trm @ F3 @ ( some_trm @ A ) @ ( some_trm @ B ) )
% 3.05/1.63 = ( some_trm @ ( F3 @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_232_combine__options__simps_I3_J,axiom,
% 3.05/1.63 ! [F3: fml > fml > fml,A: fml,B: fml] :
% 3.05/1.63 ( ( combine_options_fml @ F3 @ ( some_fml @ A ) @ ( some_fml @ B ) )
% 3.05/1.63 = ( some_fml @ ( F3 @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_233_combine__options__simps_I3_J,axiom,
% 3.05/1.63 ! [F3: game > game > game,A: game,B: game] :
% 3.05/1.63 ( ( combine_options_game @ F3 @ ( some_game @ A ) @ ( some_game @ B ) )
% 3.05/1.63 = ( some_game @ ( F3 @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_234_Differentialo_Osimps_I1_J,axiom,
% 3.05/1.63 ! [Theta2: trm] :
% 3.05/1.63 ( ( uSubst716837505ntialo @ ( some_trm @ Theta2 ) )
% 3.05/1.63 = ( some_trm @ ( differential @ Theta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_235_trm_Odistinct_I21_J,axiom,
% 3.05/1.63 ! [X22: real,X7: trm] :
% 3.05/1.63 ( ( number @ X22 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_236_trm_Odistinct_I11_J,axiom,
% 3.05/1.63 ! [X12: variable,X7: trm] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_237_trm_Odistinct_I1_J,axiom,
% 3.05/1.63 ! [X12: variable,X22: real] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( number @ X22 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_238_usubstappt_Osimps_I7_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 3.05/1.63 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 3.05/1.63 = ( uSubst716837505ntialo
% 3.05/1.63 @ ( uSubst516392818stappt @ Sigma2
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_239_trm_Odistinct_I13_J,axiom,
% 3.05/1.63 ! [X22: real,X3: char] :
% 3.05/1.63 ( ( number @ X22 )
% 3.05/1.63 != ( const @ X3 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_240_trm_Odistinct_I15_J,axiom,
% 3.05/1.63 ! [X22: real,X41: char,X42: trm] :
% 3.05/1.63 ( ( number @ X22 )
% 3.05/1.63 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_241_trm_Odistinct_I19_J,axiom,
% 3.05/1.63 ! [X22: real,X61: trm,X62: trm] :
% 3.05/1.63 ( ( number @ X22 )
% 3.05/1.63 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_242_trm_Odistinct_I17_J,axiom,
% 3.05/1.63 ! [X22: real,X51: trm,X52: trm] :
% 3.05/1.63 ( ( number @ X22 )
% 3.05/1.63 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_243_Differentialo_Oelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst716837505ntialo @ X4 )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_trm @ ( differential @ Theta ) ) ) )
% 3.05/1.63 => ~ ( ( X4 = none_trm )
% 3.05/1.63 => ( Y2 != none_trm ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_244_trm_Odistinct_I3_J,axiom,
% 3.05/1.63 ! [X12: variable,X3: char] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( const @ X3 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_245_trm_Odistinct_I5_J,axiom,
% 3.05/1.63 ! [X12: variable,X41: char,X42: trm] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_246_trm_Odistinct_I9_J,axiom,
% 3.05/1.63 ! [X12: variable,X61: trm,X62: trm] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_247_trm_Odistinct_I7_J,axiom,
% 3.05/1.63 ! [X12: variable,X51: trm,X52: trm] :
% 3.05/1.63 ( ( var @ X12 )
% 3.05/1.63 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_248_trm_Odistinct_I29_J,axiom,
% 3.05/1.63 ! [X3: char,X7: trm] :
% 3.05/1.63 ( ( const @ X3 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_249_trm_Odistinct_I35_J,axiom,
% 3.05/1.63 ! [X41: char,X42: trm,X7: trm] :
% 3.05/1.63 ( ( func @ X41 @ X42 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_250_trm_Odistinct_I41_J,axiom,
% 3.05/1.63 ! [X61: trm,X62: trm,X7: trm] :
% 3.05/1.63 ( ( times @ X61 @ X62 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_251_trm_Odistinct_I39_J,axiom,
% 3.05/1.63 ! [X51: trm,X52: trm,X7: trm] :
% 3.05/1.63 ( ( plus @ X51 @ X52 )
% 3.05/1.63 != ( differential @ X7 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_252_trm_Oexhaust,axiom,
% 3.05/1.63 ! [Y2: trm] :
% 3.05/1.63 ( ! [X13: variable] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( var @ X13 ) )
% 3.05/1.63 => ( ! [X23: real] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( number @ X23 ) )
% 3.05/1.63 => ( ! [X32: char] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( const @ X32 ) )
% 3.05/1.63 => ( ! [X412: char,X422: trm] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( func @ X412 @ X422 ) )
% 3.05/1.63 => ( ! [X512: trm,X522: trm] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( plus @ X512 @ X522 ) )
% 3.05/1.63 => ( ! [X612: trm,X622: trm] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( times @ X612 @ X622 ) )
% 3.05/1.63 => ~ ! [X72: trm] :
% 3.05/1.63 ( Y2
% 3.05/1.63 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_253_trm_Oinduct,axiom,
% 3.05/1.63 ! [P: trm > $o,Trm: trm] :
% 3.05/1.63 ( ! [X2: variable] : ( P @ ( var @ X2 ) )
% 3.05/1.63 => ( ! [X2: real] : ( P @ ( number @ X2 ) )
% 3.05/1.63 => ( ! [X2: char] : ( P @ ( const @ X2 ) )
% 3.05/1.63 => ( ! [X1a: char,X2a2: trm] :
% 3.05/1.63 ( ( P @ X2a2 )
% 3.05/1.63 => ( P @ ( func @ X1a @ X2a2 ) ) )
% 3.05/1.63 => ( ! [X1a: trm,X2a2: trm] :
% 3.05/1.63 ( ( P @ X1a )
% 3.05/1.63 => ( ( P @ X2a2 )
% 3.05/1.63 => ( P @ ( plus @ X1a @ X2a2 ) ) ) )
% 3.05/1.63 => ( ! [X1a: trm,X2a2: trm] :
% 3.05/1.63 ( ( P @ X1a )
% 3.05/1.63 => ( ( P @ X2a2 )
% 3.05/1.63 => ( P @ ( times @ X1a @ X2a2 ) ) ) )
% 3.05/1.63 => ( ! [X2: trm] :
% 3.05/1.63 ( ( P @ X2 )
% 3.05/1.63 => ( P @ ( differential @ X2 ) ) )
% 3.05/1.63 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_254_Geqo_Osimps_I2_J,axiom,
% 3.05/1.63 ! [Eta2: option_trm] :
% 3.05/1.63 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 3.05/1.63 = none_fml ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_255_Geqo__undef,axiom,
% 3.05/1.63 ! [Theta2: option_trm,Eta2: option_trm] :
% 3.05/1.63 ( ( ( uSubst152838031e_Geqo @ Theta2 @ Eta2 )
% 3.05/1.63 = none_fml )
% 3.05/1.63 = ( ( Theta2 = none_trm )
% 3.05/1.63 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_256_Differentialo_Osimps_I2_J,axiom,
% 3.05/1.63 ( ( uSubst716837505ntialo @ none_trm )
% 3.05/1.63 = none_trm ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_257_Differentialo__undef,axiom,
% 3.05/1.63 ! [Theta2: option_trm] :
% 3.05/1.63 ( ( ( uSubst716837505ntialo @ Theta2 )
% 3.05/1.63 = none_trm )
% 3.05/1.63 = ( Theta2 = none_trm ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_258_usubstappt_Osimps_I2_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,R2: real] :
% 3.05/1.63 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 3.05/1.63 = ( some_trm @ ( number @ R2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_259_usubstappt_Osimps_I1_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,X4: variable] :
% 3.05/1.63 ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 3.05/1.63 = ( some_trm @ ( var @ X4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_260_usubstappt__differential__conv,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 3.05/1.63 != none_trm )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta2 )
% 3.05/1.63 != none_trm ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_261_usubstappt_Opelims,axiom,
% 3.05/1.63 ! [X4: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ X4 @ Xa @ Xb )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ Xb ) ) )
% 3.05/1.63 => ( ! [X2: variable] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( var @ X2 ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( some_trm @ ( var @ X2 ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( var @ X2 ) ) ) ) ) )
% 3.05/1.63 => ( ! [R3: real] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( number @ R3 ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( some_trm @ ( number @ R3 ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 3.05/1.63 => ( ! [F5: char] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( const @ F5 ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( uSubst1559070963pconst @ X4 @ Xa @ F5 ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 3.05/1.63 => ( ! [F5: char,Theta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( func @ F5 @ Theta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.63 @ ^ [Sigma_theta2: trm] :
% 3.05/1.63 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta2 ) )
% 3.05/1.63 @ ^ [R: trm] :
% 3.05/1.63 ( if_option_trm
% 3.05/1.63 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 3.05/1.63 @ none_trm )
% 3.05/1.63 @ ( produc866613687on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [F4: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.63 @ X4
% 3.05/1.63 @ F5 ) )
% 3.05/1.63 @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( func @ F5 @ Theta ) ) ) ) ) )
% 3.05/1.63 => ( ! [Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( plus @ Theta @ Eta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( plus @ Theta @ Eta ) ) ) ) ) )
% 3.05/1.63 => ( ! [Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( times @ Theta @ Eta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X4 @ Xa @ Theta ) @ ( uSubst516392818stappt @ X4 @ Xa @ Eta ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( times @ Theta @ Eta ) ) ) ) ) )
% 3.05/1.63 => ~ ! [Theta: trm] :
% 3.05/1.63 ( ( Xb
% 3.05/1.63 = ( differential @ Theta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( uSubst716837505ntialo
% 3.05/1.63 @ ( uSubst516392818stappt @ X4
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta ) ) )
% 3.05/1.63 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X4 @ ( produc1482344242le_trm @ Xa @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_262_term__sem_Ocases,axiom,
% 3.05/1.63 ! [X4: produc833882726rp_trm] :
% 3.05/1.63 ( ! [I: denotational_interp,X2: variable] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( var @ X2 ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,R3: real] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( number @ R3 ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,F5: char] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( const @ F5 ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( func @ F5 @ Theta ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( plus @ Theta @ Eta ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,Theta: trm,Eta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( times @ Theta @ Eta ) ) )
% 3.05/1.63 => ~ ! [I: denotational_interp,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1132922070rp_trm @ I @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_263_term__sem_Oinduct,axiom,
% 3.05/1.63 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 3.05/1.63 ( ! [I: denotational_interp,X2: variable] : ( P @ I @ ( var @ X2 ) )
% 3.05/1.63 => ( ! [I: denotational_interp,R3: real] : ( P @ I @ ( number @ R3 ) )
% 3.05/1.63 => ( ! [I: denotational_interp,F5: char] : ( P @ I @ ( const @ F5 ) )
% 3.05/1.63 => ( ! [I: denotational_interp,F5: char,Theta: trm] :
% 3.05/1.63 ( ( P @ I @ Theta )
% 3.05/1.63 => ( P @ I @ ( func @ F5 @ Theta ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,Theta: trm] :
% 3.05/1.63 ( ( P @ I @ Theta )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( P @ I @ Eta )
% 3.05/1.63 => ( P @ I @ ( plus @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,Theta: trm] :
% 3.05/1.63 ( ( P @ I @ Theta )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( P @ I @ Eta )
% 3.05/1.63 => ( P @ I @ ( times @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ! [I: denotational_interp,Theta: trm] :
% 3.05/1.63 ( ( ? [Xa2: char] :
% 3.05/1.63 ( member_char @ Xa2
% 3.05/1.63 @ ( collect_char
% 3.05/1.63 @ ^ [Uu: char] : $true ) )
% 3.05/1.63 => ( P @ I @ Theta ) )
% 3.05/1.63 => ( P @ I @ ( differential @ Theta ) ) )
% 3.05/1.63 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_264_old_Oprod_Oinject,axiom,
% 3.05/1.63 ! [A: char,B: option_trm,A6: char,B6: option_trm] :
% 3.05/1.63 ( ( ( produc1500300866on_trm @ A @ B )
% 3.05/1.63 = ( produc1500300866on_trm @ A6 @ B6 ) )
% 3.05/1.63 = ( ( A = A6 )
% 3.05/1.63 & ( B = B6 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_265_old_Oprod_Oinject,axiom,
% 3.05/1.63 ! [A: set_variable,B: trm,A6: set_variable,B6: trm] :
% 3.05/1.63 ( ( ( produc1482344242le_trm @ A @ B )
% 3.05/1.63 = ( produc1482344242le_trm @ A6 @ B6 ) )
% 3.05/1.63 = ( ( A = A6 )
% 3.05/1.63 & ( B = B6 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_266_old_Oprod_Oinject,axiom,
% 3.05/1.63 ! [A: char > option_trm,B: produc62062515n_game,A6: char > option_trm,B6: produc62062515n_game] :
% 3.05/1.63 ( ( ( produc1618635950n_game @ A @ B )
% 3.05/1.63 = ( produc1618635950n_game @ A6 @ B6 ) )
% 3.05/1.63 = ( ( A = A6 )
% 3.05/1.63 & ( B = B6 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_267_old_Oprod_Oinject,axiom,
% 3.05/1.63 ! [A: char > option_trm,B: produc799602994n_game,A6: char > option_trm,B6: produc799602994n_game] :
% 3.05/1.63 ( ( ( produc1048060077n_game @ A @ B )
% 3.05/1.63 = ( produc1048060077n_game @ A6 @ B6 ) )
% 3.05/1.63 = ( ( A = A6 )
% 3.05/1.63 & ( B = B6 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_268_old_Oprod_Oinject,axiom,
% 3.05/1.63 ! [A: char > option_fml,B: char > option_game,A6: char > option_fml,B6: char > option_game] :
% 3.05/1.63 ( ( ( produc123610156n_game @ A @ B )
% 3.05/1.63 = ( produc123610156n_game @ A6 @ B6 ) )
% 3.05/1.63 = ( ( A = A6 )
% 3.05/1.63 & ( B = B6 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_269_prod_Oinject,axiom,
% 3.05/1.63 ! [X12: char,X22: option_trm,Y1: char,Y22: option_trm] :
% 3.05/1.63 ( ( ( produc1500300866on_trm @ X12 @ X22 )
% 3.05/1.63 = ( produc1500300866on_trm @ Y1 @ Y22 ) )
% 3.05/1.63 = ( ( X12 = Y1 )
% 3.05/1.63 & ( X22 = Y22 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_270_prod_Oinject,axiom,
% 3.05/1.63 ! [X12: set_variable,X22: trm,Y1: set_variable,Y22: trm] :
% 3.05/1.63 ( ( ( produc1482344242le_trm @ X12 @ X22 )
% 3.05/1.63 = ( produc1482344242le_trm @ Y1 @ Y22 ) )
% 3.05/1.63 = ( ( X12 = Y1 )
% 3.05/1.63 & ( X22 = Y22 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_271_prod_Oinject,axiom,
% 3.05/1.63 ! [X12: char > option_trm,X22: produc62062515n_game,Y1: char > option_trm,Y22: produc62062515n_game] :
% 3.05/1.63 ( ( ( produc1618635950n_game @ X12 @ X22 )
% 3.05/1.63 = ( produc1618635950n_game @ Y1 @ Y22 ) )
% 3.05/1.63 = ( ( X12 = Y1 )
% 3.05/1.63 & ( X22 = Y22 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_272_prod_Oinject,axiom,
% 3.05/1.63 ! [X12: char > option_trm,X22: produc799602994n_game,Y1: char > option_trm,Y22: produc799602994n_game] :
% 3.05/1.63 ( ( ( produc1048060077n_game @ X12 @ X22 )
% 3.05/1.63 = ( produc1048060077n_game @ Y1 @ Y22 ) )
% 3.05/1.63 = ( ( X12 = Y1 )
% 3.05/1.63 & ( X22 = Y22 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_273_prod_Oinject,axiom,
% 3.05/1.63 ! [X12: char > option_fml,X22: char > option_game,Y1: char > option_fml,Y22: char > option_game] :
% 3.05/1.63 ( ( ( produc123610156n_game @ X12 @ X22 )
% 3.05/1.63 = ( produc123610156n_game @ Y1 @ Y22 ) )
% 3.05/1.63 = ( ( X12 = Y1 )
% 3.05/1.63 & ( X22 = Y22 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_274_case__prodI,axiom,
% 3.05/1.63 ! [F3: char > option_trm > $o,A: char,B: option_trm] :
% 3.05/1.63 ( ( F3 @ A @ B )
% 3.05/1.63 => ( produc584666985_trm_o @ F3 @ ( produc1500300866on_trm @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_275_case__prodI,axiom,
% 3.05/1.63 ! [F3: set_variable > trm > $o,A: set_variable,B: trm] :
% 3.05/1.63 ( ( F3 @ A @ B )
% 3.05/1.63 => ( produc82209913_trm_o @ F3 @ ( produc1482344242le_trm @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_276_case__prodI,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc62062515n_game > $o,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.63 ( ( F3 @ A @ B )
% 3.05/1.63 => ( produc1707653117game_o @ F3 @ ( produc1618635950n_game @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_277_case__prodI,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc799602994n_game > $o,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.63 ( ( F3 @ A @ B )
% 3.05/1.63 => ( produc1868740670game_o @ F3 @ ( produc1048060077n_game @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_278_case__prodI,axiom,
% 3.05/1.63 ! [F3: ( char > option_fml ) > ( char > option_game ) > $o,A: char > option_fml,B: char > option_game] :
% 3.05/1.63 ( ( F3 @ A @ B )
% 3.05/1.63 => ( produc159680767game_o @ F3 @ ( produc123610156n_game @ A @ B ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_279_case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc464795408on_trm,C: char > option_trm > $o] :
% 3.05/1.63 ( ! [A4: char,B4: option_trm] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 3.05/1.63 => ( C @ A4 @ B4 ) )
% 3.05/1.63 => ( produc584666985_trm_o @ C @ P4 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_280_case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc1367888000le_trm,C: set_variable > trm > $o] :
% 3.05/1.63 ( ! [A4: set_variable,B4: trm] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 3.05/1.63 => ( C @ A4 @ B4 ) )
% 3.05/1.63 => ( produc82209913_trm_o @ C @ P4 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_281_case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc1418842292n_game,C: ( char > option_trm ) > produc62062515n_game > $o] :
% 3.05/1.63 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1618635950n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( C @ A4 @ B4 ) )
% 3.05/1.63 => ( produc1707653117game_o @ C @ P4 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_282_case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc62062515n_game,C: ( char > option_trm ) > produc799602994n_game > $o] :
% 3.05/1.63 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1048060077n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( C @ A4 @ B4 ) )
% 3.05/1.63 => ( produc1868740670game_o @ C @ P4 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_283_case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc799602994n_game,C: ( char > option_fml ) > ( char > option_game ) > $o] :
% 3.05/1.63 ( ! [A4: char > option_fml,B4: char > option_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc123610156n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( C @ A4 @ B4 ) )
% 3.05/1.63 => ( produc159680767game_o @ C @ P4 ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_284_mem__case__prodI,axiom,
% 3.05/1.63 ! [Z2: char,C: char > option_trm > set_char,A: char,B: option_trm] :
% 3.05/1.63 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc33263478t_char @ C @ ( produc1500300866on_trm @ A @ B ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_285_mem__case__prodI,axiom,
% 3.05/1.63 ! [Z2: char,C: set_variable > trm > set_char,A: set_variable,B: trm] :
% 3.05/1.63 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc836445798t_char @ C @ ( produc1482344242le_trm @ A @ B ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_286_mem__case__prodI,axiom,
% 3.05/1.63 ! [Z2: char,C: ( char > option_trm ) > produc62062515n_game > set_char,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.63 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc1002100706t_char @ C @ ( produc1618635950n_game @ A @ B ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_287_mem__case__prodI,axiom,
% 3.05/1.63 ! [Z2: char,C: ( char > option_trm ) > produc799602994n_game > set_char,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.63 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc1554403041t_char @ C @ ( produc1048060077n_game @ A @ B ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_288_mem__case__prodI,axiom,
% 3.05/1.63 ! [Z2: char,C: ( char > option_fml ) > ( char > option_game ) > set_char,A: char > option_fml,B: char > option_game] :
% 3.05/1.63 ( ( member_char @ Z2 @ ( C @ A @ B ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc629249376t_char @ C @ ( produc123610156n_game @ A @ B ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_289_mem__case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc464795408on_trm,Z2: char,C: char > option_trm > set_char] :
% 3.05/1.63 ( ! [A4: char,B4: option_trm] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc33263478t_char @ C @ P4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_290_mem__case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc1367888000le_trm,Z2: char,C: set_variable > trm > set_char] :
% 3.05/1.63 ( ! [A4: set_variable,B4: trm] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc836445798t_char @ C @ P4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_291_mem__case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc1418842292n_game,Z2: char,C: ( char > option_trm ) > produc62062515n_game > set_char] :
% 3.05/1.63 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1618635950n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc1002100706t_char @ C @ P4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_292_mem__case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc62062515n_game,Z2: char,C: ( char > option_trm ) > produc799602994n_game > set_char] :
% 3.05/1.63 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc1048060077n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc1554403041t_char @ C @ P4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_293_mem__case__prodI2,axiom,
% 3.05/1.63 ! [P4: produc799602994n_game,Z2: char,C: ( char > option_fml ) > ( char > option_game ) > set_char] :
% 3.05/1.63 ( ! [A4: char > option_fml,B4: char > option_game] :
% 3.05/1.63 ( ( P4
% 3.05/1.63 = ( produc123610156n_game @ A4 @ B4 ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( C @ A4 @ B4 ) ) )
% 3.05/1.63 => ( member_char @ Z2 @ ( produc629249376t_char @ C @ P4 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_294_case__prod__conv,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.63 ( ( produc1250175341on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 3.05/1.63 = ( F3 @ A @ B ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_295_case__prod__conv,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.63 ( ( produc1231571704on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.63 = ( F3 @ A @ B ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_296_case__prod__conv,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.63 ( ( produc1615133358on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.63 = ( F3 @ A @ B ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_297_case__prod__conv,axiom,
% 3.05/1.63 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,A: char > option_fml,B: char > option_game] :
% 3.05/1.63 ( ( produc1036610745on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.63 = ( F3 @ A @ B ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_298_case__prod__conv,axiom,
% 3.05/1.63 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,A: char > option_fml,B: char > option_game] :
% 3.05/1.63 ( ( produc1420172399on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.63 = ( F3 @ A @ B ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_299_usubstappt_Opsimps_I7_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( differential @ Theta2 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( differential @ Theta2 ) )
% 3.05/1.63 = ( uSubst716837505ntialo
% 3.05/1.63 @ ( uSubst516392818stappt @ Sigma2
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta2 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_300_usubstappt_Opsimps_I1_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,X4: variable] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( var @ X4 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( var @ X4 ) )
% 3.05/1.63 = ( some_trm @ ( var @ X4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_301_usubstappt_Opsimps_I2_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,R2: real] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( number @ R2 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( number @ R2 ) )
% 3.05/1.63 = ( some_trm @ ( number @ R2 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_302_cond__case__prod__eta,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,G: produc1418842292n_game > char > option_fml] :
% 3.05/1.63 ( ! [X2: char > option_trm,Y4: produc62062515n_game] :
% 3.05/1.63 ( ( F3 @ X2 @ Y4 )
% 3.05/1.63 = ( G @ ( produc1618635950n_game @ X2 @ Y4 ) ) )
% 3.05/1.63 => ( ( produc1250175341on_fml @ F3 )
% 3.05/1.63 = G ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_303_cond__case__prod__eta,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,G: produc62062515n_game > char > option_trm] :
% 3.05/1.63 ( ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 3.05/1.63 ( ( F3 @ X2 @ Y4 )
% 3.05/1.63 = ( G @ ( produc1048060077n_game @ X2 @ Y4 ) ) )
% 3.05/1.63 => ( ( produc1231571704on_trm @ F3 )
% 3.05/1.63 = G ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_304_cond__case__prod__eta,axiom,
% 3.05/1.63 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,G: produc62062515n_game > char > option_fml] :
% 3.05/1.63 ( ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 3.05/1.63 ( ( F3 @ X2 @ Y4 )
% 3.05/1.63 = ( G @ ( produc1048060077n_game @ X2 @ Y4 ) ) )
% 3.05/1.63 => ( ( produc1615133358on_fml @ F3 )
% 3.05/1.63 = G ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_305_cond__case__prod__eta,axiom,
% 3.05/1.63 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,G: produc799602994n_game > char > option_trm] :
% 3.05/1.63 ( ! [X2: char > option_fml,Y4: char > option_game] :
% 3.05/1.63 ( ( F3 @ X2 @ Y4 )
% 3.05/1.63 = ( G @ ( produc123610156n_game @ X2 @ Y4 ) ) )
% 3.05/1.63 => ( ( produc1036610745on_trm @ F3 )
% 3.05/1.63 = G ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_306_cond__case__prod__eta,axiom,
% 3.05/1.63 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,G: produc799602994n_game > char > option_fml] :
% 3.05/1.63 ( ! [X2: char > option_fml,Y4: char > option_game] :
% 3.05/1.63 ( ( F3 @ X2 @ Y4 )
% 3.05/1.63 = ( G @ ( produc123610156n_game @ X2 @ Y4 ) ) )
% 3.05/1.63 => ( ( produc1420172399on_fml @ F3 )
% 3.05/1.63 = G ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_307_case__prod__eta,axiom,
% 3.05/1.63 ! [F3: produc1418842292n_game > char > option_fml] :
% 3.05/1.63 ( ( produc1250175341on_fml
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 3.05/1.63 = F3 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_308_case__prod__eta,axiom,
% 3.05/1.63 ! [F3: produc62062515n_game > char > option_trm] :
% 3.05/1.63 ( ( produc1231571704on_trm
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.63 = F3 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_309_case__prod__eta,axiom,
% 3.05/1.63 ! [F3: produc62062515n_game > char > option_fml] :
% 3.05/1.63 ( ( produc1615133358on_fml
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.63 = F3 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_310_case__prod__eta,axiom,
% 3.05/1.63 ! [F3: produc799602994n_game > char > option_trm] :
% 3.05/1.63 ( ( produc1036610745on_trm
% 3.05/1.63 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.63 = F3 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_311_case__prod__eta,axiom,
% 3.05/1.63 ! [F3: produc799602994n_game > char > option_fml] :
% 3.05/1.63 ( ( produc1420172399on_fml
% 3.05/1.63 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.63 = F3 ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_312_case__prodE2,axiom,
% 3.05/1.63 ! [Q: ( char > option_fml ) > $o,P: ( char > option_trm ) > produc62062515n_game > char > option_fml,Z2: produc1418842292n_game] :
% 3.05/1.63 ( ( Q @ ( produc1250175341on_fml @ P @ Z2 ) )
% 3.05/1.63 => ~ ! [X2: char > option_trm,Y4: produc62062515n_game] :
% 3.05/1.63 ( ( Z2
% 3.05/1.63 = ( produc1618635950n_game @ X2 @ Y4 ) )
% 3.05/1.63 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_313_case__prodE2,axiom,
% 3.05/1.63 ! [Q: ( char > option_trm ) > $o,P: ( char > option_trm ) > produc799602994n_game > char > option_trm,Z2: produc62062515n_game] :
% 3.05/1.63 ( ( Q @ ( produc1231571704on_trm @ P @ Z2 ) )
% 3.05/1.63 => ~ ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 3.05/1.63 ( ( Z2
% 3.05/1.63 = ( produc1048060077n_game @ X2 @ Y4 ) )
% 3.05/1.63 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_314_case__prodE2,axiom,
% 3.05/1.63 ! [Q: ( char > option_fml ) > $o,P: ( char > option_trm ) > produc799602994n_game > char > option_fml,Z2: produc62062515n_game] :
% 3.05/1.63 ( ( Q @ ( produc1615133358on_fml @ P @ Z2 ) )
% 3.05/1.63 => ~ ! [X2: char > option_trm,Y4: produc799602994n_game] :
% 3.05/1.63 ( ( Z2
% 3.05/1.63 = ( produc1048060077n_game @ X2 @ Y4 ) )
% 3.05/1.63 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_315_case__prodE2,axiom,
% 3.05/1.63 ! [Q: ( char > option_trm ) > $o,P: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Z2: produc799602994n_game] :
% 3.05/1.63 ( ( Q @ ( produc1036610745on_trm @ P @ Z2 ) )
% 3.05/1.63 => ~ ! [X2: char > option_fml,Y4: char > option_game] :
% 3.05/1.63 ( ( Z2
% 3.05/1.63 = ( produc123610156n_game @ X2 @ Y4 ) )
% 3.05/1.63 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_316_case__prodE2,axiom,
% 3.05/1.63 ! [Q: ( char > option_fml ) > $o,P: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Z2: produc799602994n_game] :
% 3.05/1.63 ( ( Q @ ( produc1420172399on_fml @ P @ Z2 ) )
% 3.05/1.63 => ~ ! [X2: char > option_fml,Y4: char > option_game] :
% 3.05/1.63 ( ( Z2
% 3.05/1.63 = ( produc123610156n_game @ X2 @ Y4 ) )
% 3.05/1.63 => ~ ( Q @ ( P @ X2 @ Y4 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_317_inf__Int__eq2,axiom,
% 3.05/1.63 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 3.05/1.63 ( ( inf_in605351507_trm_o
% 3.05/1.63 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 )
% 3.05/1.63 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) )
% 3.05/1.63 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ ( inf_in1243659096on_trm @ R4 @ S ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_318_inf__Int__eq2,axiom,
% 3.05/1.63 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 3.05/1.63 ( ( inf_in185389155_trm_o
% 3.05/1.63 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 )
% 3.05/1.63 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) )
% 3.05/1.63 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ ( inf_in906025800le_trm @ R4 @ S ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_319_inf__Int__eq2,axiom,
% 3.05/1.63 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 3.05/1.63 ( ( inf_in1920662529game_o
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 )
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) )
% 3.05/1.63 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ ( inf_in360367996n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_320_inf__Int__eq2,axiom,
% 3.05/1.63 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 3.05/1.63 ( ( inf_in1072207554game_o
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 )
% 3.05/1.63 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) )
% 3.05/1.63 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ ( inf_in69689467n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_321_inf__Int__eq2,axiom,
% 3.05/1.63 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 3.05/1.63 ( ( inf_in243546115game_o
% 3.05/1.63 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 )
% 3.05/1.63 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) )
% 3.05/1.63 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ ( inf_in1391117306n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_322_bot__empty__eq2,axiom,
% 3.05/1.63 ( bot_bo1417568964game_o
% 3.05/1.63 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ bot_bo1302831229n_game ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_323_bot__empty__eq2,axiom,
% 3.05/1.63 ( bot_bo1895715589game_o
% 3.05/1.63 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ bot_bo456479484n_game ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_324_usubstappt_Opsimps_I3_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( const @ F3 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( const @ F3 ) )
% 3.05/1.63 = ( uSubst1559070963pconst @ Sigma2 @ U2 @ F3 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_325_usubstappt_Opsimps_I6_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( times @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_326_usubstappt_Opsimps_I5_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( plus @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_327_usubstappt_Opsimps_I4_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,F3: char,Theta2: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U2 @ ( func @ F3 @ Theta2 ) ) ) )
% 3.05/1.63 => ( ( uSubst516392818stappt @ Sigma2 @ U2 @ ( func @ F3 @ Theta2 ) )
% 3.05/1.63 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.63 @ ^ [Sigma_theta2: trm] :
% 3.05/1.63 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta2 ) )
% 3.05/1.63 @ ^ [R: trm] :
% 3.05/1.63 ( if_option_trm
% 3.05/1.63 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R )
% 3.05/1.63 @ none_trm )
% 3.05/1.63 @ ( produc866613687on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [F4: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.63 @ Sigma2
% 3.05/1.63 @ F3 ) )
% 3.05/1.63 @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_328_usubstappt_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1699626005le_trm] :
% 3.05/1.63 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X2 ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ~ ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta ) ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_329_usubstappt_Opinduct,axiom,
% 3.05/1.63 ! [A0: produc1418842292n_game,A1: set_variable,A22: trm,P: produc1418842292n_game > set_variable > trm > $o] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A0 @ ( produc1482344242le_trm @ A1 @ A22 ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X2: variable] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X2 ) ) ) )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( var @ X2 ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta ) ) ) )
% 3.05/1.63 => ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ( ! [X25: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 = ( some_trm @ X25 ) )
% 3.05/1.63 => ! [X2a: trm] :
% 3.05/1.63 ( ( ( produc866613687on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [F4: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.63 @ Sigma3
% 3.05/1.63 @ F5 )
% 3.05/1.63 = ( some_trm @ X2a ) )
% 3.05/1.63 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 => ( P @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( func @ F5 @ Theta ) ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ( ( P @ Sigma3 @ U3 @ Eta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( plus @ Theta @ Eta ) ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm,Eta: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta @ Eta ) ) ) )
% 3.05/1.63 => ( ( P @ Sigma3 @ U3 @ Theta )
% 3.05/1.63 => ( ( P @ Sigma3 @ U3 @ Eta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( times @ Theta @ Eta ) ) ) ) )
% 3.05/1.63 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta: trm] :
% 3.05/1.63 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta ) ) ) )
% 3.05/1.63 => ( ( P @ Sigma3
% 3.05/1.63 @ ( collect_variable
% 3.05/1.63 @ ^ [X: variable] : $true )
% 3.05/1.63 @ Theta )
% 3.05/1.63 => ( P @ Sigma3 @ U3 @ ( differential @ Theta ) ) ) )
% 3.05/1.63 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_330_Geqo_Oelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_fml] :
% 3.05/1.63 ( ( ( uSubst152838031e_Geqo @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( Y2
% 3.05/1.63 != ( some_fml @ ( geq @ Theta @ Eta ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( Y2 != none_fml ) )
% 3.05/1.63 => ~ ( ? [V: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_331_fml_Oinject_I2_J,axiom,
% 3.05/1.63 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 3.05/1.63 ( ( ( geq @ X21 @ X222 )
% 3.05/1.63 = ( geq @ Y21 @ Y222 ) )
% 3.05/1.63 = ( ( X21 = Y21 )
% 3.05/1.63 & ( X222 = Y222 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_332_Diamondo_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1739631244on_fml] :
% 3.05/1.63 ( ! [Alpha: game,Phi: fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) ) )
% 3.05/1.63 => ( ! [Phi: option_fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2124676926on_fml @ none_game @ Phi ) )
% 3.05/1.63 => ~ ! [V: game] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc2124676926on_fml @ ( some_game @ V ) @ none_fml ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_333_Existso_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1408538418on_fml] :
% 3.05/1.63 ( ! [X2: variable,Phi: fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1205977188on_fml @ X2 @ ( some_fml @ Phi ) ) )
% 3.05/1.63 => ~ ! [X2: variable] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1205977188on_fml @ X2 @ none_fml ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_334_Ando_Ocases,axiom,
% 3.05/1.63 ! [X4: produc46605351on_fml] :
% 3.05/1.63 ( ! [Phi: fml,Psi: fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc909629463on_fml @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) ) )
% 3.05/1.63 => ( ! [Psi: option_fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 3.05/1.63 => ~ ! [V: fml] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc909629463on_fml @ ( some_fml @ V ) @ none_fml ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_335_ODEo_Ocases,axiom,
% 3.05/1.63 ! [X4: produc464795408on_trm] :
% 3.05/1.63 ( ! [X2: char,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1500300866on_trm @ X2 @ ( some_trm @ Theta ) ) )
% 3.05/1.63 => ~ ! [X2: char] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1500300866on_trm @ X2 @ none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_336_Assigno_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1024976764on_trm] :
% 3.05/1.63 ( ! [X2: variable,Theta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1743721902on_trm @ X2 @ ( some_trm @ Theta ) ) )
% 3.05/1.63 => ~ ! [X2: variable] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1743721902on_trm @ X2 @ none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_337_Timeso_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1072747943on_trm] :
% 3.05/1.63 ( ! [Theta: trm,Eta: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) )
% 3.05/1.63 => ( ! [Eta: option_trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc709594775on_trm @ none_trm @ Eta ) )
% 3.05/1.63 => ~ ! [V: trm] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_338_Geqo_Osimps_I1_J,axiom,
% 3.05/1.63 ! [Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 3.05/1.63 = ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_339_usubstappf__geqr,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 3.05/1.63 != none_fml )
% 3.05/1.63 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_340_usubstappf__geq,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.63 != none_trm )
% 3.05/1.63 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 3.05/1.63 != none_trm )
% 3.05/1.63 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_341_Composeo_Ocases,axiom,
% 3.05/1.63 ! [X4: produc1016592119n_game] :
% 3.05/1.63 ( ! [Alpha: game,Beta: game] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 3.05/1.63 => ( ! [Alpha: option_game] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 3.05/1.63 => ~ ! [V: game] :
% 3.05/1.63 ( X4
% 3.05/1.63 != ( produc1111617711n_game @ none_game @ ( some_game @ V ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_342_usubstappf_Osimps_I2_J,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 3.05/1.63 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 ) @ ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_343_usubstappf__geq__conv,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,U2: set_variable,Theta2: trm,Eta2: trm] :
% 3.05/1.63 ( ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( geq @ Theta2 @ Eta2 ) )
% 3.05/1.63 != none_fml )
% 3.05/1.63 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.63 != none_trm )
% 3.05/1.63 & ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Eta2 )
% 3.05/1.63 != none_trm ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_344_dotsubstt__def,axiom,
% 3.05/1.63 ( uSubst1408967625substt
% 3.05/1.63 = ( ^ [Theta3: trm] :
% 3.05/1.63 ( produc1618635950n_game
% 3.05/1.63 @ ^ [F2: char] :
% 3.05/1.63 ( if_option_trm
% 3.05/1.63 @ ( F2
% 3.05/1.63 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 3.05/1.63 @ ( some_trm @ Theta3 )
% 3.05/1.63 @ none_trm )
% 3.05/1.63 @ ( produc1048060077n_game
% 3.05/1.63 @ ^ [Uu: char] : none_trm
% 3.05/1.63 @ ( produc123610156n_game
% 3.05/1.63 @ ^ [Uu: char] : none_fml
% 3.05/1.63 @ ^ [Uu: char] : none_game ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_345_Geqo_Opelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_fml] :
% 3.05/1.63 ( ( ( uSubst152838031e_Geqo @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( some_fml @ ( geq @ Theta @ Eta ) ) )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( ( Y2 = none_fml )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 3.05/1.63 => ~ ! [V: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( ( Y2 = none_fml )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_346_Timeso_Opelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst918876924Timeso @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( some_trm @ ( times @ Theta @ Eta ) ) )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( ( Y2 = none_trm )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 3.05/1.63 => ~ ! [V: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( ( Y2 = none_trm )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_347_Pluso_Opelims,axiom,
% 3.05/1.63 ! [X4: option_trm,Xa: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( ( uSubst141955042_Pluso @ X4 @ Xa )
% 3.05/1.63 = Y2 )
% 3.05/1.63 => ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ X4 @ Xa ) )
% 3.05/1.63 => ( ! [Theta: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ Theta ) )
% 3.05/1.63 => ! [Eta: trm] :
% 3.05/1.63 ( ( Xa
% 3.05/1.63 = ( some_trm @ Eta ) )
% 3.05/1.63 => ( ( Y2
% 3.05/1.63 = ( some_trm @ ( plus @ Theta @ Eta ) ) )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) ) ) ) ) )
% 3.05/1.63 => ( ( ( X4 = none_trm )
% 3.05/1.63 => ( ( Y2 = none_trm )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 3.05/1.63 => ~ ! [V: trm] :
% 3.05/1.63 ( ( X4
% 3.05/1.63 = ( some_trm @ V ) )
% 3.05/1.63 => ( ( Xa = none_trm )
% 3.05/1.63 => ( ( Y2 = none_trm )
% 3.05/1.63 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_348_dot__def,axiom,
% 3.05/1.63 ( uSubst_Mirabelle_dot
% 3.05/1.63 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_349_usubstappf__pred,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,P4: char,R2: fml,U2: set_variable,Theta2: trm,Sigma_theta: trm] :
% 3.05/1.63 ( ( ( produc1250175341on_fml
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1615133358on_fml
% 3.05/1.63 @ ^ [Uv: char > option_trm] :
% 3.05/1.63 ( produc1420172399on_fml
% 3.05/1.63 @ ^ [P3: char > option_fml,Uw: char > option_game] : P3 ) )
% 3.05/1.63 @ Sigma2
% 3.05/1.63 @ P4 )
% 3.05/1.63 = ( some_fml @ R2 ) )
% 3.05/1.63 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U2 )
% 3.05/1.63 = bot_bot_set_variable )
% 3.05/1.63 => ( ( ( uSubst516392818stappt @ Sigma2 @ U2 @ Theta2 )
% 3.05/1.63 = ( some_trm @ Sigma_theta ) )
% 3.05/1.63 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 3.05/1.63 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_350_fml_Oinject_I1_J,axiom,
% 3.05/1.63 ! [X11: char,X122: trm,Y11: char,Y12: trm] :
% 3.05/1.63 ( ( ( pred @ X11 @ X122 )
% 3.05/1.63 = ( pred @ Y11 @ Y12 ) )
% 3.05/1.63 = ( ( X11 = Y11 )
% 3.05/1.63 & ( X122 = Y12 ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(fact_351_usubstappf__pred2,axiom,
% 3.05/1.63 ! [Sigma2: produc1418842292n_game,P4: char,R2: fml,U2: set_variable,Theta2: trm] :
% 3.05/1.63 ( ( ( produc1250175341on_fml
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1615133358on_fml
% 3.05/1.63 @ ^ [Uv: char > option_trm] :
% 3.05/1.63 ( produc1420172399on_fml
% 3.05/1.63 @ ^ [P3: char > option_fml,Uw: char > option_game] : P3 ) )
% 3.05/1.63 @ Sigma2
% 3.05/1.63 @ P4 )
% 3.05/1.63 = ( some_fml @ R2 ) )
% 3.05/1.63 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U2 )
% 3.05/1.63 != bot_bot_set_variable )
% 3.05/1.63 => ( ( uSubst516392804stappf @ Sigma2 @ U2 @ ( pred @ P4 @ Theta2 ) )
% 3.05/1.63 = none_fml ) ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.63 ! [P: $o] :
% 3.05/1.63 ( ( P = $true )
% 3.05/1.63 | ( P = $false ) ) ).
% 3.05/1.63
% 3.05/1.63 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.63 ! [X4: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( if_option_trm @ $false @ X4 @ Y2 )
% 3.05/1.63 = Y2 ) ).
% 3.05/1.63
% 3.05/1.63 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.63 ! [X4: option_trm,Y2: option_trm] :
% 3.05/1.63 ( ( if_option_trm @ $true @ X4 @ Y2 )
% 3.05/1.63 = X4 ) ).
% 3.05/1.63
% 3.05/1.63 thf(conj_0,conjecture,
% 3.05/1.63 ( ( ( produc866613687on_trm
% 3.05/1.63 @ ^ [F0: char > option_trm] :
% 3.05/1.63 ( produc1231571704on_trm
% 3.05/1.63 @ ^ [Uu: char > option_trm] :
% 3.05/1.63 ( produc1036610745on_trm
% 3.05/1.63 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.63 @ sigma
% 3.05/1.63 @ f )
% 3.05/1.63 = none_trm )
% 3.05/1.63 | ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
% 3.05/1.63 = ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ).
% 3.05/1.63 ------------------------
% 3.05/1.67 % (9939)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/183Mi)
% 3.05/1.67 % (9940)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_9609 for (2999ds/4Mi)
% 3.05/1.67 % (9942)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/2Mi)
% 3.05/1.67 % (9943)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_9609 for (2999ds/2Mi)
% 3.05/1.67 % (9940)Instruction limit reached!
% 3.05/1.67 % (9940)------------------------------
% 3.05/1.67 % (9940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (9940)Termination reason: Unknown
% 3.05/1.67 % (9940)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (9940)Memory used [KB]: 1663
% 3.05/1.67 % (9940)Time elapsed: 0.003 s
% 3.05/1.67 % (9940)Instructions burned: 5 (million)
% 3.05/1.67 % (9940)------------------------------
% 3.05/1.67 % (9940)------------------------------
% 3.05/1.67 % (9942)Instruction limit reached!
% 3.05/1.67 % (9942)------------------------------
% 3.05/1.67 % (9942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (9942)Termination reason: Unknown
% 3.05/1.67 % (9942)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (9942)Memory used [KB]: 1535
% 3.05/1.67 % (9942)Time elapsed: 0.003 s
% 3.05/1.67 % (9942)Instructions burned: 4 (million)
% 3.05/1.67 % (9942)------------------------------
% 3.05/1.67 % (9942)------------------------------
% 3.05/1.67 % (9943)Instruction limit reached!
% 3.05/1.67 % (9943)------------------------------
% 3.05/1.67 % (9943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (9943)Termination reason: Unknown
% 3.05/1.67 % (9943)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (9943)Memory used [KB]: 1535
% 3.05/1.67 % (9943)Time elapsed: 0.002 s
% 3.05/1.67 % (9943)Instructions burned: 2 (million)
% 3.05/1.67 % (9943)------------------------------
% 3.05/1.67 % (9943)------------------------------
% 3.05/1.68 % (9941)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_9609 for (2999ds/27Mi)
% 3.05/1.68 % (9944)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_9609 for (2999ds/275Mi)
% 3.05/1.68 % (9945)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/18Mi)
% 3.05/1.68 % (9947)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_9609 for (2999ds/37Mi)
% 3.05/1.68 % (9948)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_9609 for (2999ds/15Mi)
% 3.05/1.69 % (9948)Instruction limit reached!
% 3.05/1.69 % (9948)------------------------------
% 3.05/1.69 % (9948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (9948)Termination reason: Unknown
% 3.05/1.69 % (9948)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (9948)Memory used [KB]: 1918
% 3.05/1.69 % (9948)Time elapsed: 0.008 s
% 3.05/1.69 % (9948)Instructions burned: 17 (million)
% 3.05/1.69 % (9948)------------------------------
% 3.05/1.69 % (9948)------------------------------
% 3.05/1.69 % (9945)Instruction limit reached!
% 3.05/1.69 % (9945)------------------------------
% 3.05/1.69 % (9945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (9945)Termination reason: Unknown
% 3.05/1.69 % (9945)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (9945)Memory used [KB]: 1918
% 3.05/1.69 % (9945)Time elapsed: 0.013 s
% 3.05/1.69 % (9945)Instructions burned: 18 (million)
% 3.05/1.69 % (9945)------------------------------
% 3.05/1.69 % (9945)------------------------------
% 3.05/1.69 % (9946)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/3Mi)
% 3.05/1.69 % (9946)Instruction limit reached!
% 3.05/1.69 % (9946)------------------------------
% 3.05/1.69 % (9946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (9946)Termination reason: Unknown
% 3.05/1.69 % (9946)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (9946)Memory used [KB]: 1535
% 3.05/1.69 % (9946)Time elapsed: 0.004 s
% 3.05/1.69 % (9946)Instructions burned: 3 (million)
% 3.05/1.69 % (9946)------------------------------
% 3.05/1.69 % (9946)------------------------------
% 3.05/1.69 % (9947)Instruction limit reached!
% 3.05/1.69 % (9947)------------------------------
% 3.05/1.69 % (9947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (9947)Termination reason: Unknown
% 3.05/1.69 % (9947)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (9947)Memory used [KB]: 2430
% 3.05/1.69 % (9947)Time elapsed: 0.012 s
% 3.05/1.69 % (9947)Instructions burned: 40 (million)
% 3.05/1.69 % (9947)------------------------------
% 3.05/1.69 % (9947)------------------------------
% 3.05/1.69 % (9941)Instruction limit reached!
% 3.05/1.69 % (9941)------------------------------
% 3.05/1.69 % (9941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (9941)Termination reason: Unknown
% 3.05/1.69 % (9941)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (9941)Memory used [KB]: 2046
% 3.05/1.69 % (9941)Time elapsed: 0.019 s
% 3.05/1.69 % (9941)Instructions burned: 28 (million)
% 3.05/1.69 % (9941)------------------------------
% 3.05/1.69 % (9941)------------------------------
% 3.09/1.70 % (9949)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_9609 for (2999ds/3Mi)
% 3.09/1.70 % (9949)Instruction limit reached!
% 3.09/1.70 % (9949)------------------------------
% 3.09/1.70 % (9949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.70 % (9949)Termination reason: Unknown
% 3.09/1.70 % (9949)Termination phase: shuffling
% 3.09/1.70
% 3.09/1.70 % (9949)Memory used [KB]: 1535
% 3.09/1.70 % (9949)Time elapsed: 0.002 s
% 3.09/1.70 % (9949)Instructions burned: 3 (million)
% 3.09/1.70 % (9949)------------------------------
% 3.09/1.70 % (9949)------------------------------
% 3.09/1.70 % (9952)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/16Mi)
% 3.09/1.70 % (9950)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_9609 for (2999ds/1041Mi)
% 3.09/1.71 % (9952)Instruction limit reached!
% 3.09/1.71 % (9952)------------------------------
% 3.09/1.71 % (9952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.71 % (9952)Termination reason: Unknown
% 3.09/1.71 % (9952)Termination phase: shuffling
% 3.09/1.71
% 3.09/1.71 % (9952)Memory used [KB]: 1918
% 3.09/1.71 % (9952)Time elapsed: 0.007 s
% 3.09/1.71 % (9952)Instructions burned: 19 (million)
% 3.09/1.71 % (9952)------------------------------
% 3.09/1.71 % (9952)------------------------------
% 3.09/1.71 % (9951)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/7Mi)
% 3.09/1.71 % (9954)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_9609 for (2999ds/3Mi)
% 3.09/1.71 % (9953)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_9609 for (2999ds/3Mi)
% 3.09/1.71 % (9954)Instruction limit reached!
% 3.09/1.71 % (9954)------------------------------
% 3.09/1.71 % (9954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.71 % (9954)Termination reason: Unknown
% 3.09/1.71 % (9954)Termination phase: shuffling
% 3.09/1.71
% 3.09/1.71 % (9954)Memory used [KB]: 1535
% 3.09/1.71 % (9954)Time elapsed: 0.003 s
% 3.09/1.71 % (9954)Instructions burned: 3 (million)
% 3.09/1.71 % (9954)------------------------------
% 3.09/1.71 % (9954)------------------------------
% 3.09/1.71 % (9953)Instruction limit reached!
% 3.09/1.71 % (9953)------------------------------
% 3.09/1.71 % (9953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.71 % (9953)Termination reason: Unknown
% 3.09/1.71 % (9953)Termination phase: shuffling
% 3.09/1.71
% 3.09/1.71 % (9953)Memory used [KB]: 1535
% 3.09/1.71 % (9953)Time elapsed: 0.004 s
% 3.09/1.71 % (9953)Instructions burned: 5 (million)
% 3.09/1.71 % (9953)------------------------------
% 3.09/1.71 % (9953)------------------------------
% 3.09/1.71 % (9951)Instruction limit reached!
% 3.09/1.71 % (9951)------------------------------
% 3.09/1.71 % (9951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.71 % (9951)Termination reason: Unknown
% 3.09/1.71 % (9951)Termination phase: shuffling
% 3.09/1.71
% 3.09/1.71 % (9951)Memory used [KB]: 1663
% 3.09/1.71 % (9951)Time elapsed: 0.007 s
% 3.09/1.71 % (9951)Instructions burned: 8 (million)
% 3.09/1.71 % (9951)------------------------------
% 3.09/1.71 % (9951)------------------------------
% 3.09/1.72 % (9955)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/7Mi)
% 3.09/1.72 % (9939)Instruction limit reached!
% 3.09/1.72 % (9939)------------------------------
% 3.09/1.72 % (9939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (9939)Termination reason: Unknown
% 3.09/1.72 % (9939)Termination phase: Saturation
% 3.09/1.72
% 3.09/1.72 % (9939)Memory used [KB]: 7675
% 3.09/1.72 % (9939)Time elapsed: 0.051 s
% 3.09/1.72 % (9939)Instructions burned: 183 (million)
% 3.09/1.72 % (9939)------------------------------
% 3.09/1.72 % (9939)------------------------------
% 3.09/1.72 % (9955)Instruction limit reached!
% 3.09/1.72 % (9955)------------------------------
% 3.09/1.72 % (9955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (9955)Termination reason: Unknown
% 3.09/1.72 % (9955)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (9955)Memory used [KB]: 1663
% 3.09/1.72 % (9955)Time elapsed: 0.004 s
% 3.09/1.72 % (9955)Instructions burned: 9 (million)
% 3.09/1.72 % (9955)------------------------------
% 3.09/1.72 % (9955)------------------------------
% 3.09/1.72 % (9956)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/3Mi)
% 3.09/1.72 % (9956)Instruction limit reached!
% 3.09/1.72 % (9956)------------------------------
% 3.09/1.72 % (9956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (9956)Termination reason: Unknown
% 3.09/1.72 % (9956)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (9956)Memory used [KB]: 1535
% 3.09/1.72 % (9956)Time elapsed: 0.003 s
% 3.09/1.72 % (9956)Instructions burned: 4 (million)
% 3.09/1.72 % (9956)------------------------------
% 3.09/1.72 % (9956)------------------------------
% 3.09/1.72 % (9957)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/4Mi)
% 3.09/1.72 % (9957)Instruction limit reached!
% 3.09/1.72 % (9957)------------------------------
% 3.09/1.72 % (9957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.72 % (9957)Termination reason: Unknown
% 3.09/1.72 % (9957)Termination phase: shuffling
% 3.09/1.72
% 3.09/1.72 % (9957)Memory used [KB]: 1535
% 3.09/1.72 % (9957)Time elapsed: 0.003 s
% 3.09/1.72 % (9957)Instructions burned: 4 (million)
% 3.09/1.72 % (9957)------------------------------
% 3.09/1.72 % (9957)------------------------------
% 3.09/1.73 % (9959)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/710Mi)
% 3.09/1.73 % (9960)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/6Mi)
% 3.09/1.73 % (9958)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/18Mi)
% 3.09/1.73 % (9960)Instruction limit reached!
% 3.09/1.73 % (9960)------------------------------
% 3.09/1.73 % (9960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.73 % (9960)Termination reason: Unknown
% 3.09/1.73 % (9960)Termination phase: shuffling
% 3.09/1.73
% 3.09/1.73 % (9960)Memory used [KB]: 1663
% 3.09/1.73 % (9960)Time elapsed: 0.003 s
% 3.09/1.73 % (9960)Instructions burned: 6 (million)
% 3.09/1.73 % (9960)------------------------------
% 3.09/1.73 % (9960)------------------------------
% 3.09/1.73 % (9961)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_9609 for (2999ds/902Mi)
% 3.09/1.73 % (9962)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_9609 for (2999ds/21Mi)
% 3.09/1.74 % (9963)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9609 for (2999ds/5Mi)
% 3.09/1.74 % (9962)Instruction limit reached!
% 3.09/1.74 % (9962)------------------------------
% 3.09/1.74 % (9962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.74 % (9962)Termination reason: Unknown
% 3.09/1.74 % (9962)Termination phase: shuffling
% 3.09/1.74
% 3.09/1.74 % (9962)Memory used [KB]: 1918
% 3.09/1.74 % (9962)Time elapsed: 0.009 s
% 3.09/1.74 % (9962)Instructions burned: 21 (million)
% 3.09/1.74 % (9962)------------------------------
% 3.09/1.74 % (9962)------------------------------
% 3.09/1.74 % (9958)Instruction limit reached!
% 3.09/1.74 % (9958)------------------------------
% 3.09/1.74 % (9958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.74 % (9958)Termination reason: Unknown
% 3.09/1.74 % (9958)Termination phase: shuffling
% 3.09/1.74
% 3.09/1.74 % (9958)Memory used [KB]: 1918
% 3.09/1.74 % (9958)Time elapsed: 0.013 s
% 3.09/1.74 % (9958)Instructions burned: 18 (million)
% 3.09/1.74 % (9958)------------------------------
% 3.09/1.74 % (9958)------------------------------
% 3.09/1.74 % (9963)Instruction limit reached!
% 3.09/1.74 % (9963)------------------------------
% 3.09/1.74 % (9963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.74 % (9963)Termination reason: Unknown
% 3.09/1.74 % (9963)Termination phase: shuffling
% 3.09/1.74
% 3.09/1.74 % (9963)Memory used [KB]: 1663
% 3.09/1.74 % (9963)Time elapsed: 0.003 s
% 3.09/1.74 % (9963)Instructions burned: 6 (million)
% 3.09/1.74 % (9963)------------------------------
% 3.09/1.74 % (9963)------------------------------
% 3.09/1.75 % (9959)First to succeed.
% 3.09/1.75 % (9966)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_9609 for (2998ds/779Mi)
% 3.09/1.75 % (9964)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_9609 for (2998ds/6Mi)
% 3.09/1.75 % (9959)Refutation found. Thanks to Tanya!
% 3.09/1.75 % SZS status Theorem for DTF2THF_9609
% 3.09/1.75 % SZS output start Proof for DTF2THF_9609
% 3.09/1.75 thf(type_def_5, type, option_trm: $tType).
% 3.09/1.75 thf(type_def_7, type, char: $tType).
% 3.09/1.75 thf(type_def_8, type, option_fml: $tType).
% 3.09/1.75 thf(type_def_9, type, option_game: $tType).
% 3.09/1.75 thf(type_def_10, type, produc799602994n_game: $tType).
% 3.09/1.75 thf(type_def_11, type, produc62062515n_game: $tType).
% 3.09/1.75 thf(type_def_12, type, set_variable: $tType).
% 3.09/1.75 thf(type_def_13, type, trm: $tType).
% 3.09/1.75 thf(type_def_14, type, variable: $tType).
% 3.09/1.75 thf(type_def_15, type, set_Pr79606376n_game: $tType).
% 3.09/1.75 thf(type_def_16, type, set_Pr739694057n_game: $tType).
% 3.09/1.75 thf(type_def_17, type, set_Pr720454634n_game: $tType).
% 3.09/1.75 thf(type_def_18, type, set_Pr1235432374le_trm: $tType).
% 3.09/1.75 thf(type_def_19, type, set_Pr943832262on_trm: $tType).
% 3.09/1.75 thf(type_def_20, type, set_char: $tType).
% 3.09/1.75 thf(type_def_21, type, fml: $tType).
% 3.09/1.75 thf(type_def_22, type, game: $tType).
% 3.09/1.75 thf(type_def_23, type, produc1418842292n_game: $tType).
% 3.09/1.75 thf(type_def_24, type, denotational_interp: $tType).
% 3.09/1.75 thf(type_def_25, type, produc833882726rp_trm: $tType).
% 3.09/1.75 thf(type_def_26, type, produc46605351on_fml: $tType).
% 3.09/1.75 thf(type_def_27, type, produc1739631244on_fml: $tType).
% 3.09/1.75 thf(type_def_28, type, produc1016592119n_game: $tType).
% 3.09/1.75 thf(type_def_29, type, produc1072747943on_trm: $tType).
% 3.09/1.75 thf(type_def_30, type, produc1367888000le_trm: $tType).
% 3.09/1.75 thf(type_def_31, type, produc1699626005le_trm: $tType).
% 3.09/1.75 thf(type_def_32, type, produc464795408on_trm: $tType).
% 3.09/1.75 thf(type_def_33, type, produc1408538418on_fml: $tType).
% 3.09/1.75 thf(type_def_34, type, produc1024976764on_trm: $tType).
% 3.09/1.75 thf(type_def_35, type, real: $tType).
% 3.09/1.75 thf(func_def_0, type, produc1699626005le_trm: $tType).
% 3.09/1.75 thf(func_def_1, type, set_Pr720454634n_game: $tType).
% 3.09/1.75 thf(func_def_2, type, produc1418842292n_game: $tType).
% 3.09/1.75 thf(func_def_3, type, set_Pr739694057n_game: $tType).
% 3.09/1.75 thf(func_def_4, type, produc62062515n_game: $tType).
% 3.09/1.75 thf(func_def_5, type, set_Pr79606376n_game: $tType).
% 3.09/1.75 thf(func_def_6, type, produc799602994n_game: $tType).
% 3.09/1.75 thf(func_def_7, type, produc1016592119n_game: $tType).
% 3.09/1.75 thf(func_def_8, type, produc1739631244on_fml: $tType).
% 3.09/1.75 thf(func_def_9, type, produc1072747943on_trm: $tType).
% 3.09/1.75 thf(func_def_10, type, produc46605351on_fml: $tType).
% 3.09/1.75 thf(func_def_11, type, set_Pr943832262on_trm: $tType).
% 3.09/1.75 thf(func_def_12, type, set_Pr1235432374le_trm: $tType).
% 3.09/1.75 thf(func_def_13, type, produc1024976764on_trm: $tType).
% 3.09/1.75 thf(func_def_14, type, produc1408538418on_fml: $tType).
% 3.09/1.75 thf(func_def_15, type, produc464795408on_trm: $tType).
% 3.09/1.75 thf(func_def_16, type, produc833882726rp_trm: $tType).
% 3.09/1.75 thf(func_def_17, type, produc1367888000le_trm: $tType).
% 3.09/1.75 thf(func_def_18, type, option_game: $tType).
% 3.09/1.75 thf(func_def_19, type, option_trm: $tType).
% 3.09/1.75 thf(func_def_20, type, option_fml: $tType).
% 3.09/1.75 thf(func_def_21, type, denotational_interp: $tType).
% 3.09/1.75 thf(func_def_22, type, set_variable: $tType).
% 3.09/1.75 thf(func_def_23, type, set_char: $tType).
% 3.09/1.75 thf(func_def_24, type, variable: $tType).
% 3.09/1.75 thf(func_def_25, type, game: $tType).
% 3.09/1.75 thf(func_def_26, type, char: $tType).
% 3.09/1.75 thf(func_def_27, type, trm: $tType).
% 3.09/1.75 thf(func_def_28, type, fml: $tType).
% 3.09/1.75 thf(func_def_29, type, real: $tType).
% 3.09/1.75 thf(func_def_30, type, if_option_trm: $o > option_trm > option_trm > option_trm).
% 3.09/1.75 thf(func_def_31, type, inf_in243546115game_o: ((char > option_fml) > (char > option_game) > $o) > ((char > option_fml) > (char > option_game) > $o) > (char > option_fml) > (char > option_game) > $o).
% 3.09/1.75 thf(func_def_32, type, inf_in1072207554game_o: ((char > option_trm) > produc799602994n_game > $o) > ((char > option_trm) > produc799602994n_game > $o) > (char > option_trm) > produc799602994n_game > $o).
% 3.09/1.75 thf(func_def_33, type, inf_in1920662529game_o: ((char > option_trm) > produc62062515n_game > $o) > ((char > option_trm) > produc62062515n_game > $o) > (char > option_trm) > produc62062515n_game > $o).
% 3.09/1.75 thf(func_def_34, type, inf_in185389155_trm_o: (set_variable > trm > $o) > (set_variable > trm > $o) > set_variable > trm > $o).
% 3.09/1.75 thf(func_def_35, type, inf_in605351507_trm_o: (char > option_trm > $o) > (char > option_trm > $o) > char > option_trm > $o).
% 3.09/1.75 thf(func_def_36, type, inf_inf_char_o: (char > $o) > (char > $o) > char > $o).
% 3.09/1.75 thf(func_def_37, type, inf_inf_variable_o: (variable > $o) > (variable > $o) > variable > $o).
% 3.09/1.75 thf(func_def_38, type, inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game).
% 3.09/1.75 thf(func_def_39, type, inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game).
% 3.09/1.75 thf(func_def_40, type, inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game).
% 3.09/1.75 thf(func_def_41, type, inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm).
% 3.09/1.75 thf(func_def_42, type, inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm).
% 3.09/1.75 thf(func_def_43, type, inf_inf_set_char: set_char > set_char > set_char).
% 3.09/1.75 thf(func_def_44, type, inf_inf_set_variable: set_variable > set_variable > set_variable).
% 3.09/1.75 thf(func_def_45, type, combine_options_fml: (fml > fml > fml) > option_fml > option_fml > option_fml).
% 3.09/1.75 thf(func_def_46, type, combine_options_game: (game > game > game) > option_game > option_game > option_game).
% 3.09/1.75 thf(func_def_47, type, combine_options_trm: (trm > trm > trm) > option_trm > option_trm > option_trm).
% 3.09/1.75 thf(func_def_48, type, none_fml: option_fml).
% 3.09/1.75 thf(func_def_49, type, none_game: option_game).
% 3.09/1.75 thf(func_def_50, type, none_trm: option_trm).
% 3.09/1.75 thf(func_def_51, type, some_fml: fml > option_fml).
% 3.09/1.75 thf(func_def_52, type, some_game: game > option_game).
% 3.09/1.75 thf(func_def_53, type, some_trm: trm > option_trm).
% 3.09/1.75 thf(func_def_54, type, case_option_o_fml: $o > (fml > $o) > option_fml > $o).
% 3.09/1.75 thf(func_def_55, type, case_option_o_game: $o > (game > $o) > option_game > $o).
% 3.09/1.75 thf(func_def_56, type, case_option_o_trm: $o > (trm > $o) > option_trm > $o).
% 3.09/1.75 thf(func_def_57, type, case_o209804997ml_fml: option_fml > (fml > option_fml) > option_fml > option_fml).
% 3.09/1.75 thf(func_def_58, type, case_o696458451e_game: option_game > (game > option_game) > option_game > option_game).
% 3.09/1.75 thf(func_def_59, type, case_o487727941rm_trm: option_trm > (trm > option_trm) > option_trm > option_trm).
% 3.09/1.75 thf(func_def_60, type, the_fml: option_fml > fml).
% 3.09/1.75 thf(func_def_61, type, the_game: option_game > game).
% 3.09/1.75 thf(func_def_62, type, the_trm: option_trm > trm).
% 3.09/1.75 thf(func_def_63, type, bot_bo1895715589game_o: (char > option_fml) > (char > option_game) > $o).
% 3.09/1.75 thf(func_def_64, type, bot_bo1417568964game_o: (char > option_trm) > produc799602994n_game > $o).
% 3.09/1.75 thf(func_def_65, type, bot_bot_char_o: char > $o).
% 3.09/1.75 thf(func_def_66, type, bot_bot_variable_o: variable > $o).
% 3.09/1.75 thf(func_def_67, type, bot_bo456479484n_game: set_Pr79606376n_game).
% 3.09/1.75 thf(func_def_68, type, bot_bo1302831229n_game: set_Pr739694057n_game).
% 3.09/1.75 thf(func_def_69, type, bot_bot_set_char: set_char).
% 3.09/1.75 thf(func_def_70, type, bot_bot_set_variable: set_variable).
% 3.09/1.75 thf(func_def_71, type, produc123610156n_game: (char > option_fml) > (char > option_game) > produc799602994n_game).
% 3.09/1.75 thf(func_def_72, type, produc1048060077n_game: (char > option_trm) > produc799602994n_game > produc62062515n_game).
% 3.09/1.75 thf(func_def_73, type, produc1618635950n_game: (char > option_trm) > produc62062515n_game > produc1418842292n_game).
% 3.09/1.75 thf(func_def_74, type, produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm).
% 3.09/1.75 thf(func_def_75, type, produc909629463on_fml: option_fml > option_fml > produc46605351on_fml).
% 3.09/1.75 thf(func_def_76, type, produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml).
% 3.09/1.75 thf(func_def_77, type, produc1111617711n_game: option_game > option_game > produc1016592119n_game).
% 3.09/1.75 thf(func_def_78, type, produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm).
% 3.09/1.75 thf(func_def_79, type, produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm).
% 3.09/1.75 thf(func_def_80, type, produc1482344242le_trm: set_variable > trm > produc1367888000le_trm).
% 3.09/1.75 thf(func_def_81, type, produc1500300866on_trm: char > option_trm > produc464795408on_trm).
% 3.09/1.75 thf(func_def_82, type, produc1205977188on_fml: variable > option_fml > produc1408538418on_fml).
% 3.09/1.75 thf(func_def_83, type, produc1743721902on_trm: variable > option_trm > produc1024976764on_trm).
% 3.09/1.75 thf(func_def_84, type, produc1598111045on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 3.09/1.75 thf(func_def_85, type, produc1214549391on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 3.09/1.75 thf(func_def_86, type, produc377919108on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 3.09/1.75 thf(func_def_87, type, produc2141841102on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 3.09/1.75 thf(func_def_88, type, produc1278328899on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 3.09/1.75 thf(func_def_89, type, produc1420172399on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 3.09/1.75 thf(func_def_90, type, produc1036610745on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 3.09/1.75 thf(func_def_91, type, produc159680767game_o: ((char > option_fml) > (char > option_game) > $o) > produc799602994n_game > $o).
% 3.09/1.75 thf(func_def_92, type, produc347802313on_fml: ((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml).
% 3.09/1.75 thf(func_def_93, type, produc885547027on_trm: ((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm).
% 3.09/1.75 thf(func_def_94, type, produc629249376t_char: ((char > option_fml) > (char > option_game) > set_char) > produc799602994n_game > set_char).
% 3.09/1.75 thf(func_def_95, type, produc1615133358on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 3.09/1.75 thf(func_def_96, type, produc1231571704on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 3.09/1.75 thf(func_def_97, type, produc1868740670game_o: ((char > option_trm) > produc799602994n_game > $o) > produc62062515n_game > $o).
% 3.09/1.75 thf(func_def_98, type, produc154833544on_fml: ((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml).
% 3.09/1.75 thf(func_def_99, type, produc692578258on_trm: ((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm).
% 3.09/1.75 thf(func_def_100, type, produc1554403041t_char: ((char > option_trm) > produc799602994n_game > set_char) > produc62062515n_game > set_char).
% 3.09/1.75 thf(func_def_101, type, produc1250175341on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 3.09/1.75 thf(func_def_102, type, produc866613687on_trm: ((char > option_trm) > produc62062515n_game > char > option_trm) > produc1418842292n_game > char > option_trm).
% 3.09/1.75 thf(func_def_103, type, produc1707653117game_o: ((char > option_trm) > produc62062515n_game > $o) > produc1418842292n_game > $o).
% 3.09/1.75 thf(func_def_104, type, produc1499310791on_fml: ((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml).
% 3.09/1.75 thf(func_def_105, type, produc1002100706t_char: ((char > option_trm) > produc62062515n_game > set_char) > produc1418842292n_game > set_char).
% 3.09/1.75 thf(func_def_106, type, produc82209913_trm_o: (set_variable > trm > $o) > produc1367888000le_trm > $o).
% 3.09/1.75 thf(func_def_107, type, produc836445798t_char: (set_variable > trm > set_char) > produc1367888000le_trm > set_char).
% 3.09/1.75 thf(func_def_108, type, produc584666985_trm_o: (char > option_trm > $o) > produc464795408on_trm > $o).
% 3.09/1.75 thf(func_def_109, type, produc33263478t_char: (char > option_trm > set_char) > produc464795408on_trm > set_char).
% 3.09/1.75 thf(func_def_110, type, collect_char: (char > $o) > set_char).
% 3.09/1.75 thf(func_def_111, type, collect_variable: (variable > $o) > set_variable).
% 3.09/1.75 thf(func_def_112, type, is_empty_variable: set_variable > $o).
% 3.09/1.75 thf(func_def_113, type, static_FVF: fml > set_variable).
% 3.09/1.75 thf(func_def_114, type, static_FVT: trm > set_variable).
% 3.09/1.75 thf(func_def_115, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 3.09/1.75 thf(func_def_116, type, geq: trm > trm > fml).
% 3.09/1.75 thf(func_def_117, type, pred: char > trm > fml).
% 3.09/1.75 thf(func_def_118, type, const: char > trm).
% 3.09/1.75 thf(func_def_119, type, differential: trm > trm).
% 3.09/1.75 thf(func_def_120, type, func: char > trm > trm).
% 3.09/1.75 thf(func_def_121, type, number: real > trm).
% 3.09/1.75 thf(func_def_122, type, plus: trm > trm > trm).
% 3.09/1.75 thf(func_def_123, type, times: trm > trm > trm).
% 3.09/1.75 thf(func_def_124, type, var: variable > trm).
% 3.09/1.75 thf(func_def_125, type, uSubst716837505ntialo: option_trm > option_trm).
% 3.09/1.75 thf(func_def_126, type, uSubst152838031e_Geqo: option_trm > option_trm > option_fml).
% 3.09/1.75 thf(func_def_127, type, uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 3.09/1.75 thf(func_def_128, type, uSubst141955042_Pluso: option_trm > option_trm > option_trm).
% 3.09/1.75 thf(func_def_129, type, uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 3.09/1.75 thf(func_def_130, type, uSubst918876924Timeso: option_trm > option_trm > option_trm).
% 3.09/1.75 thf(func_def_131, type, uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 3.09/1.75 thf(func_def_132, type, uSubst_Mirabelle_dot: trm).
% 3.09/1.75 thf(func_def_133, type, uSubst1408967625substt: trm > produc1418842292n_game).
% 3.09/1.75 thf(func_def_134, type, uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm).
% 3.09/1.75 thf(func_def_135, type, uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml).
% 3.09/1.75 thf(func_def_136, type, uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm).
% 3.09/1.75 thf(func_def_137, type, uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o).
% 3.09/1.75 thf(func_def_138, type, accp_P758790320on_trm: (produc1072747943on_trm > produc1072747943on_trm > $o) > produc1072747943on_trm > $o).
% 3.09/1.75 thf(func_def_139, type, accp_P1877119646le_trm: (produc1699626005le_trm > produc1699626005le_trm > $o) > produc1699626005le_trm > $o).
% 3.09/1.75 thf(func_def_140, type, member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o).
% 3.09/1.75 thf(func_def_141, type, member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o).
% 3.09/1.75 thf(func_def_142, type, member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o).
% 3.09/1.75 thf(func_def_143, type, member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o).
% 3.09/1.75 thf(func_def_144, type, member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o).
% 3.09/1.75 thf(func_def_145, type, member_char: char > set_char > $o).
% 3.09/1.75 thf(func_def_146, type, member_variable: variable > set_variable > $o).
% 3.09/1.75 thf(func_def_147, type, u: set_variable).
% 3.09/1.75 thf(func_def_148, type, v: set_variable).
% 3.09/1.75 thf(func_def_149, type, sigma: produc1418842292n_game).
% 3.09/1.75 thf(func_def_150, type, f: char).
% 3.09/1.75 thf(func_def_165, type, sK0: produc1418842292n_game > char > set_variable > trm).
% 3.09/1.75 thf(func_def_166, type, sK1: produc1418842292n_game > char > set_variable > trm).
% 3.09/1.75 thf(f884,plain,(
% 3.09/1.75 $false),
% 3.09/1.75 inference(avatar_sat_refutation,[status(thm)],[f858,f871,f873,f879,f883])).
% 3.09/1.75 thf(f883,plain,(
% 3.09/1.75 ~spl2_3 | ~spl2_6),
% 3.09/1.75 inference(avatar_contradiction_clause,[status(thm)],[f882])).
% 3.09/1.75 thf(f882,plain,(
% 3.09/1.75 $false | (~spl2_3 | ~spl2_6)),
% 3.09/1.75 inference(subsumption_resolution,[status(thm)],[f881,f859])).
% 3.09/1.75 thf(f859,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ v @ f) != (uSubst1559070963pconst @ sigma @ u @ f))),
% 3.09/1.75 inference(forward_demodulation,[status(thm)],[f839,f829])).
% 3.09/1.75 thf(f829,plain,(
% 3.09/1.75 ( ! [X2 : produc1418842292n_game,X0 : char,X1 : set_variable] : (((uSubst1559070963pconst @ X2 @ X1 @ X0) = (uSubst516392818stappt @ X2 @ X1 @ (const @ X0)))) )),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f798])).
% 3.09/1.75 thf(f798,plain,(
% 3.09/1.75 ! [X0 : char,X1 : set_variable,X2 : produc1418842292n_game] : ((uSubst1559070963pconst @ X2 @ X1 @ X0) = (uSubst516392818stappt @ X2 @ X1 @ (const @ X0)))),
% 3.09/1.75 inference(rectify,[status(thm)],[f8])).
% 3.09/1.75 thf(f8,axiom,(
% 3.09/1.75 ! [X14 : char,X13 : set_variable,X12 : produc1418842292n_game] : ((uSubst516392818stappt @ X12 @ X13 @ (const @ X14)) = (uSubst1559070963pconst @ X12 @ X13 @ X14))),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_7_usubstappt_Osimps_I3_J)).
% 3.09/1.75 thf(f839,plain,(
% 3.09/1.75 ((uSubst516392818stappt @ sigma @ u @ (const @ f)) != (uSubst1559070963pconst @ sigma @ v @ f))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f807])).
% 3.09/1.75 thf(f807,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) & ((uSubst516392818stappt @ sigma @ u @ (const @ f)) != (uSubst1559070963pconst @ sigma @ v @ f))),
% 3.09/1.75 inference(ennf_transformation,[status(thm)],[f589])).
% 3.09/1.75 thf(f589,plain,(
% 3.09/1.75 ~(((uSubst516392818stappt @ sigma @ u @ (const @ f)) = (uSubst1559070963pconst @ sigma @ v @ f)) | (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))),
% 3.09/1.75 inference(fool_elimination,[status(thm)],[f588])).
% 3.09/1.75 thf(f588,plain,(
% 3.09/1.75 ~(((uSubst516392818stappt @ sigma @ u @ (const @ f)) = (uSubst1559070963pconst @ sigma @ v @ f)) | ((produc866613687on_trm @ (^[X0 : char > option_trm] : (produc1231571704on_trm @ (^[X1 : char > option_trm] : (produc1036610745on_trm @ (^[X2 : char > option_fml, X3 : char > option_game] : (X0)))))) @ sigma @ f) = none_trm))),
% 3.09/1.75 inference(rectify,[status(thm)],[f357])).
% 3.09/1.75 thf(f357,negated_conjecture,(
% 3.09/1.75 ~(((uSubst516392818stappt @ sigma @ u @ (const @ f)) = (uSubst1559070963pconst @ sigma @ v @ f)) | ((produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f) = none_trm))),
% 3.09/1.75 inference(negated_conjecture,[status(cth)],[f356])).
% 3.09/1.75 thf(f356,conjecture,(
% 3.09/1.75 ((uSubst516392818stappt @ sigma @ u @ (const @ f)) = (uSubst1559070963pconst @ sigma @ v @ f)) | ((produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f) = none_trm)),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',conj_0)).
% 3.09/1.75 thf(f881,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ v @ f) = (uSubst1559070963pconst @ sigma @ u @ f)) | (~spl2_3 | ~spl2_6)),
% 3.09/1.75 inference(forward_demodulation,[status(thm)],[f878,f857])).
% 3.09/1.75 thf(f857,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | ~spl2_3),
% 3.09/1.75 inference(avatar_component_clause,[status(thm)],[f855])).
% 3.09/1.75 thf(f855,definition,(
% 3.09/1.75 spl2_3 <=> ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))))),
% 3.09/1.75 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 3.09/1.75 thf(f878,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | ~spl2_6),
% 3.09/1.75 inference(avatar_component_clause,[status(thm)],[f876])).
% 3.09/1.75 thf(f876,definition,(
% 3.09/1.75 spl2_6 <=> ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))))),
% 3.09/1.75 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 3.09/1.75 thf(f879,plain,(
% 3.09/1.75 ~spl2_5 | spl2_6),
% 3.09/1.75 inference(avatar_split_clause,[status(thm)],[f874,f876,f866])).
% 3.09/1.75 thf(f866,definition,(
% 3.09/1.75 spl2_5 <=> (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 3.09/1.75 thf(f874,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(subsumption_resolution,[status(thm)],[f822,f840])).
% 3.09/1.75 thf(f840,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f807])).
% 3.09/1.75 thf(f822,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f810])).
% 3.09/1.75 thf(f810,plain,(
% 3.09/1.75 (((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v)) | (none_trm = (uSubst1559070963pconst @ sigma @ v @ f))) & ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v)) | ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))))) | (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))),
% 3.09/1.75 inference(ennf_transformation,[status(thm)],[f378])).
% 3.09/1.75 thf(f378,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) => (((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v)) => ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))))) & ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v)) => (none_trm = (uSubst1559070963pconst @ sigma @ v @ f))))),
% 3.09/1.75 inference(fool_elimination,[status(thm)],[f377])).
% 3.09/1.75 thf(f377,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X0 : char > option_trm] : (produc1231571704on_trm @ (^[X1 : char > option_trm] : (produc1036610745on_trm @ (^[X2 : char > option_fml, X3 : char > option_game] : (X0)))))) @ sigma @ f)) => (((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X4 : char > option_trm] : (produc1231571704on_trm @ (^[X5 : char > option_trm] : (produc1036610745on_trm @ (^[X6 : char > option_fml, X7 : char > option_game] : (X4)))))) @ sigma @ f))) @ v)) => ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[X8 : char > option_trm] : (produc1231571704on_trm @ (^[X9 : char > option_trm] : (produc1036610745on_trm @ (^[X10 : char > option_fml, X11 : char > option_game] : (X8)))))) @ sigma @ f))))) & (((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X12 : char > option_trm] : (produc1231571704on_trm @ (^[X13 : char > option_trm] : (produc1036610745on_trm @ (^[X14 : char > option_fml, X15 : char > option_game] : (X12)))))) @ sigma @ f))) @ v) != bot_bot_set_variable) => (none_trm = (uSubst1559070963pconst @ sigma @ v @ f))))),
% 3.09/1.75 inference(rectify,[status(thm)],[f10])).
% 3.09/1.75 thf(f10,axiom,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f)) => (((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ v)) => ((uSubst1559070963pconst @ sigma @ v @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))))) & (((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ v) != bot_bot_set_variable) => (none_trm = (uSubst1559070963pconst @ sigma @ v @ f))))),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062)).
% 3.09/1.75 thf(f873,plain,(
% 3.09/1.75 spl2_2),
% 3.09/1.75 inference(avatar_split_clause,[status(thm)],[f872,f848])).
% 3.09/1.75 thf(f848,definition,(
% 3.09/1.75 spl2_2 <=> (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 3.09/1.75 thf(f872,plain,(
% 3.09/1.75 (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(subsumption_resolution,[status(thm)],[f836,f840])).
% 3.09/1.75 thf(f836,plain,(
% 3.09/1.75 (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f802])).
% 3.09/1.75 thf(f802,plain,(
% 3.09/1.75 (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(ennf_transformation,[status(thm)],[f368])).
% 3.09/1.75 thf(f368,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) => (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(fool_elimination,[status(thm)],[f367])).
% 3.09/1.75 thf(f367,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X0 : char > option_trm] : (produc1231571704on_trm @ (^[X1 : char > option_trm] : (produc1036610745on_trm @ (^[X2 : char > option_fml, X3 : char > option_game] : (X0)))))) @ sigma @ f)) => (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X4 : char > option_trm] : (produc1231571704on_trm @ (^[X5 : char > option_trm] : (produc1036610745on_trm @ (^[X6 : char > option_fml, X7 : char > option_game] : (X4)))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(rectify,[status(thm)],[f4])).
% 3.09/1.75 thf(f4,axiom,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f)) => (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ u))),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_3_f3)).
% 3.09/1.75 thf(f871,plain,(
% 3.09/1.75 spl2_5),
% 3.09/1.75 inference(avatar_split_clause,[status(thm)],[f870,f866])).
% 3.09/1.75 thf(f870,plain,(
% 3.09/1.75 (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(subsumption_resolution,[status(thm)],[f818,f840])).
% 3.09/1.75 thf(f818,plain,(
% 3.09/1.75 (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f801])).
% 3.09/1.75 thf(f801,plain,(
% 3.09/1.75 (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(ennf_transformation,[status(thm)],[f643])).
% 3.09/1.75 thf(f643,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) => (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ v))),
% 3.09/1.75 inference(fool_elimination,[status(thm)],[f642])).
% 3.09/1.75 thf(f642,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X0 : char > option_trm] : (produc1231571704on_trm @ (^[X1 : char > option_trm] : (produc1036610745on_trm @ (^[X2 : char > option_fml, X3 : char > option_game] : (X0)))))) @ sigma @ f)) => ((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X4 : char > option_trm] : (produc1231571704on_trm @ (^[X5 : char > option_trm] : (produc1036610745on_trm @ (^[X6 : char > option_fml, X7 : char > option_game] : (X4)))))) @ sigma @ f))) @ v) = bot_bot_set_variable)),
% 3.09/1.75 inference(rectify,[status(thm)],[f5])).
% 3.09/1.75 thf(f5,axiom,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f)) => ((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ v) = bot_bot_set_variable)),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062)).
% 3.09/1.75 thf(f858,plain,(
% 3.09/1.75 ~spl2_2 | spl2_3),
% 3.09/1.75 inference(avatar_split_clause,[status(thm)],[f853,f855,f848])).
% 3.09/1.75 thf(f853,plain,(
% 3.09/1.75 (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u)) | ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))))),
% 3.09/1.75 inference(subsumption_resolution,[status(thm)],[f819,f840])).
% 3.09/1.75 thf(f819,plain,(
% 3.09/1.75 ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))),
% 3.09/1.75 inference(cnf_transformation,[status(thm)],[f800])).
% 3.09/1.75 thf(f800,plain,(
% 3.09/1.75 (none_trm = (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) | (((none_trm = (uSubst1559070963pconst @ sigma @ u @ f)) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))) & (((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)))) | (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u))))),
% 3.09/1.75 inference(ennf_transformation,[status(thm)],[f795])).
% 3.09/1.75 thf(f795,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f)) => (((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u)) => ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))))) & ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[Y0 : char > option_trm]: (produc1231571704on_trm @ (^[Y1 : char > option_trm]: (produc1036610745on_trm @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y0)))))))) @ sigma @ f))) @ u)) => (none_trm = (uSubst1559070963pconst @ sigma @ u @ f))))),
% 3.09/1.75 inference(fool_elimination,[status(thm)],[f794])).
% 3.09/1.75 thf(f794,plain,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X0 : char > option_trm] : (produc1231571704on_trm @ (^[X1 : char > option_trm] : (produc1036610745on_trm @ (^[X2 : char > option_fml, X3 : char > option_game] : (X0)))))) @ sigma @ f)) => ((((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X4 : char > option_trm] : (produc1231571704on_trm @ (^[X5 : char > option_trm] : (produc1036610745on_trm @ (^[X6 : char > option_fml, X7 : char > option_game] : (X4)))))) @ sigma @ f))) @ u) != bot_bot_set_variable) => (none_trm = (uSubst1559070963pconst @ sigma @ u @ f))) & (((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X8 : char > option_trm] : (produc1231571704on_trm @ (^[X9 : char > option_trm] : (produc1036610745on_trm @ (^[X10 : char > option_fml, X11 : char > option_game] : (X8)))))) @ sigma @ f))) @ u) = bot_bot_set_variable) => ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[X12 : char > option_trm] : (produc1231571704on_trm @ (^[X13 : char > option_trm] : (produc1036610745on_trm @ (^[X14 : char > option_fml, X15 : char > option_game] : (X12)))))) @ sigma @ f))))))),
% 3.09/1.75 inference(rectify,[status(thm)],[f11])).
% 3.09/1.75 thf(f11,axiom,(
% 3.09/1.75 (none_trm != (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f)) => ((((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ u) != bot_bot_set_variable) => (none_trm = (uSubst1559070963pconst @ sigma @ u @ f))) & (((inf_inf_set_variable @ (static_FVT @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))) @ u) = bot_bot_set_variable) => ((uSubst1559070963pconst @ sigma @ u @ f) = (some_trm @ (the_trm @ (produc866613687on_trm @ (^[X3 : char > option_trm] : (produc1231571704on_trm @ (^[X4 : char > option_trm] : (produc1036610745on_trm @ (^[X5 : char > option_fml, X6 : char > option_game] : (X3)))))) @ sigma @ f))))))),
% 3.09/1.75 file('/export/starexec/sandbox/tmp/tmp.61FlU5Q32e/DTF2THF_9609.p',fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062)).
% 3.09/1.75 % SZS output end Proof for DTF2THF_9609
% 3.09/1.75 % (9959)------------------------------
% 3.09/1.75 % (9959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.75 % (9959)Termination reason: Refutation
% 3.09/1.75
% 3.09/1.75 % (9959)Memory used [KB]: 6780
% 3.09/1.75 % (9959)Time elapsed: 0.024 s
% 3.09/1.75 % (9959)Instructions burned: 69 (million)
% 3.09/1.75 % (9959)------------------------------
% 3.09/1.75 % (9959)------------------------------
% 3.09/1.75 % (9938)Success in time 0.111 s
%------------------------------------------------------------------------------