%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP200^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:47 AM UTC 2026
% Result : Theorem 0.28s 0.41s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 47 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 143 ( 27 ~; 12 |; 4 &; 96 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 440 ( 438 usr; 11 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
produc1699626005le_trm: $tType ).
thf(type_def_6,type,
produc1418842292n_game: $tType ).
thf(type_def_7,type,
set_Pr1918373977on_fml: $tType ).
thf(type_def_8,type,
set_Pr1062384839on_trm: $tType ).
thf(type_def_9,type,
set_Pr519625031on_fml: $tType ).
thf(type_def_10,type,
set_Pr1588097095on_trm: $tType ).
thf(type_def_11,type,
set_Pr1045337287on_fml: $tType ).
thf(type_def_12,type,
produc1928189433on_fml: $tType ).
thf(type_def_13,type,
produc2024965863on_trm: $tType ).
thf(type_def_14,type,
produc591588199on_fml: $tType ).
thf(type_def_15,type,
produc1158546023on_trm: $tType ).
thf(type_def_16,type,
produc1872652007on_fml: $tType ).
thf(type_def_17,type,
set_Pr1481565921on_trm: $tType ).
thf(type_def_18,type,
set_Pr1969262145le_trm: $tType ).
thf(type_def_19,type,
produc2018724225on_trm: $tType ).
thf(type_def_20,type,
produc1279577057le_trm: $tType ).
thf(type_def_21,type,
set_Pr1625152599n_game: $tType ).
thf(type_def_22,type,
set_Pr622314946on_fml: $tType ).
thf(type_def_23,type,
set_Pr1471344007on_trm: $tType ).
thf(type_def_24,type,
set_Pr927595527on_fml: $tType ).
thf(type_def_25,type,
set_Pr181266295riable: $tType ).
thf(type_def_26,type,
produc1016592119n_game: $tType ).
thf(type_def_27,type,
produc1739631244on_fml: $tType ).
thf(type_def_28,type,
produc1072747943on_trm: $tType ).
thf(type_def_29,type,
produc1456309597on_fml: $tType ).
thf(type_def_30,type,
produc1810527345on_trm: $tType ).
thf(type_def_31,type,
produc46605351on_fml: $tType ).
thf(type_def_32,type,
produc432717079riable: $tType ).
thf(type_def_33,type,
set_Pr943832262on_trm: $tType ).
thf(type_def_34,type,
set_Pr1235432374le_trm: $tType ).
thf(type_def_35,type,
produc1024976764on_trm: $tType ).
thf(type_def_36,type,
produc1408538418on_fml: $tType ).
thf(type_def_37,type,
produc464795408on_trm: $tType ).
thf(type_def_38,type,
produc833882726rp_trm: $tType ).
thf(type_def_39,type,
produc1367888000le_trm: $tType ).
thf(type_def_40,type,
set_Pr604539619r_char: $tType ).
thf(type_def_41,type,
set_Pr491793543rm_trm: $tType ).
thf(type_def_42,type,
produc1593312387r_char: $tType ).
thf(type_def_43,type,
product_prod_trm_trm: $tType ).
thf(type_def_44,type,
option_game: $tType ).
thf(type_def_45,type,
option_trm: $tType ).
thf(type_def_46,type,
option_fml: $tType ).
thf(type_def_47,type,
denotational_interp: $tType ).
thf(type_def_48,type,
set_variable: $tType ).
thf(type_def_49,type,
set_char: $tType ).
thf(type_def_50,type,
variable: $tType ).
thf(type_def_51,type,
game: $tType ).
thf(type_def_52,type,
char: $tType ).
thf(type_def_53,type,
trm: $tType ).
thf(type_def_54,type,
fml: $tType ).
thf(type_def_55,type,
real: $tType ).
thf(type_def_56,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_1,type,
bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_2,type,
bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_3,type,
bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
thf(func_def_4,type,
bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_5,type,
bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_6,type,
bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_7,type,
bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_8,type,
bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
thf(func_def_9,type,
bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_10,type,
bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_11,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_12,type,
none_fml: option_fml ).
thf(func_def_13,type,
none_game: option_game ).
thf(func_def_14,type,
none_trm: option_trm ).
thf(func_def_15,type,
some_fml: fml > option_fml ).
thf(func_def_16,type,
some_game: game > option_game ).
thf(func_def_17,type,
some_trm: trm > option_trm ).
thf(func_def_18,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_19,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_20,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_21,type,
the_fml: option_fml > fml ).
thf(func_def_22,type,
the_game: option_game > game ).
thf(func_def_23,type,
the_trm: option_trm > trm ).
thf(func_def_24,type,
ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
thf(func_def_25,type,
ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
thf(func_def_26,type,
ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
thf(func_def_27,type,
ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
thf(func_def_28,type,
ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
thf(func_def_29,type,
ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
thf(func_def_30,type,
ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
thf(func_def_31,type,
ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
thf(func_def_32,type,
ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
thf(func_def_33,type,
ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
thf(func_def_34,type,
ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
thf(func_def_35,type,
ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
thf(func_def_36,type,
ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
thf(func_def_37,type,
ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
thf(func_def_38,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_39,type,
ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_40,type,
ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_41,type,
ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_42,type,
ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_43,type,
ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_44,type,
ord_less_eq_set_char: set_char > set_char > $o ).
thf(func_def_45,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_46,type,
order_272405634riable: ( set_variable > $o ) > set_variable ).
thf(func_def_47,type,
produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
thf(func_def_48,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(func_def_49,type,
produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
thf(func_def_50,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_51,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_52,type,
produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
thf(func_def_53,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(func_def_54,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(func_def_55,type,
produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
thf(func_def_56,type,
produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
thf(func_def_57,type,
produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
thf(func_def_58,type,
produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
thf(func_def_59,type,
produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
thf(func_def_60,type,
produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
thf(func_def_61,type,
produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
thf(func_def_62,type,
produc1766592463riable: set_variable > set_variable > produc432717079riable ).
thf(func_def_63,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(func_def_64,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(func_def_65,type,
produc19545147r_char: char > char > produc1593312387r_char ).
thf(func_def_66,type,
product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
thf(func_def_67,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(func_def_68,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(func_def_69,type,
collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
thf(func_def_70,type,
collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
thf(func_def_71,type,
collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
thf(func_def_72,type,
collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
thf(func_def_73,type,
collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
thf(func_def_74,type,
collect_char: ( char > $o ) > set_char ).
thf(func_def_75,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_76,type,
geq: trm > trm > fml ).
thf(func_def_77,type,
assign: variable > trm > game ).
thf(func_def_78,type,
ode: char > trm > game ).
thf(func_def_79,type,
test: fml > game ).
thf(func_def_80,type,
const: char > trm ).
thf(func_def_81,type,
differential: trm > trm ).
thf(func_def_82,type,
func: char > trm > trm ).
thf(func_def_83,type,
number: real > trm ).
thf(func_def_84,type,
plus: trm > trm > trm ).
thf(func_def_85,type,
times: trm > trm > trm ).
thf(func_def_86,type,
var: variable > trm ).
thf(func_def_87,type,
uSubst834381837ssigno: variable > option_trm > option_game ).
thf(func_def_88,type,
uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
thf(func_def_89,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(func_def_90,type,
uSubst2051024824lo_rel: option_trm > option_trm > $o ).
thf(func_def_91,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_92,type,
uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_93,type,
uSubst1827052306e_ODEo: char > option_trm > option_game ).
thf(func_def_94,type,
uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
thf(func_def_95,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(func_def_96,type,
uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_97,type,
uSubst1367128042_Testo: option_fml > option_game ).
thf(func_def_98,type,
uSubst954181007to_rel: option_fml > option_fml > $o ).
thf(func_def_99,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_100,type,
uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_101,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_102,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_103,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_104,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(func_def_105,type,
accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
thf(func_def_106,type,
accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
thf(func_def_107,type,
accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
thf(func_def_108,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(func_def_109,type,
accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
thf(func_def_110,type,
accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
thf(func_def_111,type,
lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
thf(func_def_112,type,
lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
thf(func_def_113,type,
lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
thf(func_def_114,type,
lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
thf(func_def_115,type,
lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
thf(func_def_116,type,
lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
thf(func_def_117,type,
lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
thf(func_def_118,type,
member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_119,type,
member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_120,type,
member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
thf(func_def_121,type,
member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_122,type,
member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
thf(func_def_123,type,
member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
thf(func_def_124,type,
member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
thf(func_def_125,type,
member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
thf(func_def_126,type,
member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
thf(func_def_127,type,
member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
thf(func_def_128,type,
member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
thf(func_def_129,type,
member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
thf(func_def_130,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_131,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_132,type,
member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
thf(func_def_133,type,
member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
thf(func_def_134,type,
member_char: char > set_char > $o ).
thf(func_def_135,type,
member_variable: variable > set_variable > $o ).
thf(func_def_136,type,
u: set_variable ).
thf(func_def_137,type,
ua: set_variable ).
thf(func_def_138,type,
eta: trm ).
thf(func_def_139,type,
nu: variable > real ).
thf(func_def_140,type,
nu2: variable > real ).
thf(func_def_141,type,
omega: variable > real ).
thf(func_def_142,type,
omega2: variable > real ).
thf(func_def_143,type,
sigma: produc1418842292n_game ).
thf(func_def_144,type,
theta: trm ).
thf(func_def_148,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_149,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_150,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_151,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_152,type,
vOR: $o > $o > $o ).
thf(func_def_153,type,
vAND: $o > $o > $o ).
thf(func_def_154,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_155,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_156,type,
vIMP: $o > $o > $o ).
thf(func_def_157,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_158,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_160,type,
vNOT: $o > $o ).
thf(func_def_161,type,
sP0: option_trm > option_trm > option_trm > $o ).
thf(func_def_162,type,
sP1: option_trm > option_trm > option_trm > $o ).
thf(func_def_163,type,
sP2: option_trm > option_trm > option_trm > $o ).
thf(func_def_164,type,
sP3: option_trm > option_trm > option_trm > $o ).
thf(func_def_165,type,
sP4: ( trm > $o ) > $o ).
thf(func_def_166,type,
sP5: option_fml > option_trm > option_trm > $o ).
thf(func_def_167,type,
sP6: option_trm > option_fml > option_trm > $o ).
thf(func_def_168,type,
sP7: ( denotational_interp > trm > $o ) > $o ).
thf(func_def_169,type,
sK8: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_170,type,
sK9: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_171,type,
sK10: ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_172,type,
sK11: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_173,type,
sK12: option_game > game ).
thf(func_def_174,type,
sK13: ( variable > option_trm > $o ) > trm ).
thf(func_def_175,type,
sK14: ( variable > option_trm > $o ) > variable ).
thf(func_def_176,type,
sK15: ( variable > option_trm > $o ) > variable ).
thf(func_def_177,type,
sK16: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_178,type,
sK17: set_Pr927595527on_fml > set_Pr927595527on_fml > option_fml ).
thf(func_def_179,type,
sK18: set_Pr927595527on_fml > set_Pr927595527on_fml > option_fml ).
thf(func_def_180,type,
sK19: option_trm > trm ).
thf(func_def_181,type,
sK20: option_trm > option_trm > option_trm > trm ).
thf(func_def_182,type,
sK21: option_trm > option_trm > option_trm > trm ).
thf(func_def_183,type,
sK22: option_trm > option_trm > option_trm > trm ).
thf(func_def_184,type,
sK23: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > produc464795408on_trm ).
thf(func_def_185,type,
sK24: option_trm > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_186,type,
sK25: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_187,type,
sK26: option_trm > option_trm > option_trm > trm ).
thf(func_def_188,type,
sK27: option_trm > option_trm > option_trm > trm ).
thf(func_def_189,type,
sK28: option_trm > trm ).
thf(func_def_190,type,
sK29: produc1072747943on_trm > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_191,type,
sK30: ( option_fml > option_trm > $o ) > option_trm > option_fml > fml ).
thf(func_def_192,type,
sK31: ( option_fml > option_trm > $o ) > option_trm > option_fml > trm ).
thf(func_def_193,type,
sK32: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_194,type,
sK33: option_trm > option_game > ( option_trm > option_game > $o ) > game ).
thf(func_def_195,type,
sK34: option_trm > option_game > ( option_trm > option_game > $o ) > trm ).
thf(func_def_196,type,
sK35: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > produc1072747943on_trm ).
thf(func_def_197,type,
sK36: set_Pr943832262on_trm > set_Pr943832262on_trm > char ).
thf(func_def_198,type,
sK37: set_Pr943832262on_trm > set_Pr943832262on_trm > option_trm ).
thf(func_def_199,type,
sK38: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_200,type,
sK39: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_201,type,
sK40: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_202,type,
sK41: ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_203,type,
sK42: ( set_variable > set_variable ) > set_variable ).
thf(func_def_204,type,
sK43: ( set_variable > set_variable ) > set_variable ).
thf(func_def_205,type,
sK44: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_206,type,
sK45: set_char > set_char > char ).
thf(func_def_207,type,
sK46: option_trm > char > option_game > trm ).
thf(func_def_208,type,
sK47: ( set_variable > set_variable ) > set_variable ).
thf(func_def_209,type,
sK48: ( set_variable > set_variable ) > set_variable ).
thf(func_def_210,type,
sK49: produc1024976764on_trm > variable ).
thf(func_def_211,type,
sK50: produc1024976764on_trm > trm ).
thf(func_def_212,type,
sK51: produc1024976764on_trm > variable ).
thf(func_def_213,type,
sK52: ( option_trm > $o ) > trm ).
thf(func_def_214,type,
sK53: ( option_fml > $o ) > fml ).
thf(func_def_215,type,
sK54: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_216,type,
sK55: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_217,type,
sK56: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_218,type,
sK57: option_trm > option_trm > option_trm > trm ).
thf(func_def_219,type,
sK58: option_trm > option_trm > option_trm > trm ).
thf(func_def_220,type,
sK59: option_trm > trm ).
thf(func_def_221,type,
sK60: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_222,type,
sK61: set_Pr622314946on_fml > set_Pr622314946on_fml > option_fml ).
thf(func_def_223,type,
sK62: set_Pr622314946on_fml > set_Pr622314946on_fml > option_game ).
thf(func_def_224,type,
sK63: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_225,type,
sK64: produc46605351on_fml > fml ).
thf(func_def_226,type,
sK65: produc46605351on_fml > fml ).
thf(func_def_227,type,
sK66: produc46605351on_fml > fml ).
thf(func_def_228,type,
sK67: produc46605351on_fml > option_fml ).
thf(func_def_229,type,
sK68: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_230,type,
sK69: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_231,type,
sK70: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_232,type,
sK71: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_233,type,
sK72: ( set_variable > set_variable ) > set_variable ).
thf(func_def_234,type,
sK73: ( set_variable > set_variable ) > set_variable ).
thf(func_def_235,type,
sK74: set_variable > set_variable > variable ).
thf(func_def_236,type,
sK75: produc1408538418on_fml > variable ).
thf(func_def_237,type,
sK76: produc1408538418on_fml > variable ).
thf(func_def_238,type,
sK77: produc1408538418on_fml > fml ).
thf(func_def_239,type,
sK78: ( option_game > option_fml > $o ) > option_fml ).
thf(func_def_240,type,
sK79: ( option_game > option_fml > $o ) > fml ).
thf(func_def_241,type,
sK80: ( option_game > option_fml > $o ) > game ).
thf(func_def_242,type,
sK81: ( option_game > option_fml > $o ) > game ).
thf(func_def_243,type,
sK82: produc1739631244on_fml > game ).
thf(func_def_244,type,
sK83: produc1739631244on_fml > option_fml ).
thf(func_def_245,type,
sK84: produc1739631244on_fml > fml ).
thf(func_def_246,type,
sK85: produc1739631244on_fml > game ).
thf(func_def_247,type,
sK86: option_trm > trm ).
thf(func_def_248,type,
sK87: ( option_game > option_game > $o ) > game ).
thf(func_def_249,type,
sK88: ( option_game > option_game > $o ) > option_game ).
thf(func_def_250,type,
sK89: ( option_game > option_game > $o ) > game ).
thf(func_def_251,type,
sK90: ( option_game > option_game > $o ) > game ).
thf(func_def_252,type,
sK91: option_trm > option_trm > option_trm > trm ).
thf(func_def_253,type,
sK92: option_trm > option_trm > option_trm > trm ).
thf(func_def_254,type,
sK93: option_trm > option_trm > option_trm > trm ).
thf(func_def_255,type,
sK94: ( set_variable > $o ) > set_variable > set_variable ).
thf(func_def_256,type,
sK95: ( set_variable > $o ) > ( set_variable > $o ) > set_variable ).
thf(func_def_257,type,
sK96: produc1024976764on_trm > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_258,type,
sK97: produc1024976764on_trm > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_259,type,
sK98: option_trm > trm ).
thf(func_def_260,type,
sK99: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_261,type,
sK100: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_262,type,
sK101: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_263,type,
sK102: ( option_fml > option_fml > $o ) > ( option_fml > $o ) > option_fml ).
thf(func_def_264,type,
sK103: produc464795408on_trm > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_265,type,
sK104: option_game > game ).
thf(func_def_266,type,
sK105: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_267,type,
sK106: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_268,type,
sK107: trm > variable ).
thf(func_def_269,type,
sK108: trm > trm ).
thf(func_def_270,type,
sK109: trm > trm ).
thf(func_def_271,type,
sK110: trm > real ).
thf(func_def_272,type,
sK111: trm > trm ).
thf(func_def_273,type,
sK112: trm > trm ).
thf(func_def_274,type,
sK113: trm > char ).
thf(func_def_275,type,
sK114: trm > trm ).
thf(func_def_276,type,
sK115: trm > char ).
thf(func_def_277,type,
sK116: trm > trm ).
thf(func_def_278,type,
sK117: set_variable > ( set_variable > $o ) > set_variable ).
thf(func_def_279,type,
sK118: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_280,type,
sK119: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_281,type,
sK120: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_282,type,
sK121: ( option_trm > option_fml > $o ) > option_trm > option_fml > fml ).
thf(func_def_283,type,
sK122: ( option_trm > option_fml > $o ) > option_trm > option_fml > trm ).
thf(func_def_284,type,
sK123: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_285,type,
sK124: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_286,type,
sK125: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_287,type,
sK126: option_trm > trm ).
thf(func_def_288,type,
sK127: option_game > game ).
thf(func_def_289,type,
sK128: ( option_fml > option_fml > $o ) > option_fml > option_fml ).
thf(func_def_290,type,
sK129: option_game > game ).
thf(func_def_291,type,
sK130: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_292,type,
sK131: ( option_trm > option_trm > $o ) > option_trm > option_trm ).
thf(func_def_293,type,
sK132: option_trm > ( option_trm > option_trm > $o ) > option_trm > trm ).
thf(func_def_294,type,
sK133: option_trm > ( option_trm > option_trm > $o ) > option_trm > trm ).
thf(func_def_295,type,
sK134: ( variable > option_fml > $o ) > variable ).
thf(func_def_296,type,
sK135: ( variable > option_fml > $o ) > variable ).
thf(func_def_297,type,
sK136: ( variable > option_fml > $o ) > fml ).
thf(func_def_298,type,
sK137: option_trm > ( option_game > option_trm > $o ) > option_game > trm ).
thf(func_def_299,type,
sK138: option_trm > ( option_game > option_trm > $o ) > option_game > game ).
thf(func_def_300,type,
sK139: ( trm > $o ) > trm ).
thf(func_def_301,type,
sK140: ( trm > $o ) > trm ).
thf(func_def_302,type,
sK141: ( trm > $o ) > variable ).
thf(func_def_303,type,
sK142: ( trm > $o ) > char ).
thf(func_def_304,type,
sK143: ( trm > $o ) > trm ).
thf(func_def_305,type,
sK144: ( trm > $o ) > char ).
thf(func_def_306,type,
sK145: ( trm > $o ) > real ).
thf(func_def_307,type,
sK146: ( trm > $o ) > trm ).
thf(func_def_308,type,
sK147: ( trm > $o ) > trm ).
thf(func_def_309,type,
sK148: ( trm > $o ) > trm ).
thf(func_def_310,type,
sK149: ( trm > $o ) > option_trm > trm ).
thf(func_def_311,type,
sK150: ( option_game > $o ) > game ).
thf(func_def_312,type,
sK151: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_313,type,
sK152: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_314,type,
sK153: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_315,type,
sK154: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_316,type,
sK155: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_317,type,
sK156: option_game > option_fml > fml ).
thf(func_def_318,type,
sK157: ( char > option_trm > $o ) > trm ).
thf(func_def_319,type,
sK158: ( char > option_trm > $o ) > char ).
thf(func_def_320,type,
sK159: ( char > option_trm > $o ) > char ).
thf(func_def_321,type,
sK160: produc833882726rp_trm > char ).
thf(func_def_322,type,
sK161: produc833882726rp_trm > denotational_interp ).
thf(func_def_323,type,
sK162: produc833882726rp_trm > real ).
thf(func_def_324,type,
sK163: produc833882726rp_trm > denotational_interp ).
thf(func_def_325,type,
sK164: produc833882726rp_trm > denotational_interp ).
thf(func_def_326,type,
sK165: produc833882726rp_trm > trm ).
thf(func_def_327,type,
sK166: produc833882726rp_trm > trm ).
thf(func_def_328,type,
sK167: produc833882726rp_trm > char ).
thf(func_def_329,type,
sK168: produc833882726rp_trm > trm ).
thf(func_def_330,type,
sK169: produc833882726rp_trm > denotational_interp ).
thf(func_def_331,type,
sK170: produc833882726rp_trm > variable ).
thf(func_def_332,type,
sK171: produc833882726rp_trm > denotational_interp ).
thf(func_def_333,type,
sK172: produc833882726rp_trm > trm ).
thf(func_def_334,type,
sK173: produc833882726rp_trm > denotational_interp ).
thf(func_def_335,type,
sK174: produc833882726rp_trm > denotational_interp ).
thf(func_def_336,type,
sK175: produc833882726rp_trm > trm ).
thf(func_def_337,type,
sK176: produc833882726rp_trm > trm ).
thf(func_def_338,type,
sK177: option_fml > option_game > fml ).
thf(func_def_339,type,
sK178: option_game > option_trm > variable > trm ).
thf(func_def_340,type,
sK179: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_341,type,
sK180: option_trm > option_trm > trm ).
thf(func_def_342,type,
sK181: option_fml > fml ).
thf(func_def_343,type,
sK182: ( option_fml > $o ) > ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_344,type,
sK183: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_345,type,
sK184: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_346,type,
sK185: ( option_game > $o ) > game ).
thf(func_def_347,type,
sK186: ( option_fml > $o ) > fml ).
thf(func_def_348,type,
sK187: set_variable > ( variable > $o ) > variable ).
thf(func_def_349,type,
sK188: option_fml > fml ).
thf(func_def_350,type,
sK189: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_351,type,
sK190: ( option_trm > $o ) > trm ).
thf(func_def_352,type,
sK191: produc464795408on_trm > char ).
thf(func_def_353,type,
sK192: produc464795408on_trm > trm ).
thf(func_def_354,type,
sK193: produc464795408on_trm > char ).
thf(func_def_355,type,
sK194: produc1016592119n_game > game ).
thf(func_def_356,type,
sK195: produc1016592119n_game > option_game ).
thf(func_def_357,type,
sK196: produc1016592119n_game > game ).
thf(func_def_358,type,
sK197: produc1016592119n_game > game ).
thf(func_def_359,type,
sK198: produc1699626005le_trm > set_variable ).
thf(func_def_360,type,
sK199: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_361,type,
sK200: produc1699626005le_trm > real ).
thf(func_def_362,type,
sK201: produc1699626005le_trm > trm ).
thf(func_def_363,type,
sK202: produc1699626005le_trm > set_variable ).
thf(func_def_364,type,
sK203: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_365,type,
sK204: produc1699626005le_trm > char ).
thf(func_def_366,type,
sK205: produc1699626005le_trm > set_variable ).
thf(func_def_367,type,
sK206: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_368,type,
sK207: produc1699626005le_trm > trm ).
thf(func_def_369,type,
sK208: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_370,type,
sK209: produc1699626005le_trm > trm ).
thf(func_def_371,type,
sK210: produc1699626005le_trm > set_variable ).
thf(func_def_372,type,
sK211: produc1699626005le_trm > trm ).
thf(func_def_373,type,
sK212: produc1699626005le_trm > char ).
thf(func_def_374,type,
sK213: produc1699626005le_trm > set_variable ).
thf(func_def_375,type,
sK214: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_376,type,
sK215: produc1699626005le_trm > variable ).
thf(func_def_377,type,
sK216: produc1699626005le_trm > set_variable ).
thf(func_def_378,type,
sK217: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_379,type,
sK218: produc1699626005le_trm > trm ).
thf(func_def_380,type,
sK219: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_381,type,
sK220: produc1699626005le_trm > set_variable ).
thf(func_def_382,type,
sK221: produc1699626005le_trm > trm ).
thf(func_def_383,type,
sK222: set_char > ( char > $o ) > ( char > $o ) > char ).
thf(func_def_384,type,
sK223: option_trm > option_game > char > trm ).
thf(func_def_385,type,
sK224: option_fml > fml ).
thf(func_def_386,type,
sK225: set_char > ( char > $o ) > char ).
thf(func_def_387,type,
sK226: produc1072747943on_trm > option_trm ).
thf(func_def_388,type,
sK227: produc1072747943on_trm > trm ).
thf(func_def_389,type,
sK228: produc1072747943on_trm > trm ).
thf(func_def_390,type,
sK229: produc1072747943on_trm > trm ).
thf(func_def_391,type,
sK230: option_fml > fml ).
thf(func_def_392,type,
sK231: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_393,type,
sK232: option_fml > option_trm > option_trm > trm ).
thf(func_def_394,type,
sK233: option_fml > option_trm > option_trm > trm ).
thf(func_def_395,type,
sK234: option_trm > option_fml > option_trm > trm ).
thf(func_def_396,type,
sK235: set_variable > ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_397,type,
sK236: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_398,type,
sK237: set_Pr1235432374le_trm > set_Pr1235432374le_trm > trm ).
thf(func_def_399,type,
sK238: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_variable ).
thf(func_def_400,type,
sK239: option_trm > trm ).
thf(func_def_401,type,
sK240: option_fml > fml ).
thf(func_def_402,type,
sK241: option_game > ( option_fml > option_game > $o ) > option_fml > game ).
thf(func_def_403,type,
sK242: option_game > ( option_fml > option_game > $o ) > option_fml > fml ).
thf(func_def_404,type,
sK243: variable > option_game > option_trm > trm ).
thf(func_def_405,type,
sK244: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_406,type,
sK245: ( fml > $o ) > option_fml > fml ).
thf(func_def_407,type,
sK246: option_trm > option_fml > option_trm > trm ).
thf(func_def_408,type,
sK247: option_trm > option_fml > option_trm > trm ).
thf(func_def_409,type,
sK248: option_trm > trm ).
thf(func_def_410,type,
sK249: ( option_fml > option_fml > $o ) > option_fml > option_fml ).
thf(func_def_411,type,
sK250: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_412,type,
sK251: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_413,type,
sK252: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_414,type,
sK253: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_415,type,
sK254: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_416,type,
sK255: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_417,type,
sK256: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_418,type,
sK257: ( denotational_interp > trm > $o ) > char ).
thf(func_def_419,type,
sK258: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_420,type,
sK259: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_421,type,
sK260: ( denotational_interp > trm > $o ) > char ).
thf(func_def_422,type,
sK261: ( denotational_interp > trm > $o ) > real ).
thf(func_def_423,type,
sK262: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_424,type,
sK263: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_425,type,
sK264: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_426,type,
sK265: ( denotational_interp > trm > $o ) > variable ).
thf(func_def_427,type,
sK266: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_428,type,
sK267: set_Pr1471344007on_trm > set_Pr1471344007on_trm > option_trm ).
thf(func_def_429,type,
sK268: set_Pr1471344007on_trm > set_Pr1471344007on_trm > option_trm ).
thf(func_def_430,type,
sK269: ( set_variable > set_variable ) > set_variable ).
thf(func_def_431,type,
sK270: ( set_variable > set_variable ) > set_variable ).
thf(func_def_432,type,
sK271: option_trm > option_trm > trm ).
thf(func_def_433,type,
sK272: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_434,type,
sK273: option_game > ( game > $o ) > game ).
thf(func_def_435,type,
sK274: ( option_game > option_fml > $o ) > option_game > option_fml > fml ).
thf(func_def_436,type,
sK275: ( option_game > option_fml > $o ) > option_game > option_fml > game ).
thf(func_def_437,type,
sK276: option_game > game ).
thf(f2,axiom,
! [X0: produc1418842292n_game,X2: trm,X3: trm,X1: set_variable] :
( ( ( uSubst516392804stappf @ X0 @ X1 @ ( geq @ X2 @ X3 ) )
!= none_fml )
=> ( ( ( uSubst516392818stappt @ X0 @ X1 @ X2 )
!= none_trm )
& ( ( uSubst516392818stappt @ X0 @ X1 @ X3 )
!= none_trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_usubstappf__geq__conv) ).
thf(f3,axiom,
( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
!= none_fml ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Geq_Oprems_I1_J) ).
thf(f353,conjecture,
( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= none_trm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f354,negated_conjecture,
~ ( ( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= none_trm ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f850,plain,
! [X1: trm,X3: set_variable,X2: trm,X0: produc1418842292n_game] :
( ( none_fml
!= ( uSubst516392804stappf @ X0 @ X3 @ ( geq @ X1 @ X2 ) ) )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X0 @ X3 @ X1 ) )
& ( none_trm
!= ( uSubst516392818stappt @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f909,plain,
( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
inference(flattening,[],[f354]) ).
thf(f1061,plain,
! [X2: trm,X1: trm,X0: produc1418842292n_game,X3: set_variable] :
( ( ( none_trm
!= ( uSubst516392818stappt @ X0 @ X3 @ X1 ) )
& ( none_trm
!= ( uSubst516392818stappt @ X0 @ X3 @ X2 ) ) )
| ( none_fml
= ( uSubst516392804stappf @ X0 @ X3 @ ( geq @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f850]) ).
thf(f1513,plain,
! [X0: trm,X1: trm,X2: produc1418842292n_game,X3: set_variable] :
( ( ( none_trm
!= ( uSubst516392818stappt @ X2 @ X3 @ X1 ) )
& ( none_trm
!= ( uSubst516392818stappt @ X2 @ X3 @ X0 ) ) )
| ( none_fml
= ( uSubst516392804stappf @ X2 @ X3 @ ( geq @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1061]) ).
thf(f1804,plain,
( none_fml
!= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f2208,plain,
! [X2: produc1418842292n_game,X3: set_variable,X0: trm,X1: trm] :
( ( none_fml
= ( uSubst516392804stappf @ X2 @ X3 @ ( geq @ X1 @ X0 ) ) )
| ( none_trm
!= ( uSubst516392818stappt @ X2 @ X3 @ X1 ) ) ),
inference(cnf_transformation,[],[f1513]) ).
thf(f2269,plain,
( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
inference(cnf_transformation,[],[f909]) ).
thf(f2841,definition,
( spl277_12
<=> ( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ),
introduced(definition,[new_symbols(definition,[spl277_12])],[avatar_definition]) ).
thf(f2843,plain,
( ( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) )
| ~ spl277_12 ),
inference(avatar_component_clause,[],[f2841]) ).
thf(f2844,plain,
spl277_12,
inference(avatar_split_clause,[],[f2269,f2841]) ).
thf(f3045,definition,
( spl277_55
<=> ( none_fml
= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) ) ) ),
introduced(definition,[new_symbols(definition,[spl277_55])],[avatar_definition]) ).
thf(f3047,plain,
( ( none_fml
!= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) ) )
| spl277_55 ),
inference(avatar_component_clause,[],[f3045]) ).
thf(f3048,plain,
~ spl277_55,
inference(avatar_split_clause,[],[f1804,f3045]) ).
thf(f3065,plain,
( ( none_fml != none_fml )
| ( none_trm
!= ( uSubst516392818stappt @ sigma @ ua @ theta ) )
| spl277_55 ),
inference(superposition,[],[f3047,f2208]) ).
thf(f3066,plain,
( ( none_trm
!= ( uSubst516392818stappt @ sigma @ ua @ theta ) )
| spl277_55 ),
inference(trivial_inequality_removal,[],[f3065]) ).
thf(f3067,plain,
( $false
| ~ spl277_12
| spl277_55 ),
inference(forward_subsumption_resolution,[],[f3066,f2843]) ).
thf(f3068,plain,
( ~ spl277_12
| spl277_55 ),
inference(avatar_contradiction_clause,[],[f3067]) ).
cnf(s10,plain,
spl277_12,
inference(sat_conversion,[],[f2844]) ).
cnf(s58,plain,
~ spl277_55,
inference(sat_conversion,[],[f3048]) ).
cnf(s62,plain,
( ~ spl277_12
| spl277_55 ),
inference(sat_conversion,[],[f3068]) ).
cnf(s63,plain,
~ spl277_12,
inference(rat,[],[s62,s58]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s10,s63]) ).
thf(f3069,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP200^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:15:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.41 % (851956)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.41 % (851964)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1851833603:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.28/0.41 % (851962)lrs+10_16_si=on:nwc=1.5:random_seed=1266129946:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.41 % (851961)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=383136014:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.41 % (851963)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2139913773:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.41 % (851963)Instruction limit reached!
% 0.28/0.41 % (851963)------------------------------
% 0.28/0.41 % (851963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851963)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851963)Termination reason: Instruction limit
% 0.28/0.41 % (851963)Termination phase: shuffling
% 0.28/0.41 % (851963)Time elapsed: 0.002 s
% 0.28/0.41 % (851963)Peak memory usage: 10 MB
% 0.28/0.41 % (851963)Instructions burned: 3 (million)
% 0.28/0.41 % (851962)Instruction limit reached!
% 0.28/0.41 % (851962)------------------------------
% 0.28/0.41 % (851962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851962)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851962)Termination reason: Instruction limit
% 0.28/0.41 % (851962)Termination phase: shuffling
% 0.28/0.41 % (851962)Time elapsed: 0.010 s
% 0.28/0.41 % (851962)Peak memory usage: 10 MB
% 0.28/0.41 % (851962)Instructions burned: 20 (million)
% 0.28/0.41 % (851967)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.41 % (851967)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.28/0.41 % (851966)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3502880960:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.41 % (851965)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1480167821:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.41 % (851967)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1358939285:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.41 % (851972)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1188341088:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.41 % (851973)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1341854906:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.28/0.41 % (851965)Instruction limit reached!
% 0.28/0.41 % (851965)------------------------------
% 0.28/0.41 % (851965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851965)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851965)Termination reason: Instruction limit
% 0.28/0.41 % (851965)Termination phase: Property scanning
% 0.28/0.41 % (851965)Time elapsed: 0.013 s
% 0.28/0.41 % (851965)Peak memory usage: 11 MB
% 0.28/0.41 % (851965)Instructions burned: 25 (million)
% 0.28/0.41 % (851972)Instruction limit reached!
% 0.28/0.41 % (851972)------------------------------
% 0.28/0.41 % (851972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851972)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851972)Termination reason: Instruction limit
% 0.28/0.41 % (851972)Termination phase: shuffling
% 0.28/0.41 % (851972)Time elapsed: 0.003 s
% 0.28/0.41 % (851972)Peak memory usage: 10 MB
% 0.28/0.41 % (851972)Instructions burned: 6 (million)
% 0.28/0.41 % (851973)Instruction limit reached!
% 0.28/0.41 % (851973)------------------------------
% 0.28/0.41 % (851973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851973)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851973)Termination reason: Instruction limit
% 0.28/0.41 % (851973)Termination phase: shuffling
% 0.28/0.41 % (851973)Time elapsed: 0.003 s
% 0.28/0.41 % (851973)Peak memory usage: 10 MB
% 0.28/0.41 % (851973)Instructions burned: 5 (million)
% 0.28/0.41 % (851961)Instruction limit reached!
% 0.28/0.41 % (851961)------------------------------
% 0.28/0.41 % (851961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851961)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851961)Termination reason: Instruction limit
% 0.28/0.41 % (851961)Termination phase: Property scanning
% 0.28/0.41 % (851961)Time elapsed: 0.044 s
% 0.28/0.41 % (851961)Peak memory usage: 12 MB
% 0.28/0.41 % (851961)Instructions burned: 88 (million)
% 0.28/0.41 % (851979)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.41 % (851964) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-851956-851964"...
% 0.28/0.41 % (851981)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.28/0.41 % (851981)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.41 % (851964)...printing done.
% 0.28/0.41 % (851979)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3085911826:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.28/0.41 % (851964)Refutation found. Thanks to Tanya!
% 0.28/0.41 % SZS status Theorem for theBenchmark
% 0.28/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.41 % (851964)------------------------------
% 0.28/0.41 % (851964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.41 % (851964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.41 % (851964)CaDiCaL version: 2.1.3
% 0.28/0.41 % (851964)Termination reason: Refutation
% 0.28/0.41 % (851964)Time elapsed: 0.059 s
% 0.28/0.41 % (851964)Peak memory usage: 16 MB
% 0.28/0.41 % (851964)Instructions burned: 219 (million)
% 0.28/0.41 % (851956)Success in time 0.106 s
% 0.28/0.41 % Vampire exiting
%------------------------------------------------------------------------------