TSTP Solution File: ITP200^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP200^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.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 : Mon May 20 22:56:08 EDT 2024
% Result : Theorem 1.93s 0.65s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1202
% Syntax : Number of formulae : 2560 ( 543 unt; 564 typ; 0 def)
% Number of atoms : 21253 (4589 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 5716 (1825 ~;1608 |; 919 &; 0 @)
% ( 336 <=>;1028 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 2770 (2769 >; 1 *; 0 +; 0 <<)
% Number of symbols : 803 ( 800 usr; 346 con; 0-6 aty)
% Number of variables : 4699 ( 14 ^4169 !; 501 ?;4699 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_char: $tType ).
thf(type_def_6,type,
char: $tType ).
thf(type_def_7,type,
option_fml: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_9,type,
set_Pr927595527on_fml: $tType ).
thf(type_def_10,type,
option_game: $tType ).
thf(type_def_11,type,
set_Pr622314946on_fml: $tType ).
thf(type_def_12,type,
option_trm: $tType ).
thf(type_def_13,type,
set_Pr1471344007on_trm: $tType ).
thf(type_def_14,type,
set_variable: $tType ).
thf(type_def_15,type,
trm: $tType ).
thf(type_def_16,type,
set_Pr1235432374le_trm: $tType ).
thf(type_def_17,type,
set_Pr943832262on_trm: $tType ).
thf(type_def_18,type,
variable: $tType ).
thf(type_def_19,type,
real: $tType ).
thf(type_def_20,type,
fml: $tType ).
thf(type_def_21,type,
game: $tType ).
thf(type_def_22,type,
produc1072747943on_trm: $tType ).
thf(type_def_23,type,
produc464795408on_trm: $tType ).
thf(type_def_24,type,
produc1024976764on_trm: $tType ).
thf(type_def_25,type,
denotational_interp: $tType ).
thf(type_def_26,type,
produc833882726rp_trm: $tType ).
thf(type_def_27,type,
produc46605351on_fml: $tType ).
thf(type_def_28,type,
produc1810527345on_trm: $tType ).
thf(type_def_29,type,
produc1739631244on_fml: $tType ).
thf(type_def_30,type,
produc1016592119n_game: $tType ).
thf(type_def_31,type,
produc1456309597on_fml: $tType ).
thf(type_def_32,type,
produc1418842292n_game: $tType ).
thf(type_def_33,type,
produc1367888000le_trm: $tType ).
thf(type_def_34,type,
produc1699626005le_trm: $tType ).
thf(type_def_35,type,
produc1872652007on_fml: $tType ).
thf(type_def_36,type,
produc1158546023on_trm: $tType ).
thf(type_def_37,type,
produc1928189433on_fml: $tType ).
thf(type_def_38,type,
produc591588199on_fml: $tType ).
thf(type_def_39,type,
produc2024965863on_trm: $tType ).
thf(type_def_40,type,
produc1279577057le_trm: $tType ).
thf(type_def_41,type,
produc2018724225on_trm: $tType ).
thf(type_def_42,type,
produc432717079riable: $tType ).
thf(type_def_43,type,
produc1593312387r_char: $tType ).
thf(type_def_44,type,
product_prod_trm_trm: $tType ).
thf(type_def_45,type,
produc1408538418on_fml: $tType ).
thf(type_def_46,type,
set_Pr1045337287on_fml: $tType ).
thf(type_def_47,type,
set_Pr1588097095on_trm: $tType ).
thf(type_def_48,type,
set_Pr1625152599n_game: $tType ).
thf(type_def_49,type,
set_Pr1918373977on_fml: $tType ).
thf(type_def_50,type,
set_Pr519625031on_fml: $tType ).
thf(type_def_51,type,
set_Pr1062384839on_trm: $tType ).
thf(type_def_52,type,
set_Pr181266295riable: $tType ).
thf(type_def_53,type,
set_Pr491793543rm_trm: $tType ).
thf(type_def_54,type,
set_Pr1969262145le_trm: $tType ).
thf(type_def_55,type,
set_Pr604539619r_char: $tType ).
thf(type_def_56,type,
set_Pr1481565921on_trm: $tType ).
thf(func_def_0,type,
produc1699626005le_trm: $tType ).
thf(func_def_1,type,
produc1418842292n_game: $tType ).
thf(func_def_2,type,
set_Pr1918373977on_fml: $tType ).
thf(func_def_3,type,
set_Pr1062384839on_trm: $tType ).
thf(func_def_4,type,
set_Pr519625031on_fml: $tType ).
thf(func_def_5,type,
set_Pr1588097095on_trm: $tType ).
thf(func_def_6,type,
set_Pr1045337287on_fml: $tType ).
thf(func_def_7,type,
produc1928189433on_fml: $tType ).
thf(func_def_8,type,
produc2024965863on_trm: $tType ).
thf(func_def_9,type,
produc591588199on_fml: $tType ).
thf(func_def_10,type,
produc1158546023on_trm: $tType ).
thf(func_def_11,type,
produc1872652007on_fml: $tType ).
thf(func_def_12,type,
set_Pr1481565921on_trm: $tType ).
thf(func_def_13,type,
set_Pr1969262145le_trm: $tType ).
thf(func_def_14,type,
produc2018724225on_trm: $tType ).
thf(func_def_15,type,
produc1279577057le_trm: $tType ).
thf(func_def_16,type,
set_Pr1625152599n_game: $tType ).
thf(func_def_17,type,
set_Pr622314946on_fml: $tType ).
thf(func_def_18,type,
set_Pr1471344007on_trm: $tType ).
thf(func_def_19,type,
set_Pr927595527on_fml: $tType ).
thf(func_def_20,type,
set_Pr181266295riable: $tType ).
thf(func_def_21,type,
produc1016592119n_game: $tType ).
thf(func_def_22,type,
produc1739631244on_fml: $tType ).
thf(func_def_23,type,
produc1072747943on_trm: $tType ).
thf(func_def_24,type,
produc1456309597on_fml: $tType ).
thf(func_def_25,type,
produc1810527345on_trm: $tType ).
thf(func_def_26,type,
produc46605351on_fml: $tType ).
thf(func_def_27,type,
produc432717079riable: $tType ).
thf(func_def_28,type,
set_Pr943832262on_trm: $tType ).
thf(func_def_29,type,
set_Pr1235432374le_trm: $tType ).
thf(func_def_30,type,
produc1024976764on_trm: $tType ).
thf(func_def_31,type,
produc1408538418on_fml: $tType ).
thf(func_def_32,type,
produc464795408on_trm: $tType ).
thf(func_def_33,type,
produc833882726rp_trm: $tType ).
thf(func_def_34,type,
produc1367888000le_trm: $tType ).
thf(func_def_35,type,
set_Pr604539619r_char: $tType ).
thf(func_def_36,type,
set_Pr491793543rm_trm: $tType ).
thf(func_def_37,type,
produc1593312387r_char: $tType ).
thf(func_def_38,type,
product_prod_trm_trm: $tType ).
thf(func_def_39,type,
option_game: $tType ).
thf(func_def_40,type,
option_trm: $tType ).
thf(func_def_41,type,
option_fml: $tType ).
thf(func_def_42,type,
denotational_interp: $tType ).
thf(func_def_43,type,
set_variable: $tType ).
thf(func_def_44,type,
set_char: $tType ).
thf(func_def_45,type,
variable: $tType ).
thf(func_def_46,type,
game: $tType ).
thf(func_def_47,type,
char: $tType ).
thf(func_def_48,type,
trm: $tType ).
thf(func_def_49,type,
fml: $tType ).
thf(func_def_50,type,
real: $tType ).
thf(func_def_51,type,
bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_52,type,
bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_53,type,
bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_54,type,
bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
thf(func_def_55,type,
bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_56,type,
bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_57,type,
bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_58,type,
bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_59,type,
bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
thf(func_def_60,type,
bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_61,type,
bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_62,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_63,type,
none_fml: option_fml ).
thf(func_def_64,type,
none_game: option_game ).
thf(func_def_65,type,
none_trm: option_trm ).
thf(func_def_66,type,
some_fml: fml > option_fml ).
thf(func_def_67,type,
some_game: game > option_game ).
thf(func_def_68,type,
some_trm: trm > option_trm ).
thf(func_def_69,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_70,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_71,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_72,type,
the_fml: option_fml > fml ).
thf(func_def_73,type,
the_game: option_game > game ).
thf(func_def_74,type,
the_trm: option_trm > trm ).
thf(func_def_75,type,
ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
thf(func_def_76,type,
ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
thf(func_def_77,type,
ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
thf(func_def_78,type,
ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
thf(func_def_79,type,
ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
thf(func_def_80,type,
ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
thf(func_def_81,type,
ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
thf(func_def_82,type,
ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
thf(func_def_83,type,
ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
thf(func_def_84,type,
ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
thf(func_def_85,type,
ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
thf(func_def_86,type,
ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
thf(func_def_87,type,
ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
thf(func_def_88,type,
ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
thf(func_def_89,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_90,type,
ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_91,type,
ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_92,type,
ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_93,type,
ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_94,type,
ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_95,type,
ord_less_eq_set_char: set_char > set_char > $o ).
thf(func_def_96,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_97,type,
order_272405634riable: ( set_variable > $o ) > set_variable ).
thf(func_def_98,type,
produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
thf(func_def_99,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(func_def_100,type,
produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
thf(func_def_101,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_102,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_103,type,
produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
thf(func_def_104,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(func_def_105,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(func_def_106,type,
produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
thf(func_def_107,type,
produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
thf(func_def_108,type,
produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
thf(func_def_109,type,
produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
thf(func_def_110,type,
produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
thf(func_def_111,type,
produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
thf(func_def_112,type,
produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
thf(func_def_113,type,
produc1766592463riable: set_variable > set_variable > produc432717079riable ).
thf(func_def_114,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(func_def_115,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(func_def_116,type,
produc19545147r_char: char > char > produc1593312387r_char ).
thf(func_def_117,type,
product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
thf(func_def_118,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(func_def_119,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(func_def_120,type,
collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
thf(func_def_121,type,
collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
thf(func_def_122,type,
collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
thf(func_def_123,type,
collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
thf(func_def_124,type,
collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
thf(func_def_125,type,
collect_char: ( char > $o ) > set_char ).
thf(func_def_126,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_127,type,
geq: trm > trm > fml ).
thf(func_def_128,type,
assign: variable > trm > game ).
thf(func_def_129,type,
ode: char > trm > game ).
thf(func_def_130,type,
test: fml > game ).
thf(func_def_131,type,
const: char > trm ).
thf(func_def_132,type,
differential: trm > trm ).
thf(func_def_133,type,
func: char > trm > trm ).
thf(func_def_134,type,
number: real > trm ).
thf(func_def_135,type,
plus: trm > trm > trm ).
thf(func_def_136,type,
times: trm > trm > trm ).
thf(func_def_137,type,
var: variable > trm ).
thf(func_def_138,type,
uSubst834381837ssigno: variable > option_trm > option_game ).
thf(func_def_139,type,
uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
thf(func_def_140,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(func_def_141,type,
uSubst2051024824lo_rel: option_trm > option_trm > $o ).
thf(func_def_142,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_143,type,
uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_144,type,
uSubst1827052306e_ODEo: char > option_trm > option_game ).
thf(func_def_145,type,
uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
thf(func_def_146,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(func_def_147,type,
uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_148,type,
uSubst1367128042_Testo: option_fml > option_game ).
thf(func_def_149,type,
uSubst954181007to_rel: option_fml > option_fml > $o ).
thf(func_def_150,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_151,type,
uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_152,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_153,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_154,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_155,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(func_def_156,type,
accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
thf(func_def_157,type,
accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
thf(func_def_158,type,
accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
thf(func_def_159,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(func_def_160,type,
accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
thf(func_def_161,type,
accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
thf(func_def_162,type,
lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
thf(func_def_163,type,
lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
thf(func_def_164,type,
lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
thf(func_def_165,type,
lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
thf(func_def_166,type,
lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
thf(func_def_167,type,
lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
thf(func_def_168,type,
lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
thf(func_def_169,type,
member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_170,type,
member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_171,type,
member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
thf(func_def_172,type,
member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_173,type,
member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
thf(func_def_174,type,
member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
thf(func_def_175,type,
member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
thf(func_def_176,type,
member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
thf(func_def_177,type,
member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
thf(func_def_178,type,
member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
thf(func_def_179,type,
member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
thf(func_def_180,type,
member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
thf(func_def_181,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_182,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_183,type,
member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
thf(func_def_184,type,
member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
thf(func_def_185,type,
member_char: char > set_char > $o ).
thf(func_def_186,type,
member_variable: variable > set_variable > $o ).
thf(func_def_187,type,
u: set_variable ).
thf(func_def_188,type,
ua: set_variable ).
thf(func_def_189,type,
eta: trm ).
thf(func_def_190,type,
nu: variable > real ).
thf(func_def_191,type,
nu2: variable > real ).
thf(func_def_192,type,
omega: variable > real ).
thf(func_def_193,type,
omega2: variable > real ).
thf(func_def_194,type,
sigma: produc1418842292n_game ).
thf(func_def_195,type,
theta: trm ).
thf(func_def_199,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_200,type,
vAND: $o > $o > $o ).
thf(func_def_201,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_202,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_203,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_204,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_205,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_206,type,
vOR: $o > $o > $o ).
thf(func_def_207,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_208,type,
vIMP: $o > $o > $o ).
thf(func_def_209,type,
vNOT: $o > $o ).
thf(func_def_210,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_211,type,
sP0: option_fml > option_game > $o ).
thf(func_def_212,type,
sP1: option_trm > option_trm > $o ).
thf(func_def_213,type,
sP2: ( trm > $o ) > $o ).
thf(func_def_214,type,
sP3: ( trm > $o ) > $o ).
thf(func_def_215,type,
sP4: option_trm > option_game > variable > $o ).
thf(func_def_216,type,
sP5: option_trm > option_game > char > $o ).
thf(func_def_217,type,
sP6: option_trm > option_trm > option_fml > $o ).
thf(func_def_218,type,
sP7: option_trm > option_trm > option_fml > $o ).
thf(func_def_219,type,
sP8: option_trm > option_trm > option_fml > $o ).
thf(func_def_220,type,
sP9: option_trm > option_trm > option_fml > $o ).
thf(func_def_221,type,
sP10: option_trm > option_trm > option_trm > $o ).
thf(func_def_222,type,
sP11: option_trm > option_trm > option_trm > $o ).
thf(func_def_223,type,
sP12: option_trm > option_trm > option_trm > $o ).
thf(func_def_224,type,
sP13: option_trm > option_trm > option_trm > $o ).
thf(func_def_225,type,
sP14: option_trm > option_trm > option_trm > $o ).
thf(func_def_226,type,
sP15: option_trm > option_trm > option_trm > $o ).
thf(func_def_227,type,
sP16: option_trm > option_trm > option_trm > $o ).
thf(func_def_228,type,
sP17: option_trm > option_trm > option_trm > $o ).
thf(func_def_229,type,
sP18: ( option_game > option_game > $o ) > option_game > option_game > $o ).
thf(func_def_230,type,
sP19: ( option_game > option_fml > $o ) > option_game > option_fml > $o ).
thf(func_def_231,type,
sP20: ( option_game > option_trm > $o ) > option_game > option_trm > $o ).
thf(func_def_232,type,
sP21: ( option_fml > option_game > $o ) > option_fml > option_game > $o ).
thf(func_def_233,type,
sP22: ( option_fml > option_fml > $o ) > option_fml > option_fml > $o ).
thf(func_def_234,type,
sP23: ( option_fml > option_trm > $o ) > option_fml > option_trm > $o ).
thf(func_def_235,type,
sP24: ( option_trm > option_game > $o ) > option_trm > option_game > $o ).
thf(func_def_236,type,
sP25: ( option_trm > option_fml > $o ) > option_trm > option_fml > $o ).
thf(func_def_237,type,
sP26: ( option_trm > option_trm > $o ) > option_trm > option_trm > $o ).
thf(func_def_238,type,
sP27: ( denotational_interp > trm > $o ) > $o ).
thf(func_def_239,type,
sP28: ( denotational_interp > trm > $o ) > $o ).
thf(func_def_240,type,
sP29: ( set_variable > $o ) > ( set_variable > $o ) > $o ).
thf(func_def_241,type,
sP30: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
thf(func_def_242,type,
sP31: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
thf(func_def_243,type,
sP32: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
thf(func_def_244,type,
sP33: ( option_fml > option_fml > $o ) > ( option_fml > $o ) > $o ).
thf(func_def_245,type,
sP34: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > $o ).
thf(func_def_246,type,
sK35: option_game > game ).
thf(func_def_247,type,
sK36: option_fml > fml ).
thf(func_def_248,type,
sK37: option_trm > trm ).
thf(func_def_249,type,
sK38: option_game > game ).
thf(func_def_250,type,
sK39: option_fml > fml ).
thf(func_def_251,type,
sK40: trm > trm ).
thf(func_def_252,type,
sK41: trm > trm ).
thf(func_def_253,type,
sK42: trm > trm ).
thf(func_def_254,type,
sK43: trm > trm ).
thf(func_def_255,type,
sK44: trm > trm ).
thf(func_def_256,type,
sK45: trm > char ).
thf(func_def_257,type,
sK46: trm > trm ).
thf(func_def_258,type,
sK47: trm > char ).
thf(func_def_259,type,
sK48: trm > real ).
thf(func_def_260,type,
sK49: trm > variable ).
thf(func_def_261,type,
sK50: option_trm > trm ).
thf(func_def_262,type,
sK51: produc1408538418on_fml > variable ).
thf(func_def_263,type,
sK52: produc1408538418on_fml > variable ).
thf(func_def_264,type,
sK53: produc1408538418on_fml > fml ).
thf(func_def_265,type,
sK54: produc833882726rp_trm > denotational_interp ).
thf(func_def_266,type,
sK55: produc833882726rp_trm > trm ).
thf(func_def_267,type,
sK56: produc833882726rp_trm > denotational_interp ).
thf(func_def_268,type,
sK57: produc833882726rp_trm > trm ).
thf(func_def_269,type,
sK58: produc833882726rp_trm > trm ).
thf(func_def_270,type,
sK59: produc833882726rp_trm > denotational_interp ).
thf(func_def_271,type,
sK60: produc833882726rp_trm > trm ).
thf(func_def_272,type,
sK61: produc833882726rp_trm > trm ).
thf(func_def_273,type,
sK62: produc833882726rp_trm > denotational_interp ).
thf(func_def_274,type,
sK63: produc833882726rp_trm > char ).
thf(func_def_275,type,
sK64: produc833882726rp_trm > trm ).
thf(func_def_276,type,
sK65: produc833882726rp_trm > denotational_interp ).
thf(func_def_277,type,
sK66: produc833882726rp_trm > char ).
thf(func_def_278,type,
sK67: produc833882726rp_trm > denotational_interp ).
thf(func_def_279,type,
sK68: produc833882726rp_trm > real ).
thf(func_def_280,type,
sK69: produc833882726rp_trm > denotational_interp ).
thf(func_def_281,type,
sK70: produc833882726rp_trm > variable ).
thf(func_def_282,type,
sK71: produc1024976764on_trm > variable ).
thf(func_def_283,type,
sK72: produc1024976764on_trm > variable ).
thf(func_def_284,type,
sK73: produc1024976764on_trm > trm ).
thf(func_def_285,type,
sK74: produc464795408on_trm > char ).
thf(func_def_286,type,
sK75: produc464795408on_trm > char ).
thf(func_def_287,type,
sK76: produc464795408on_trm > trm ).
thf(func_def_288,type,
sK77: produc1016592119n_game > game ).
thf(func_def_289,type,
sK78: produc1016592119n_game > option_game ).
thf(func_def_290,type,
sK79: produc1016592119n_game > game ).
thf(func_def_291,type,
sK80: produc1016592119n_game > game ).
thf(func_def_292,type,
sK81: produc1739631244on_fml > game ).
thf(func_def_293,type,
sK82: produc1739631244on_fml > option_fml ).
thf(func_def_294,type,
sK83: produc1739631244on_fml > game ).
thf(func_def_295,type,
sK84: produc1739631244on_fml > fml ).
thf(func_def_296,type,
sK85: produc46605351on_fml > fml ).
thf(func_def_297,type,
sK86: produc46605351on_fml > option_fml ).
thf(func_def_298,type,
sK87: produc46605351on_fml > fml ).
thf(func_def_299,type,
sK88: produc46605351on_fml > fml ).
thf(func_def_300,type,
sK89: produc1072747943on_trm > trm ).
thf(func_def_301,type,
sK90: produc1072747943on_trm > option_trm ).
thf(func_def_302,type,
sK91: produc1072747943on_trm > trm ).
thf(func_def_303,type,
sK92: produc1072747943on_trm > trm ).
thf(func_def_304,type,
sK93: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_305,type,
sK94: produc1699626005le_trm > set_variable ).
thf(func_def_306,type,
sK95: produc1699626005le_trm > trm ).
thf(func_def_307,type,
sK96: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_308,type,
sK97: produc1699626005le_trm > set_variable ).
thf(func_def_309,type,
sK98: produc1699626005le_trm > trm ).
thf(func_def_310,type,
sK99: produc1699626005le_trm > trm ).
thf(func_def_311,type,
sK100: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_312,type,
sK101: produc1699626005le_trm > set_variable ).
thf(func_def_313,type,
sK102: produc1699626005le_trm > trm ).
thf(func_def_314,type,
sK103: produc1699626005le_trm > trm ).
thf(func_def_315,type,
sK104: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_316,type,
sK105: produc1699626005le_trm > set_variable ).
thf(func_def_317,type,
sK106: produc1699626005le_trm > char ).
thf(func_def_318,type,
sK107: produc1699626005le_trm > trm ).
thf(func_def_319,type,
sK108: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_320,type,
sK109: produc1699626005le_trm > set_variable ).
thf(func_def_321,type,
sK110: produc1699626005le_trm > char ).
thf(func_def_322,type,
sK111: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_323,type,
sK112: produc1699626005le_trm > set_variable ).
thf(func_def_324,type,
sK113: produc1699626005le_trm > real ).
thf(func_def_325,type,
sK114: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_326,type,
sK115: produc1699626005le_trm > set_variable ).
thf(func_def_327,type,
sK116: produc1699626005le_trm > variable ).
thf(func_def_328,type,
sK117: option_game > option_fml > fml ).
thf(func_def_329,type,
sK118: option_fml > option_game > fml ).
thf(func_def_330,type,
sK119: option_trm > option_trm > trm ).
thf(func_def_331,type,
sK120: option_trm > option_trm > trm ).
thf(func_def_332,type,
sK121: produc1024976764on_trm > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_333,type,
sK122: produc464795408on_trm > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_334,type,
sK123: produc1072747943on_trm > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_335,type,
sK124: option_fml > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_336,type,
sK125: option_trm > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_337,type,
sK126: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_338,type,
sK127: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_339,type,
sK128: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_340,type,
sK129: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_341,type,
sK130: set_char > set_char > char ).
thf(func_def_342,type,
sK131: set_variable > set_variable > variable ).
thf(func_def_343,type,
sK132: produc1024976764on_trm > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_344,type,
sK133: produc464795408on_trm > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_345,type,
sK134: produc1072747943on_trm > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_346,type,
sK135: option_fml > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_347,type,
sK136: option_trm > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_348,type,
sK137: ( option_game > $o ) > game ).
thf(func_def_349,type,
sK138: ( option_fml > $o ) > fml ).
thf(func_def_350,type,
sK139: ( trm > $o ) > trm ).
thf(func_def_351,type,
sK140: ( trm > $o ) > trm ).
thf(func_def_352,type,
sK141: ( trm > $o ) > trm ).
thf(func_def_353,type,
sK142: ( trm > $o ) > trm ).
thf(func_def_354,type,
sK143: ( trm > $o ) > trm ).
thf(func_def_355,type,
sK144: ( trm > $o ) > char ).
thf(func_def_356,type,
sK145: ( trm > $o ) > trm ).
thf(func_def_357,type,
sK146: ( trm > $o ) > char ).
thf(func_def_358,type,
sK147: ( trm > $o ) > real ).
thf(func_def_359,type,
sK148: ( trm > $o ) > variable ).
thf(func_def_360,type,
sK149: ( option_trm > $o ) > trm ).
thf(func_def_361,type,
sK150: set_Pr622314946on_fml > set_Pr622314946on_fml > option_game ).
thf(func_def_362,type,
sK151: set_Pr622314946on_fml > set_Pr622314946on_fml > option_fml ).
thf(func_def_363,type,
sK152: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_variable ).
thf(func_def_364,type,
sK153: set_Pr1235432374le_trm > set_Pr1235432374le_trm > trm ).
thf(func_def_365,type,
sK154: set_Pr943832262on_trm > set_Pr943832262on_trm > char ).
thf(func_def_366,type,
sK155: set_Pr943832262on_trm > set_Pr943832262on_trm > option_trm ).
thf(func_def_367,type,
sK156: set_Pr1471344007on_trm > set_Pr1471344007on_trm > option_trm ).
thf(func_def_368,type,
sK157: set_Pr1471344007on_trm > set_Pr1471344007on_trm > option_trm ).
thf(func_def_369,type,
sK158: set_Pr927595527on_fml > set_Pr927595527on_fml > option_fml ).
thf(func_def_370,type,
sK159: set_Pr927595527on_fml > set_Pr927595527on_fml > option_fml ).
thf(func_def_371,type,
sK160: ( option_game > $o ) > game ).
thf(func_def_372,type,
sK161: ( option_fml > $o ) > fml ).
thf(func_def_373,type,
sK162: ( option_trm > $o ) > trm ).
thf(func_def_374,type,
sK163: set_variable > ( set_variable > $o ) > set_variable ).
thf(func_def_375,type,
sK164: option_game > option_trm > variable > trm ).
thf(func_def_376,type,
sK165: option_trm > option_game > variable > trm ).
thf(func_def_377,type,
sK166: option_game > option_trm > char > trm ).
thf(func_def_378,type,
sK167: option_trm > option_game > char > trm ).
thf(func_def_379,type,
sK168: option_trm > trm ).
thf(func_def_380,type,
sK169: option_trm > option_trm > option_fml > trm ).
thf(func_def_381,type,
sK170: option_trm > option_trm > option_fml > trm ).
thf(func_def_382,type,
sK171: option_trm > option_trm > option_fml > trm ).
thf(func_def_383,type,
sK172: option_trm > option_trm > option_fml > trm ).
thf(func_def_384,type,
sK173: option_trm > option_trm > option_fml > trm ).
thf(func_def_385,type,
sK174: option_trm > trm ).
thf(func_def_386,type,
sK175: option_trm > option_trm > option_trm > trm ).
thf(func_def_387,type,
sK176: option_trm > option_trm > option_trm > trm ).
thf(func_def_388,type,
sK177: option_trm > trm ).
thf(func_def_389,type,
sK178: option_trm > option_trm > option_trm > trm ).
thf(func_def_390,type,
sK179: option_trm > option_trm > option_trm > trm ).
thf(func_def_391,type,
sK180: option_trm > option_trm > option_trm > trm ).
thf(func_def_392,type,
sK181: option_trm > option_trm > option_trm > trm ).
thf(func_def_393,type,
sK182: option_trm > option_trm > option_trm > trm ).
thf(func_def_394,type,
sK183: option_trm > option_trm > option_trm > trm ).
thf(func_def_395,type,
sK184: option_trm > option_trm > option_trm > trm ).
thf(func_def_396,type,
sK185: option_trm > option_trm > option_trm > trm ).
thf(func_def_397,type,
sK186: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_398,type,
sK187: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_399,type,
sK188: ( option_game > option_fml > $o ) > option_game > option_fml > game ).
thf(func_def_400,type,
sK189: ( option_game > option_fml > $o ) > option_game > option_fml > fml ).
thf(func_def_401,type,
sK190: ( option_game > option_trm > $o ) > option_game > option_trm > game ).
thf(func_def_402,type,
sK191: ( option_game > option_trm > $o ) > option_game > option_trm > trm ).
thf(func_def_403,type,
sK192: ( option_fml > option_game > $o ) > option_fml > option_game > fml ).
thf(func_def_404,type,
sK193: ( option_fml > option_game > $o ) > option_fml > option_game > game ).
thf(func_def_405,type,
sK194: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_406,type,
sK195: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_407,type,
sK196: ( option_fml > option_trm > $o ) > option_fml > option_trm > fml ).
thf(func_def_408,type,
sK197: ( option_fml > option_trm > $o ) > option_fml > option_trm > trm ).
thf(func_def_409,type,
sK198: ( option_trm > option_game > $o ) > option_trm > option_game > trm ).
thf(func_def_410,type,
sK199: ( option_trm > option_game > $o ) > option_trm > option_game > game ).
thf(func_def_411,type,
sK200: ( option_trm > option_fml > $o ) > option_trm > option_fml > trm ).
thf(func_def_412,type,
sK201: ( option_trm > option_fml > $o ) > option_trm > option_fml > fml ).
thf(func_def_413,type,
sK202: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_414,type,
sK203: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_415,type,
sK204: ( variable > option_fml > $o ) > variable ).
thf(func_def_416,type,
sK205: ( variable > option_fml > $o ) > variable ).
thf(func_def_417,type,
sK206: ( variable > option_fml > $o ) > fml ).
thf(func_def_418,type,
sK207: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_419,type,
sK208: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_420,type,
sK209: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_421,type,
sK210: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_422,type,
sK211: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_423,type,
sK212: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_424,type,
sK213: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_425,type,
sK214: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_426,type,
sK215: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_427,type,
sK216: ( denotational_interp > trm > $o ) > char ).
thf(func_def_428,type,
sK217: ( denotational_interp > trm > $o ) > trm ).
thf(func_def_429,type,
sK218: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_430,type,
sK219: ( denotational_interp > trm > $o ) > char ).
thf(func_def_431,type,
sK220: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_432,type,
sK221: ( denotational_interp > trm > $o ) > real ).
thf(func_def_433,type,
sK222: ( denotational_interp > trm > $o ) > denotational_interp ).
thf(func_def_434,type,
sK223: ( denotational_interp > trm > $o ) > variable ).
thf(func_def_435,type,
sK224: ( variable > option_trm > $o ) > variable ).
thf(func_def_436,type,
sK225: ( variable > option_trm > $o ) > variable ).
thf(func_def_437,type,
sK226: ( variable > option_trm > $o ) > trm ).
thf(func_def_438,type,
sK227: ( char > option_trm > $o ) > char ).
thf(func_def_439,type,
sK228: ( char > option_trm > $o ) > char ).
thf(func_def_440,type,
sK229: ( char > option_trm > $o ) > trm ).
thf(func_def_441,type,
sK230: ( option_game > option_game > $o ) > game ).
thf(func_def_442,type,
sK231: ( option_game > option_game > $o ) > option_game ).
thf(func_def_443,type,
sK232: ( option_game > option_game > $o ) > game ).
thf(func_def_444,type,
sK233: ( option_game > option_game > $o ) > game ).
thf(func_def_445,type,
sK234: ( option_game > option_fml > $o ) > game ).
thf(func_def_446,type,
sK235: ( option_game > option_fml > $o ) > option_fml ).
thf(func_def_447,type,
sK236: ( option_game > option_fml > $o ) > game ).
thf(func_def_448,type,
sK237: ( option_game > option_fml > $o ) > fml ).
thf(func_def_449,type,
sK238: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_450,type,
sK239: ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_451,type,
sK240: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_452,type,
sK241: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_453,type,
sK242: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_454,type,
sK243: ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_455,type,
sK244: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_456,type,
sK245: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_457,type,
sK246: ( set_variable > $o ) > ( set_variable > $o ) > set_variable ).
thf(func_def_458,type,
sK247: set_variable > ( set_variable > $o ) > set_variable ).
thf(func_def_459,type,
sK248: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_460,type,
sK249: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_461,type,
sK250: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_462,type,
sK251: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_463,type,
sK252: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_464,type,
sK253: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_465,type,
sK254: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_466,type,
sK255: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_467,type,
sK256: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_468,type,
sK257: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_469,type,
sK258: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_470,type,
sK259: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_471,type,
sK260: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_472,type,
sK261: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_473,type,
sK262: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_474,type,
sK263: option_game > ( game > $o ) > game ).
thf(func_def_475,type,
sK264: option_fml > ( fml > $o ) > fml ).
thf(func_def_476,type,
sK265: option_trm > ( trm > $o ) > trm ).
thf(func_def_477,type,
sK266: ( set_variable > set_variable ) > set_variable ).
thf(func_def_478,type,
sK267: ( set_variable > set_variable ) > set_variable ).
thf(func_def_479,type,
sK268: ( char > $o ) > ( char > $o ) > set_char > char ).
thf(func_def_480,type,
sK269: ( set_variable > set_variable ) > set_variable ).
thf(func_def_481,type,
sK270: ( set_variable > set_variable ) > set_variable ).
thf(func_def_482,type,
sK271: ( variable > $o ) > ( variable > $o ) > set_variable > variable ).
thf(func_def_483,type,
sK272: ( set_variable > set_variable ) > set_variable ).
thf(func_def_484,type,
sK273: ( set_variable > set_variable ) > set_variable ).
thf(func_def_485,type,
sK274: ( set_variable > set_variable ) > set_variable ).
thf(func_def_486,type,
sK275: ( set_variable > set_variable ) > set_variable ).
thf(func_def_487,type,
sK276: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_488,type,
sK277: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_489,type,
sK278: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > produc1024976764on_trm ).
thf(func_def_490,type,
sK279: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_491,type,
sK280: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_492,type,
sK281: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > produc464795408on_trm ).
thf(func_def_493,type,
sK282: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_494,type,
sK283: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_495,type,
sK284: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > produc1072747943on_trm ).
thf(func_def_496,type,
sK285: ( option_fml > option_fml > $o ) > ( option_fml > $o ) > option_fml ).
thf(func_def_497,type,
sK286: ( option_fml > option_fml > $o ) > ( option_fml > $o ) > option_fml ).
thf(func_def_498,type,
sK287: ( option_fml > $o ) > ( option_fml > option_fml > $o ) > ( option_fml > $o ) > option_fml ).
thf(func_def_499,type,
sK288: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_500,type,
sK289: ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_501,type,
sK290: ( option_trm > $o ) > ( option_trm > option_trm > $o ) > ( option_trm > $o ) > option_trm ).
thf(func_def_503,type,
sK292: set_variable > ( variable > $o ) > variable ).
thf(func_def_504,type,
sK293: set_char > ( char > $o ) > char ).
thf(func_def_505,type,
sK294: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_506,type,
sK295: ( char > $o ) > ( char > $o ) > char ).
thf(func_def_507,type,
sK296: option_trm > trm ).
thf(func_def_508,type,
sK297: option_fml > fml ).
thf(func_def_509,type,
sK298: option_game > game ).
thf(func_def_510,type,
sK299: option_trm > trm ).
thf(func_def_511,type,
sK300: option_trm > trm ).
thf(func_def_512,type,
sK301: option_fml > fml ).
thf(func_def_513,type,
sK302: option_fml > fml ).
thf(func_def_514,type,
sK303: option_game > game ).
thf(func_def_515,type,
sK304: option_game > game ).
thf(f5541,plain,
$false,
inference(avatar_sat_refutation,[],[f2908,f2913,f2917,f2950,f2955,f2959,f2963,f2967,f2971,f2975,f2979,f2983,f2987,f2991,f2995,f2999,f3003,f3007,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3039,f3043,f3047,f3051,f3055,f3059,f3063,f3067,f3071,f3075,f3079,f3099,f3103,f3107,f3111,f3115,f3119,f3123,f3127,f3131,f3136,f3140,f3144,f3148,f3152,f3156,f3160,f3164,f3179,f3183,f3194,f3198,f3202,f3206,f3210,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3258,f3262,f3269,f3273,f3277,f3281,f3285,f3289,f3293,f3329,f3340,f3345,f3350,f3354,f3358,f3366,f3377,f3384,f3388,f3392,f3396,f3404,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3443,f3503,f3507,f3511,f3515,f3519,f3523,f3547,f3551,f3555,f3559,f3563,f3571,f3575,f3579,f3611,f3629,f3633,f3637,f3641,f3645,f3649,f3658,f3687,f3691,f3695,f3721,f3725,f3729,f3733,f3737,f3741,f3745,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3801,f3837,f3841,f3845,f3857,f3864,f3868,f3872,f3876,f3888,f3892,f3896,f3900,f3915,f3919,f3923,f3927,f3931,f3935,f3949,f3953,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4055,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4185,f4209,f4237,f4283,f4287,f4291,f4295,f4299,f4303,f4317,f4321,f4325,f4329,f4333,f4337,f4341,f4345,f4349,f4353,f4357,f4361,f4365,f4369,f4374,f4378,f4382,f4597,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4643,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4701,f4705,f4709,f4713,f4717,f4721,f4725,f4729,f4737,f4751,f4916,f4920,f4925,f4929,f4933,f4937,f4941,f4945,f4949,f4953,f4957,f4961,f4976,f4980,f4984,f4988,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5131,f5183,f5232,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5339,f5343,f5347,f5351,f5379,f5383,f5399,f5403,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5498,f5502,f5506,f5540]) ).
thf(f5540,plain,
( spl291_92
| ~ spl291_302 ),
inference(avatar_contradiction_clause,[],[f5539]) ).
thf(f5539,plain,
( $false
| spl291_92
| ~ spl291_302 ),
inference(trivial_inequality_removal,[],[f5538]) ).
thf(f5538,plain,
( ( none_fml != none_fml )
| spl291_92
| ~ spl291_302 ),
inference(superposition,[],[f3410,f5237]) ).
thf(f5237,plain,
( ! [X0: trm] : ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),X0)) )
| ~ spl291_302 ),
inference(avatar_component_clause,[],[f5236]) ).
thf(f5236,plain,
( spl291_302
<=> ! [X0: trm] : ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_302])]) ).
thf(f3410,plain,
( ( none_fml != vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),eta)) )
| spl291_92 ),
inference(avatar_component_clause,[],[f3408]) ).
thf(f3408,plain,
( spl291_92
<=> ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),eta)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_92])]) ).
thf(f5506,plain,
spl291_336,
inference(avatar_split_clause,[],[f2395,f5504]) ).
thf(f5504,plain,
( spl291_336
<=> ! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X0) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_336])]) ).
thf(f2395,plain,
! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X0) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) ) ),
inference(equality_resolution,[],[f2032]) ).
thf(f2032,plain,
! [X2: option_game,X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1288]) ).
thf(f1288,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ( $true = vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(definition_folding,[],[f1083,f1287]) ).
thf(f1287,plain,
! [X0: char,X2: option_game,X1: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),X2),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1083,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(flattening,[],[f1082]) ).
thf(f1082,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f953]) ).
thf(f953,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = X2 )
=> ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
=> ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) ) ) ) ) ) ),
inference(flattening,[],[f648]) ).
thf(f648,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = X2 )
=> ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1)) )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
=> ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) ) ) ) ) ) ),
inference(fool_elimination,[],[f647]) ).
thf(f647,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = X2 )
=> ( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),X1))
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
=> ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),none_trm)) ) ) ) ) ),
inference(rectify,[],[f350]) ).
thf(f350,axiom,
! [X23: char,X53: option_trm,X36: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X23),X53) = X36 )
=> ( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X23),X53))
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X53 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X23),X54)) = X36 )
=> ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X23),vAPP(trm,option_trm,some_trm,X54))) ) )
=> ~ ( ( none_trm = X53 )
=> ( ( none_game = X36 )
=> ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X23),none_trm)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_ODEo_Opelims) ).
thf(f5502,plain,
spl291_335,
inference(avatar_split_clause,[],[f2388,f5500]) ).
thf(f5500,plain,
( spl291_335
<=> ! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X0) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_335])]) ).
thf(f2388,plain,
! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X0) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) ) ),
inference(equality_resolution,[],[f2022]) ).
thf(f2022,plain,
! [X2: option_game,X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),X2),X0) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1286]) ).
thf(f1286,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ( $true = vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),X2),X0) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(definition_folding,[],[f1079,f1285]) ).
thf(f1285,plain,
! [X0: variable,X2: option_game,X1: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),X2),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1079,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(flattening,[],[f1078]) ).
thf(f1078,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) )
& ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f951]) ).
thf(f951,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = X2 )
=> ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
=> ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) ) ) ) ) ) ),
inference(flattening,[],[f646]) ).
thf(f646,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = X2 )
=> ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1)) )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
=> ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) ) ) ) ) ) ),
inference(fool_elimination,[],[f645]) ).
thf(f645,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = X2 )
=> ( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),X1))
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
=> ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) ) )
=> ~ ( ( none_trm = X1 )
=> ( ( none_game = X2 )
=> ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),none_trm)) ) ) ) ) ),
inference(rectify,[],[f343]) ).
thf(f343,axiom,
! [X23: variable,X53: option_trm,X36: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X23),X53) = X36 )
=> ( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X23),X53))
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X53 )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X23),X54)) = X36 )
=> ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X23),vAPP(trm,option_trm,some_trm,X54))) ) )
=> ~ ( ( none_trm = X53 )
=> ( ( none_game = X36 )
=> ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X23),none_trm)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_Assigno_Opelims) ).
thf(f5498,plain,
spl291_334,
inference(avatar_split_clause,[],[f2235,f5496]) ).
thf(f5496,plain,
( spl291_334
<=> ! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_334])]) ).
thf(f2235,plain,
! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1685]) ).
thf(f1685,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK262])],[f1190,f1684]) ).
thf(f1684,plain,
! [X0: option_trm > option_trm > $o,X2: option_trm > $o] :
( ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
=> ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1190,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(flattening,[],[f1189]) ).
thf(f1189,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f752]) ).
thf(f752,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ( ! [X3: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) )
=> ( ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(option_trm,$o,X2,X4) ) )
=> ( $true = vAPP(option_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f751]) ).
thf(f751,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1)
=> ( ! [X3: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3)
=> ( ! [X4: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3)
=> vAPP(option_trm,$o,X2,X4) )
=> vAPP(option_trm,$o,X2,X3) ) )
=> vAPP(option_trm,$o,X2,X1) ) ),
inference(rectify,[],[f209]) ).
thf(f209,axiom,
! [X86: option_trm > option_trm > $o,X30: option_trm,X26: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X30)
=> ( ! [X22: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X22)
=> ( ! [X72: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X72),X22)
=> vAPP(option_trm,$o,X26,X72) )
=> vAPP(option_trm,$o,X26,X22) ) )
=> vAPP(option_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_accp__induct) ).
thf(f5482,plain,
spl291_333,
inference(avatar_split_clause,[],[f2232,f5480]) ).
thf(f5480,plain,
( spl291_333
<=> ! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_333])]) ).
thf(f2232,plain,
! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1683]) ).
thf(f1683,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK261])],[f1188,f1682]) ).
thf(f1682,plain,
! [X0: option_trm > option_trm > $o,X2: option_trm > $o] :
( ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
=> ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1188,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(flattening,[],[f1187]) ).
thf(f1187,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f750]) ).
thf(f750,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ( ! [X3: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3) )
=> ( ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(option_trm,$o,X2,X4) ) )
=> ( $true = vAPP(option_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f749]) ).
thf(f749,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1)
=> ( ! [X3: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X3)
=> ( ! [X4: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3)
=> vAPP(option_trm,$o,X2,X4) )
=> vAPP(option_trm,$o,X2,X3) ) )
=> vAPP(option_trm,$o,X2,X1) ) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X86: option_trm > option_trm > $o,X30: option_trm,X26: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X30)
=> ( ! [X22: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X22)
=> ( ! [X72: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X72),X22)
=> vAPP(option_trm,$o,X26,X72) )
=> vAPP(option_trm,$o,X26,X22) ) )
=> vAPP(option_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_accp__induct__rule) ).
thf(f5478,plain,
spl291_332,
inference(avatar_split_clause,[],[f2225,f5476]) ).
thf(f5476,plain,
( spl291_332
<=> ! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_332])]) ).
thf(f2225,plain,
! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1678]) ).
thf(f1678,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK259])],[f1182,f1677]) ).
thf(f1677,plain,
! [X0: option_fml > option_fml > $o,X2: option_fml > $o] :
( ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
=> ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1182,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(flattening,[],[f1181]) ).
thf(f1181,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(ennf_transformation,[],[f744]) ).
thf(f744,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ( ! [X3: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) )
=> ( ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) )
=> ( $true = vAPP(option_fml,$o,X2,X4) ) )
=> ( $true = vAPP(option_fml,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_fml,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f743]) ).
thf(f743,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1)
=> ( ! [X3: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3)
=> ( ! [X4: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3)
=> vAPP(option_fml,$o,X2,X4) )
=> vAPP(option_fml,$o,X2,X3) ) )
=> vAPP(option_fml,$o,X2,X1) ) ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X86: option_fml > option_fml > $o,X30: option_fml,X26: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X30)
=> ( ! [X22: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X22)
=> ( ! [X72: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X72),X22)
=> vAPP(option_fml,$o,X26,X72) )
=> vAPP(option_fml,$o,X26,X22) ) )
=> vAPP(option_fml,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_accp__induct) ).
thf(f5474,plain,
spl291_331,
inference(avatar_split_clause,[],[f2222,f5472]) ).
thf(f5472,plain,
( spl291_331
<=> ! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_331])]) ).
thf(f2222,plain,
! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1676]) ).
thf(f1676,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK258])],[f1180,f1675]) ).
thf(f1675,plain,
! [X0: option_fml > option_fml > $o,X2: option_fml > $o] :
( ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
=> ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1180,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(flattening,[],[f1179]) ).
thf(f1179,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(ennf_transformation,[],[f742]) ).
thf(f742,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ( ! [X3: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3) )
=> ( ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) )
=> ( $true = vAPP(option_fml,$o,X2,X4) ) )
=> ( $true = vAPP(option_fml,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_fml,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f741]) ).
thf(f741,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1)
=> ( ! [X3: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X3)
=> ( ! [X4: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3)
=> vAPP(option_fml,$o,X2,X4) )
=> vAPP(option_fml,$o,X2,X3) ) )
=> vAPP(option_fml,$o,X2,X1) ) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X86: option_fml > option_fml > $o,X30: option_fml,X26: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X30)
=> ( ! [X22: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X22)
=> ( ! [X72: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X72),X22)
=> vAPP(option_fml,$o,X26,X72) )
=> vAPP(option_fml,$o,X26,X22) ) )
=> vAPP(option_fml,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_accp__induct__rule) ).
thf(f5470,plain,
spl291_330,
inference(avatar_split_clause,[],[f2215,f5468]) ).
thf(f5468,plain,
( spl291_330
<=> ! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_330])]) ).
thf(f2215,plain,
! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1671]) ).
thf(f1671,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK256])],[f1174,f1670]) ).
thf(f1670,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm > $o] :
( ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1174,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(flattening,[],[f1173]) ).
thf(f1173,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f736]) ).
thf(f736,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ( ! [X3: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) )
=> ( ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f735]) ).
thf(f735,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1)
=> ( ! [X3: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3)
=> ( ! [X4: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3)
=> vAPP(produc1072747943on_trm,$o,X2,X4) )
=> vAPP(produc1072747943on_trm,$o,X2,X3) ) )
=> vAPP(produc1072747943on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X86: produc1072747943on_trm > produc1072747943on_trm > $o,X30: produc1072747943on_trm,X26: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X30)
=> ( ! [X22: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X22)
=> ( ! [X72: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X72),X22)
=> vAPP(produc1072747943on_trm,$o,X26,X72) )
=> vAPP(produc1072747943on_trm,$o,X26,X22) ) )
=> vAPP(produc1072747943on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_accp__induct__rule) ).
thf(f5466,plain,
spl291_329,
inference(avatar_split_clause,[],[f2212,f5464]) ).
thf(f5464,plain,
( spl291_329
<=> ! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_329])]) ).
thf(f2212,plain,
! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1669]) ).
thf(f1669,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK255])],[f1172,f1668]) ).
thf(f1668,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm > $o] :
( ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1172,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(flattening,[],[f1171]) ).
thf(f1171,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f734]) ).
thf(f734,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ( ! [X3: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3) )
=> ( ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f733]) ).
thf(f733,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1)
=> ( ! [X3: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X3)
=> ( ! [X4: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3)
=> vAPP(produc1072747943on_trm,$o,X2,X4) )
=> vAPP(produc1072747943on_trm,$o,X2,X3) ) )
=> vAPP(produc1072747943on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X86: produc1072747943on_trm > produc1072747943on_trm > $o,X30: produc1072747943on_trm,X26: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X30)
=> ( ! [X22: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X22)
=> ( ! [X72: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X72),X22)
=> vAPP(produc1072747943on_trm,$o,X26,X72) )
=> vAPP(produc1072747943on_trm,$o,X26,X22) ) )
=> vAPP(produc1072747943on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_accp__induct) ).
thf(f5462,plain,
spl291_328,
inference(avatar_split_clause,[],[f2205,f5460]) ).
thf(f5460,plain,
( spl291_328
<=> ! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_328])]) ).
thf(f2205,plain,
! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1664]) ).
thf(f1664,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK253])],[f1166,f1663]) ).
thf(f1663,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm > $o] :
( ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1166,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(flattening,[],[f1165]) ).
thf(f1165,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f728]) ).
thf(f728,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ( ! [X3: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) )
=> ( ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f727]) ).
thf(f727,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1)
=> ( ! [X3: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3)
=> ( ! [X4: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3)
=> vAPP(produc464795408on_trm,$o,X2,X4) )
=> vAPP(produc464795408on_trm,$o,X2,X3) ) )
=> vAPP(produc464795408on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f208]) ).
thf(f208,axiom,
! [X86: produc464795408on_trm > produc464795408on_trm > $o,X30: produc464795408on_trm,X26: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X30)
=> ( ! [X22: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X22)
=> ( ! [X72: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X72),X22)
=> vAPP(produc464795408on_trm,$o,X26,X72) )
=> vAPP(produc464795408on_trm,$o,X26,X22) ) )
=> vAPP(produc464795408on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_accp__induct) ).
thf(f5458,plain,
spl291_327,
inference(avatar_split_clause,[],[f2202,f5456]) ).
thf(f5456,plain,
( spl291_327
<=> ! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_327])]) ).
thf(f2202,plain,
! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1662]) ).
thf(f1662,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK252])],[f1164,f1661]) ).
thf(f1661,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm > $o] :
( ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1164,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(flattening,[],[f1163]) ).
thf(f1163,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f726]) ).
thf(f726,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ( ! [X3: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3) )
=> ( ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f725]) ).
thf(f725,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1)
=> ( ! [X3: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X3)
=> ( ! [X4: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3)
=> vAPP(produc464795408on_trm,$o,X2,X4) )
=> vAPP(produc464795408on_trm,$o,X2,X3) ) )
=> vAPP(produc464795408on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X86: produc464795408on_trm > produc464795408on_trm > $o,X30: produc464795408on_trm,X26: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X30)
=> ( ! [X22: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X22)
=> ( ! [X72: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X72),X22)
=> vAPP(produc464795408on_trm,$o,X26,X72) )
=> vAPP(produc464795408on_trm,$o,X26,X22) ) )
=> vAPP(produc464795408on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_accp__induct__rule) ).
thf(f5454,plain,
spl291_326,
inference(avatar_split_clause,[],[f2195,f5452]) ).
thf(f5452,plain,
( spl291_326
<=> ! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_326])]) ).
thf(f2195,plain,
! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1657]) ).
thf(f1657,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK250])],[f1158,f1656]) ).
thf(f1656,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm > $o] :
( ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1158,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(flattening,[],[f1157]) ).
thf(f1157,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f720]) ).
thf(f720,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ( ! [X3: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) )
=> ( ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f719]) ).
thf(f719,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1)
=> ( ! [X3: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3)
=> ( ! [X4: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3)
=> vAPP(produc1024976764on_trm,$o,X2,X4) )
=> vAPP(produc1024976764on_trm,$o,X2,X3) ) )
=> vAPP(produc1024976764on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f226]) ).
thf(f226,axiom,
! [X86: produc1024976764on_trm > produc1024976764on_trm > $o,X30: produc1024976764on_trm,X26: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X30)
=> ( ! [X22: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X22)
=> ( ! [X72: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X72),X22)
=> vAPP(produc1024976764on_trm,$o,X26,X72) )
=> vAPP(produc1024976764on_trm,$o,X26,X22) ) )
=> vAPP(produc1024976764on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_accp__induct__rule) ).
thf(f5450,plain,
spl291_325,
inference(avatar_split_clause,[],[f2192,f5448]) ).
thf(f5448,plain,
( spl291_325
<=> ! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_325])]) ).
thf(f2192,plain,
! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1655]) ).
thf(f1655,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK249])],[f1156,f1654]) ).
thf(f1654,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm > $o] :
( ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1156,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(flattening,[],[f1155]) ).
thf(f1155,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f718]) ).
thf(f718,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ( ! [X3: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3) )
=> ( ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f717]) ).
thf(f717,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1)
=> ( ! [X3: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X3)
=> ( ! [X4: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3)
=> vAPP(produc1024976764on_trm,$o,X2,X4) )
=> vAPP(produc1024976764on_trm,$o,X2,X3) ) )
=> vAPP(produc1024976764on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X86: produc1024976764on_trm > produc1024976764on_trm > $o,X30: produc1024976764on_trm,X26: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X30)
=> ( ! [X22: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X22)
=> ( ! [X72: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X72),X22)
=> vAPP(produc1024976764on_trm,$o,X26,X72) )
=> vAPP(produc1024976764on_trm,$o,X26,X22) ) )
=> vAPP(produc1024976764on_trm,$o,X26,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_accp__induct) ).
thf(f5446,plain,
spl291_324,
inference(avatar_split_clause,[],[f2011,f5444]) ).
thf(f5444,plain,
( spl291_324
<=> ! [X2: trm,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) = vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_324])]) ).
thf(f2011,plain,
! [X2: trm,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) = vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2)) ),
inference(cnf_transformation,[],[f638]) ).
thf(f638,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) = vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2)) ),
inference(fool_elimination,[],[f637]) ).
thf(f637,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) = vAPP(option_trm,option_trm,uSubst716837505ntialo,
vAPP(trm,option_trm,
vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X3: variable] : $true)),
X2)) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) = vAPP(option_trm,option_trm,uSubst716837505ntialo,
vAPP(trm,option_trm,
vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X25: variable] : $true)),
X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_usubstappt_Osimps_I7_J) ).
thf(f5403,plain,
spl291_323,
inference(avatar_split_clause,[],[f2176,f5401]) ).
thf(f5401,plain,
( spl291_323
<=> ! [X2: set_variable > $o,X0: set_variable > $o,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ( $true = vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) )
| ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_323])]) ).
thf(f2176,plain,
! [X2: set_variable > $o,X0: set_variable > $o,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ( $true = vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) )
| ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1650]) ).
thf(f1650,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ( $true = vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) )
| ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK247])],[f1329,f1649]) ).
thf(f1649,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ? [X3: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) )
& ( $true = vAPP(set_variable,$o,X0,X3) ) )
=> ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK247,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1329,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ( $true = vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) )
| ? [X3: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) )
& ( $true = vAPP(set_variable,$o,X0,X3) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(definition_folding,[],[f1132,f1328]) ).
thf(f1328,plain,
! [X2: set_variable > $o,X0: set_variable > $o] :
( ? [X4: set_variable] :
( ( $true != vAPP(set_variable,$o,X2,X4) )
& ! [X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) )
| ( $true != vAPP(set_variable,$o,X0,X5) ) )
& ( $true = vAPP(set_variable,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1132,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ? [X4: set_variable] :
( ( $true != vAPP(set_variable,$o,X2,X4) )
& ! [X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) )
| ( $true != vAPP(set_variable,$o,X0,X5) ) )
& ( $true = vAPP(set_variable,$o,X0,X4) ) )
| ? [X3: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) )
& ( $true = vAPP(set_variable,$o,X0,X3) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(flattening,[],[f1131]) ).
thf(f1131,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) )
| ? [X4: set_variable] :
( ( $true != vAPP(set_variable,$o,X2,X4) )
& ! [X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) )
| ( $true != vAPP(set_variable,$o,X0,X5) ) )
& ( $true = vAPP(set_variable,$o,X0,X4) ) )
| ? [X3: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) )
& ( $true = vAPP(set_variable,$o,X0,X3) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f692]) ).
thf(f692,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X0,X1) )
=> ( ! [X3: set_variable] :
( ( $true = vAPP(set_variable,$o,X0,X3) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) ) )
=> ( ! [X4: set_variable] :
( ( $true = vAPP(set_variable,$o,X0,X4) )
=> ( ! [X5: set_variable] :
( ( $true = vAPP(set_variable,$o,X0,X5) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) ) )
=> ( $true = vAPP(set_variable,$o,X2,X4) ) ) )
=> ( $true = vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) ) ) ) ),
inference(fool_elimination,[],[f691]) ).
thf(f691,plain,
! [X0: set_variable > $o,X1: set_variable,X2: set_variable > $o] :
( vAPP(set_variable,$o,X0,X1)
=> ( ! [X3: set_variable] :
( vAPP(set_variable,$o,X0,X3)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X1) )
=> ( ! [X4: set_variable] :
( vAPP(set_variable,$o,X0,X4)
=> ( ! [X5: set_variable] :
( vAPP(set_variable,$o,X0,X5)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) )
=> vAPP(set_variable,$o,X2,X4) ) )
=> vAPP(set_variable,$o,X2,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0)) ) ) ),
inference(rectify,[],[f155]) ).
thf(f155,axiom,
! [X26: set_variable > $o,X23: set_variable,X38: set_variable > $o] :
( vAPP(set_variable,$o,X26,X23)
=> ( ! [X41: set_variable] :
( vAPP(set_variable,$o,X26,X41)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X41),X23) )
=> ( ! [X22: set_variable] :
( vAPP(set_variable,$o,X26,X22)
=> ( ! [X72: set_variable] :
( vAPP(set_variable,$o,X26,X72)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X72),X22) )
=> vAPP(set_variable,$o,X38,X22) ) )
=> vAPP(set_variable,$o,X38,vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_GreatestI2__order) ).
thf(f5399,plain,
spl291_322,
inference(avatar_split_clause,[],[f2092,f5397]) ).
thf(f5397,plain,
( spl291_322
<=> ! [X2: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_322])]) ).
thf(f2092,plain,
! [X2: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) ) ),
inference(cnf_transformation,[],[f1096]) ).
thf(f1096,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) ) ),
inference(ennf_transformation,[],[f656]) ).
thf(f656,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) )
=> ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))),X2) ) ),
inference(fool_elimination,[],[f655]) ).
thf(f655,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) )
=> ( vAPP(trm,option_trm,
vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X3: variable] : $true)),
X2) != none_trm ) ),
inference(rectify,[],[f150]) ).
thf(f150,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,differential,X2)) )
=> ( vAPP(trm,option_trm,
vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X25: variable] : $true)),
X2) != none_trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_usubstappt__differential__conv) ).
thf(f5383,plain,
spl291_321,
inference(avatar_split_clause,[],[f2415,f5381]) ).
thf(f5381,plain,
( spl291_321
<=> ! [X2: set_variable > set_variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),vAPP(set_variable,set_variable,X2,X1)) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2)),vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2)) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_321])]) ).
thf(f2415,plain,
! [X2: set_variable > set_variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),vAPP(set_variable,set_variable,X2,X1)) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2)),vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2)) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(equality_resolution,[],[f2285]) ).
thf(f2285,plain,
! [X2: set_variable > set_variable,X3: set_variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2)),vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2)) )
| ( vAPP(set_variable,set_variable,X2,X1) != X3 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(cnf_transformation,[],[f1697]) ).
thf(f1697,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable > set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) )
| ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2))),vAPP(set_variable,set_variable,X2,vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2))) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2)),vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2)) ) )
| ( vAPP(set_variable,set_variable,X2,X1) != X3 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK269,sK270])],[f1223,f1696]) ).
thf(f1696,plain,
! [X2: set_variable > set_variable] :
( ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X4)),vAPP(set_variable,set_variable,X2,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
=> ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2))),vAPP(set_variable,set_variable,X2,vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2))) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK269,X2)),vAPP(sTfun(set_variable,set_variable),set_variable,sK270,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1223,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable > set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) )
| ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X4)),vAPP(set_variable,set_variable,X2,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
| ( vAPP(set_variable,set_variable,X2,X1) != X3 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(flattening,[],[f1222]) ).
thf(f1222,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable > set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) )
| ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X4)),vAPP(set_variable,set_variable,X2,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
| ( vAPP(set_variable,set_variable,X2,X1) != X3 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(ennf_transformation,[],[f792]) ).
thf(f792,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable > set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
=> ( ( vAPP(set_variable,set_variable,X2,X1) = X3 )
=> ( ! [X4: set_variable,X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X4)),vAPP(set_variable,set_variable,X2,X5)) ) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f791]) ).
thf(f791,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable > set_variable,X3: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1)
=> ( ( vAPP(set_variable,set_variable,X2,X1) = X3 )
=> ( ! [X4: set_variable,X5: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X4)),vAPP(set_variable,set_variable,X2,X5)) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X2,X0)),X3) ) ) ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
! [X30: set_variable,X29: set_variable,X40: set_variable > set_variable,X35: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X30),X29)
=> ( ( vAPP(set_variable,set_variable,X40,X29) = X35 )
=> ( ! [X22: set_variable,X41: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X22),X41)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X40,X22)),vAPP(set_variable,set_variable,X40,X41)) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X40,X30)),X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_ord__le__eq__subst) ).
thf(f5379,plain,
spl291_320,
inference(avatar_split_clause,[],[f2413,f5377]) ).
thf(f5377,plain,
( spl291_320
<=> ! [X2: set_variable,X1: set_variable > set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X2)),vAPP(set_variable,set_variable,X1,X3)) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1)),vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1)) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_320])]) ).
thf(f2413,plain,
! [X2: set_variable,X3: set_variable,X1: set_variable > set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X2)),vAPP(set_variable,set_variable,X1,X3)) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1)),vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1)) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) ) ),
inference(equality_resolution,[],[f2268]) ).
thf(f2268,plain,
! [X2: set_variable,X3: set_variable,X0: set_variable,X1: set_variable > set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) )
| ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1)),vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1)) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) )
| ( vAPP(set_variable,set_variable,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1693]) ).
thf(f1693,plain,
! [X0: set_variable,X1: set_variable > set_variable,X2: set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) )
| ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1))),vAPP(set_variable,set_variable,X1,vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1))) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1)),vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1)) ) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) )
| ( vAPP(set_variable,set_variable,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK266,sK267])],[f1205,f1692]) ).
thf(f1692,plain,
! [X1: set_variable > set_variable] :
( ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X4)),vAPP(set_variable,set_variable,X1,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
=> ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1))),vAPP(set_variable,set_variable,X1,vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1))) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,set_variable),set_variable,sK266,X1)),vAPP(sTfun(set_variable,set_variable),set_variable,sK267,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1205,plain,
! [X0: set_variable,X1: set_variable > set_variable,X2: set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) )
| ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X4)),vAPP(set_variable,set_variable,X1,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) )
| ( vAPP(set_variable,set_variable,X1,X2) != X0 ) ),
inference(flattening,[],[f1204]) ).
thf(f1204,plain,
! [X0: set_variable,X1: set_variable > set_variable,X2: set_variable,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) )
| ? [X4: set_variable,X5: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X4)),vAPP(set_variable,set_variable,X1,X5)) )
& ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) ) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) )
| ( vAPP(set_variable,set_variable,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f784]) ).
thf(f784,plain,
! [X0: set_variable,X1: set_variable > set_variable,X2: set_variable,X3: set_variable] :
( ( vAPP(set_variable,set_variable,X1,X2) = X0 )
=> ( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3) )
=> ( ! [X4: set_variable,X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X4)),vAPP(set_variable,set_variable,X1,X5)) ) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f783]) ).
thf(f783,plain,
! [X0: set_variable,X1: set_variable > set_variable,X2: set_variable,X3: set_variable] :
( ( vAPP(set_variable,set_variable,X1,X2) = X0 )
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X3)
=> ( ! [X4: set_variable,X5: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X4),X5)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X1,X4)),vAPP(set_variable,set_variable,X1,X5)) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),vAPP(set_variable,set_variable,X1,X3)) ) ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X30: set_variable,X40: set_variable > set_variable,X29: set_variable,X35: set_variable] :
( ( vAPP(set_variable,set_variable,X40,X29) = X30 )
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X29),X35)
=> ( ! [X22: set_variable,X41: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X22),X41)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(set_variable,set_variable,X40,X22)),vAPP(set_variable,set_variable,X40,X41)) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X30),vAPP(set_variable,set_variable,X40,X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_ord__eq__le__subst) ).
thf(f5351,plain,
spl291_319,
inference(avatar_split_clause,[],[f2391,f5349]) ).
thf(f5349,plain,
( spl291_319
<=> ! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_319])]) ).
thf(f2391,plain,
! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0))) ) ),
inference(equality_resolution,[],[f2026]) ).
thf(f2026,plain,
! [X2: option_game,X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0))) = X2 )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f1501,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0))) = X2 )
& ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0)) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f1081,f1500]) ).
thf(f1500,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0))) = X2 )
& ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1081,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(flattening,[],[f1080]) ).
thf(f1080,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f952]) ).
thf(f952,plain,
! [X0: char,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) = X2 )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) != X2 ) )
=> ~ ( ( none_trm = X1 )
=> ( none_game != X2 ) ) ) ),
inference(rectify,[],[f349]) ).
thf(f349,axiom,
! [X23: char,X53: option_trm,X36: option_game] :
( ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X23),X53) = X36 )
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X53 )
=> ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X23),X54)) != X36 ) )
=> ~ ( ( none_trm = X53 )
=> ( none_game != X36 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_ODEo_Oelims) ).
thf(f5347,plain,
spl291_318,
inference(avatar_split_clause,[],[f2384,f5345]) ).
thf(f5345,plain,
( spl291_318
<=> ! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_318])]) ).
thf(f2384,plain,
! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0))) ) ),
inference(equality_resolution,[],[f2016]) ).
thf(f2016,plain,
! [X2: option_game,X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0))) = X2 )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1495]) ).
thf(f1495,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0))) = X2 )
& ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0)) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f1077,f1494]) ).
thf(f1494,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
=> ( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0))) = X2 )
& ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1077,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(flattening,[],[f1076]) ).
thf(f1076,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( ( none_game = X2 )
& ( none_trm = X1 ) )
| ? [X3: trm] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f950]) ).
thf(f950,plain,
! [X0: variable,X1: option_trm,X2: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) = X2 )
=> ( ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X1 )
=> ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) != X2 ) )
=> ~ ( ( none_trm = X1 )
=> ( none_game != X2 ) ) ) ),
inference(rectify,[],[f342]) ).
thf(f342,axiom,
! [X23: variable,X53: option_trm,X36: option_game] :
( ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X23),X53) = X36 )
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X53 )
=> ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X23),X54)) != X36 ) )
=> ~ ( ( none_trm = X53 )
=> ( none_game != X36 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_Assigno_Oelims) ).
thf(f5343,plain,
spl291_317,
inference(avatar_split_clause,[],[f2162,f5341]) ).
thf(f5341,plain,
( spl291_317
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0))) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_317])]) ).
thf(f2162,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0))) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(cnf_transformation,[],[f1609]) ).
thf(f1609,plain,
! [X0: denotational_interp > trm > $o] :
( ( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0))) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK210,sK211,sK212])],[f1606,f1608,f1607]) ).
thf(f1607,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X1: denotational_interp,X2: trm] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X2) ) )
=> ( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1608,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),X3) ) )
=> ( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0))) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1606,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X1: denotational_interp,X2: trm] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X2) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(rectify,[],[f1605]) ).
thf(f1605,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X12: denotational_interp,X13: trm] :
( ? [X14: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X13),X14)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),X14) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),X13) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(nnf_transformation,[],[f1325]) ).
thf(f1325,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X12: denotational_interp,X13: trm] :
( ? [X14: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X13),X14)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),X14) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X12),X13) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5339,plain,
spl291_316,
inference(avatar_split_clause,[],[f2159,f5337]) ).
thf(f5337,plain,
( spl291_316
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0))) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_316])]) ).
thf(f2159,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0))) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(cnf_transformation,[],[f1604]) ).
thf(f1604,plain,
! [X0: denotational_interp > trm > $o] :
( ( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0))) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK207,sK208,sK209])],[f1601,f1603,f1602]) ).
thf(f1602,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X1: denotational_interp,X2: trm] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X2) ) )
=> ( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1603,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),X3) ) )
=> ( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0))) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1601,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X1: denotational_interp,X2: trm] :
( ? [X3: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X3) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X1),X2) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(rectify,[],[f1600]) ).
thf(f1600,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X15: denotational_interp,X16: trm] :
( ? [X17: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X16),X17)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),X17) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),X16) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(nnf_transformation,[],[f1326]) ).
thf(f1326,plain,
! [X0: denotational_interp > trm > $o] :
( ? [X15: denotational_interp,X16: trm] :
( ? [X17: trm] :
( ( $true != vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X16),X17)) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),X17) ) )
& ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,X15),X16) ) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5290,plain,
spl291_315,
inference(avatar_split_clause,[],[f2030,f5288]) ).
thf(f5288,plain,
( spl291_315
<=> ! [X2: option_trm,X0: char,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0))) = X1 )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_315])]) ).
thf(f2030,plain,
! [X2: option_trm,X0: char,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0))) = X1 )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1505]) ).
thf(f1505,plain,
! [X0: char,X1: option_game,X2: option_trm] :
( ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f1503,f1504]) ).
thf(f1504,plain,
! [X0: char,X1: option_game,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1503,plain,
! [X0: char,X1: option_game,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ),
inference(rectify,[],[f1502]) ).
thf(f1502,plain,
! [X0: char,X2: option_game,X1: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,uSubst299938919Eo_rel),vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X1),X2),X0) ) ),
inference(nnf_transformation,[],[f1287]) ).
thf(f5286,plain,
spl291_314,
inference(avatar_split_clause,[],[f2020,f5284]) ).
thf(f5284,plain,
( spl291_314
<=> ! [X2: option_trm,X0: variable,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0))) = X1 )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_314])]) ).
thf(f2020,plain,
! [X2: option_trm,X0: variable,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0))) = X1 )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1499]) ).
thf(f1499,plain,
! [X0: variable,X1: option_game,X2: option_trm] :
( ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f1497,f1498]) ).
thf(f1498,plain,
! [X0: variable,X1: option_game,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1497,plain,
! [X0: variable,X1: option_game,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ),
inference(rectify,[],[f1496]) ).
thf(f1496,plain,
! [X0: variable,X2: option_game,X1: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,uSubst157155628no_rel),vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X0),vAPP(trm,option_trm,some_trm,X3))) )
& ( vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X3)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X1),X2),X0) ) ),
inference(nnf_transformation,[],[f1285]) ).
thf(f5282,plain,
( spl291_313
| ~ spl291_2
| ~ spl291_277 ),
inference(avatar_split_clause,[],[f5039,f4986,f2910,f5280]) ).
thf(f5280,plain,
( spl291_313
<=> ! [X0: trm] : ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),theta)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_313])]) ).
thf(f2910,plain,
( spl291_2
<=> ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_2])]) ).
thf(f4986,plain,
( spl291_277
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_277])]) ).
thf(f5039,plain,
( ! [X0: trm] : ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),theta)) )
| ~ spl291_2
| ~ spl291_277 ),
inference(trivial_inequality_removal,[],[f5035]) ).
thf(f5035,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),theta)) ) )
| ~ spl291_2
| ~ spl291_277 ),
inference(superposition,[],[f4987,f2912]) ).
thf(f2912,plain,
( ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta) )
| ~ spl291_2 ),
inference(avatar_component_clause,[],[f2910]) ).
thf(f4987,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) )
| ~ spl291_277 ),
inference(avatar_component_clause,[],[f4986]) ).
thf(f5278,plain,
spl291_312,
inference(avatar_split_clause,[],[f1967,f5276]) ).
thf(f5276,plain,
( spl291_312
<=> ! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_312])]) ).
thf(f1967,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X1) ) ),
inference(cnf_transformation,[],[f1485]) ).
thf(f1485,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ( ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X1) )
& ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158,sK159])],[f1046,f1484]) ).
thf(f1484,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ? [X2: option_fml,X3: option_fml] :
( ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X1) )
& ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X0) ) )
=> ( ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X1) )
& ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1046,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ? [X2: option_fml,X3: option_fml] :
( ( $true != vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X1) )
& ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X0) ) ) ),
inference(ennf_transformation,[],[f586]) ).
thf(f586,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ! [X2: option_fml,X3: option_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X0) )
=> ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X1) ) )
=> ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) ) ),
inference(fool_elimination,[],[f585]) ).
thf(f585,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ! [X2: option_fml,X3: option_fml] :
( vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X0)
=> vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X2),X3)),X1) )
=> vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X86: set_Pr927595527on_fml,X88: set_Pr927595527on_fml] :
( ! [X22: option_fml,X41: option_fml] :
( vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X22),X41)),X86)
=> vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,X22),X41)),X88) )
=> vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X86),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_subrelI) ).
thf(f5274,plain,
spl291_311,
inference(avatar_split_clause,[],[f1966,f5272]) ).
thf(f5272,plain,
( spl291_311
<=> ! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_311])]) ).
thf(f1966,plain,
! [X0: set_Pr927595527on_fml,X1: set_Pr927595527on_fml] :
( ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,$o),ord_le778974119on_fml,X0),X1) )
| ( $true = vAPP(set_Pr927595527on_fml,$o,vAPP(produc46605351on_fml,sTfun(set_Pr927595527on_fml,$o),member1287158352on_fml,vAPP(option_fml,produc46605351on_fml,vAPP(option_fml,sTfun(option_fml,produc46605351on_fml),produc909629463on_fml,vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK158,X1),X0)),vAPP(set_Pr927595527on_fml,option_fml,vAPP(set_Pr927595527on_fml,sTfun(set_Pr927595527on_fml,option_fml),sK159,X1),X0))),X0) ) ),
inference(cnf_transformation,[],[f1485]) ).
thf(f5270,plain,
spl291_310,
inference(avatar_split_clause,[],[f1965,f5268]) ).
thf(f5268,plain,
( spl291_310
<=> ! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_310])]) ).
thf(f1965,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X1) ) ),
inference(cnf_transformation,[],[f1483]) ).
thf(f1483,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ( ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X1) )
& ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156,sK157])],[f1045,f1482]) ).
thf(f1482,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ? [X2: option_trm,X3: option_trm] :
( ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X0) ) )
=> ( ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X1) )
& ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1045,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ? [X2: option_trm,X3: option_trm] :
( ( $true != vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X0) ) ) ),
inference(ennf_transformation,[],[f584]) ).
thf(f584,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ! [X2: option_trm,X3: option_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X0) )
=> ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X1) ) )
=> ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) ) ),
inference(fool_elimination,[],[f583]) ).
thf(f583,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ! [X2: option_trm,X3: option_trm] :
( vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X0)
=> vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X2),X3)),X1) )
=> vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X86: set_Pr1471344007on_trm,X88: set_Pr1471344007on_trm] :
( ! [X22: option_trm,X41: option_trm] :
( vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X22),X41)),X86)
=> vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,X22),X41)),X88) )
=> vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X86),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_subrelI) ).
thf(f5266,plain,
spl291_309,
inference(avatar_split_clause,[],[f1964,f5264]) ).
thf(f5264,plain,
( spl291_309
<=> ! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_309])]) ).
thf(f1964,plain,
! [X0: set_Pr1471344007on_trm,X1: set_Pr1471344007on_trm] :
( ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,$o),ord_le1322722599on_trm,X0),X1) )
| ( $true = vAPP(set_Pr1471344007on_trm,$o,vAPP(produc1072747943on_trm,sTfun(set_Pr1471344007on_trm,$o),member165817296on_trm,vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK156,X1),X0)),vAPP(set_Pr1471344007on_trm,option_trm,vAPP(set_Pr1471344007on_trm,sTfun(set_Pr1471344007on_trm,option_trm),sK157,X1),X0))),X0) ) ),
inference(cnf_transformation,[],[f1483]) ).
thf(f5262,plain,
spl291_308,
inference(avatar_split_clause,[],[f1963,f5260]) ).
thf(f5260,plain,
( spl291_308
<=> ! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_308])]) ).
thf(f1963,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X1) ) ),
inference(cnf_transformation,[],[f1481]) ).
thf(f1481,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ( ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X1) )
& ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155])],[f1044,f1480]) ).
thf(f1480,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ? [X2: char,X3: option_trm] :
( ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X0) ) )
=> ( ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X1) )
& ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1044,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ? [X2: char,X3: option_trm] :
( ( $true != vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X0) ) ) ),
inference(ennf_transformation,[],[f582]) ).
thf(f582,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ! [X2: char,X3: option_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X0) )
=> ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X1) ) )
=> ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) ) ),
inference(fool_elimination,[],[f581]) ).
thf(f581,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ! [X2: char,X3: option_trm] :
( vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X0)
=> vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),X3)),X1) )
=> vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X86: set_Pr943832262on_trm,X88: set_Pr943832262on_trm] :
( ! [X22: char,X41: option_trm] :
( vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X22),X41)),X86)
=> vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X22),X41)),X88) )
=> vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X86),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_subrelI) ).
thf(f5258,plain,
spl291_307,
inference(avatar_split_clause,[],[f1962,f5256]) ).
thf(f5256,plain,
( spl291_307
<=> ! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_307])]) ).
thf(f1962,plain,
! [X0: set_Pr943832262on_trm,X1: set_Pr943832262on_trm] :
( ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,$o),ord_le541293862on_trm,X0),X1) )
| ( $true = vAPP(set_Pr943832262on_trm,$o,vAPP(produc464795408on_trm,sTfun(set_Pr943832262on_trm,$o),member694524327on_trm,vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(set_Pr943832262on_trm,char,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,char),sK154,X1),X0)),vAPP(set_Pr943832262on_trm,option_trm,vAPP(set_Pr943832262on_trm,sTfun(set_Pr943832262on_trm,option_trm),sK155,X1),X0))),X0) ) ),
inference(cnf_transformation,[],[f1481]) ).
thf(f5254,plain,
spl291_306,
inference(avatar_split_clause,[],[f1961,f5252]) ).
thf(f5252,plain,
( spl291_306
<=> ! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_306])]) ).
thf(f1961,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X1) ) ),
inference(cnf_transformation,[],[f1479]) ).
thf(f1479,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ( ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X1) )
& ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153])],[f1043,f1478]) ).
thf(f1478,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ? [X2: set_variable,X3: trm] :
( ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X0) ) )
=> ( ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X1) )
& ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1043,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ? [X2: set_variable,X3: trm] :
( ( $true != vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X1) )
& ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X0) ) ) ),
inference(ennf_transformation,[],[f580]) ).
thf(f580,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ! [X2: set_variable,X3: trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X0) )
=> ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X1) ) )
=> ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) ) ),
inference(fool_elimination,[],[f579]) ).
thf(f579,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ! [X2: set_variable,X3: trm] :
( vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X0)
=> vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X2),X3)),X1) )
=> vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) ),
inference(rectify,[],[f237]) ).
thf(f237,axiom,
! [X86: set_Pr1235432374le_trm,X88: set_Pr1235432374le_trm] :
( ! [X22: set_variable,X41: trm] :
( vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X22),X41)),X86)
=> vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,X22),X41)),X88) )
=> vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X86),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subrelI) ).
thf(f5250,plain,
spl291_305,
inference(avatar_split_clause,[],[f1960,f5248]) ).
thf(f5248,plain,
( spl291_305
<=> ! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_305])]) ).
thf(f1960,plain,
! [X0: set_Pr1235432374le_trm,X1: set_Pr1235432374le_trm] :
( ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,$o),ord_le2102862870le_trm,X0),X1) )
| ( $true = vAPP(set_Pr1235432374le_trm,$o,vAPP(produc1367888000le_trm,sTfun(set_Pr1235432374le_trm,$o),member2122665623le_trm,vAPP(trm,produc1367888000le_trm,vAPP(set_variable,sTfun(trm,produc1367888000le_trm),produc1482344242le_trm,vAPP(set_Pr1235432374le_trm,set_variable,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,set_variable),sK152,X1),X0)),vAPP(set_Pr1235432374le_trm,trm,vAPP(set_Pr1235432374le_trm,sTfun(set_Pr1235432374le_trm,trm),sK153,X1),X0))),X0) ) ),
inference(cnf_transformation,[],[f1479]) ).
thf(f5246,plain,
spl291_304,
inference(avatar_split_clause,[],[f1959,f5244]) ).
thf(f5244,plain,
( spl291_304
<=> ! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_304])]) ).
thf(f1959,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X1) ) ),
inference(cnf_transformation,[],[f1477]) ).
thf(f1477,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ( ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X1) )
& ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151])],[f1042,f1476]) ).
thf(f1476,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ? [X2: option_game,X3: option_fml] :
( ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X1) )
& ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X0) ) )
=> ( ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X1) )
& ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1042,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ? [X2: option_game,X3: option_fml] :
( ( $true != vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X1) )
& ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X0) ) ) ),
inference(ennf_transformation,[],[f578]) ).
thf(f578,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ! [X2: option_game,X3: option_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X0) )
=> ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X1) ) )
=> ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) ) ),
inference(fool_elimination,[],[f577]) ).
thf(f577,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ! [X2: option_game,X3: option_fml] :
( vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X0)
=> vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X2),X3)),X1) )
=> vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) ),
inference(rectify,[],[f233]) ).
thf(f233,axiom,
! [X86: set_Pr622314946on_fml,X88: set_Pr622314946on_fml] :
( ! [X22: option_game,X41: option_fml] :
( vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X22),X41)),X86)
=> vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,X22),X41)),X88) )
=> vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X86),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subrelI) ).
thf(f5242,plain,
spl291_303,
inference(avatar_split_clause,[],[f1958,f5240]) ).
thf(f5240,plain,
( spl291_303
<=> ! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_303])]) ).
thf(f1958,plain,
! [X0: set_Pr622314946on_fml,X1: set_Pr622314946on_fml] :
( ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,$o),ord_le782333474on_fml,X0),X1) )
| ( $true = vAPP(set_Pr622314946on_fml,$o,vAPP(produc1739631244on_fml,sTfun(set_Pr622314946on_fml,$o),member1883102883on_fml,vAPP(option_fml,produc1739631244on_fml,vAPP(option_game,sTfun(option_fml,produc1739631244on_fml),produc2124676926on_fml,vAPP(set_Pr622314946on_fml,option_game,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_game),sK150,X1),X0)),vAPP(set_Pr622314946on_fml,option_fml,vAPP(set_Pr622314946on_fml,sTfun(set_Pr622314946on_fml,option_fml),sK151,X1),X0))),X0) ) ),
inference(cnf_transformation,[],[f1477]) ).
thf(f5238,plain,
( spl291_302
| ~ spl291_2
| ~ spl291_276 ),
inference(avatar_split_clause,[],[f5034,f4982,f2910,f5236]) ).
thf(f4982,plain,
( spl291_276
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_276])]) ).
thf(f5034,plain,
( ! [X0: trm] : ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),X0)) )
| ~ spl291_2
| ~ spl291_276 ),
inference(trivial_inequality_removal,[],[f5030]) ).
thf(f5030,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_fml = vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),X0)) ) )
| ~ spl291_2
| ~ spl291_276 ),
inference(superposition,[],[f4983,f2912]) ).
thf(f4983,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) )
| ~ spl291_276 ),
inference(avatar_component_clause,[],[f4982]) ).
thf(f5232,plain,
spl291_301,
inference(avatar_split_clause,[],[f2174,f5230]) ).
thf(f5230,plain,
( spl291_301
<=> ! [X0: set_variable > $o,X1: set_variable > $o,X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X1,X3) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_301])]) ).
thf(f2174,plain,
! [X3: set_variable,X0: set_variable > $o,X1: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X1,X3) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ),
inference(cnf_transformation,[],[f1648]) ).
thf(f1648,plain,
! [X0: set_variable > $o,X1: set_variable > $o] :
( ( ( $true != vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
& ! [X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X1,X3) ) )
& ( $true = vAPP(set_variable,$o,X1,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) ) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK246])],[f1646,f1647]) ).
thf(f1647,plain,
! [X0: set_variable > $o,X1: set_variable > $o] :
( ? [X2: set_variable] :
( ( $true != vAPP(set_variable,$o,X0,X2) )
& ! [X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X2) )
| ( $true != vAPP(set_variable,$o,X1,X3) ) )
& ( $true = vAPP(set_variable,$o,X1,X2) ) )
=> ( ( $true != vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
& ! [X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X1,X3) ) )
& ( $true = vAPP(set_variable,$o,X1,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1646,plain,
! [X0: set_variable > $o,X1: set_variable > $o] :
( ? [X2: set_variable] :
( ( $true != vAPP(set_variable,$o,X0,X2) )
& ! [X3: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X3),X2) )
| ( $true != vAPP(set_variable,$o,X1,X3) ) )
& ( $true = vAPP(set_variable,$o,X1,X2) ) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ),
inference(rectify,[],[f1645]) ).
thf(f1645,plain,
! [X2: set_variable > $o,X0: set_variable > $o] :
( ? [X4: set_variable] :
( ( $true != vAPP(set_variable,$o,X2,X4) )
& ! [X5: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X5),X4) )
| ( $true != vAPP(set_variable,$o,X0,X5) ) )
& ( $true = vAPP(set_variable,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X0),X2) ) ),
inference(nnf_transformation,[],[f1328]) ).
thf(f5183,plain,
( spl291_300
| ~ spl291_2
| ~ spl291_275 ),
inference(avatar_split_clause,[],[f5029,f4978,f2910,f5181]) ).
thf(f5181,plain,
( spl291_300
<=> ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),theta)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_300])]) ).
thf(f4978,plain,
( spl291_275
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_275])]) ).
thf(f5029,plain,
( ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),theta)) )
| ~ spl291_2
| ~ spl291_275 ),
inference(trivial_inequality_removal,[],[f5025]) ).
thf(f5025,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),theta)) ) )
| ~ spl291_2
| ~ spl291_275 ),
inference(superposition,[],[f4979,f2912]) ).
thf(f4979,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) )
| ~ spl291_275 ),
inference(avatar_component_clause,[],[f4978]) ).
thf(f5131,plain,
( spl291_299
| ~ spl291_2
| ~ spl291_274 ),
inference(avatar_split_clause,[],[f5024,f4974,f2910,f5129]) ).
thf(f5129,plain,
( spl291_299
<=> ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,theta),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_299])]) ).
thf(f4974,plain,
( spl291_274
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_274])]) ).
thf(f5024,plain,
( ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,theta),X0)) )
| ~ spl291_2
| ~ spl291_274 ),
inference(trivial_inequality_removal,[],[f5020]) ).
thf(f5020,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,theta),X0)) ) )
| ~ spl291_2
| ~ spl291_274 ),
inference(superposition,[],[f4975,f2912]) ).
thf(f4975,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) )
| ~ spl291_274 ),
inference(avatar_component_clause,[],[f4974]) ).
thf(f5123,plain,
spl291_298,
inference(avatar_split_clause,[],[f2251,f5121]) ).
thf(f5121,plain,
( spl291_298
<=> ! [X2: set_variable,X0: variable > real,X1: variable > real] :
( ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_298])]) ).
thf(f2251,plain,
! [X2: set_variable,X0: variable > real,X1: variable > real] :
( ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1199]) ).
thf(f1199,plain,
! [X0: variable > real,X1: variable > real,X2: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),X2) ) ),
inference(ennf_transformation,[],[f762]) ).
thf(f762,plain,
! [X0: variable > real,X1: variable > real,X2: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),X2) )
=> ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0),X2) ) ),
inference(fool_elimination,[],[f761]) ).
thf(f761,plain,
! [X0: variable > real,X1: variable > real,X2: set_variable] :
( vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),X2)
=> vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0),X2) ),
inference(rectify,[],[f79]) ).
thf(f79,axiom,
! [X18: variable > real,X19: variable > real,X1: set_variable] :
( vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X18),X19),X1)
=> vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X19),X18),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Uvariation__sym__rel) ).
thf(f5119,plain,
spl291_297,
inference(avatar_split_clause,[],[f2150,f5117]) ).
thf(f5117,plain,
( spl291_297
<=> ! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK203,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_297])]) ).
thf(f2150,plain,
! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK203,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1595]) ).
thf(f1595,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm > option_trm > $o] :
( ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK203,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK202,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202,sK203])],[f1593,f1594]) ).
thf(f1594,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm > option_trm > $o] :
( ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
=> ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK203,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK202,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1593,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm > option_trm > $o] :
( ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ),
inference(rectify,[],[f1592]) ).
thf(f1592,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm > option_trm > $o] :
( ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1323]) ).
thf(f1323,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm > option_trm > $o] :
( ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5115,plain,
spl291_296,
inference(avatar_split_clause,[],[f2149,f5113]) ).
thf(f5113,plain,
( spl291_296
<=> ! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK202,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_296])]) ).
thf(f2149,plain,
! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,trm)),sK202,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1595]) ).
thf(f5111,plain,
spl291_295,
inference(avatar_split_clause,[],[f2143,f5109]) ).
thf(f5109,plain,
( spl291_295
<=> ! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_trm,sTfun(option_fml,fml),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,fml)),sK201,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_295])]) ).
thf(f2143,plain,
! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_trm,sTfun(option_fml,fml),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,fml)),sK201,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1591]) ).
thf(f1591,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm > option_fml > $o] :
( ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_trm,sTfun(option_fml,fml),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,fml)),sK201,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,trm)),sK200,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201])],[f1589,f1590]) ).
thf(f1590,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm > option_fml > $o] :
( ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
=> ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_trm,sTfun(option_fml,fml),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,fml)),sK201,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,trm)),sK200,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1589,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm > option_fml > $o] :
( ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ),
inference(rectify,[],[f1588]) ).
thf(f1588,plain,
! [X2: option_fml,X0: option_trm,X1: option_trm > option_fml > $o] :
( ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1321]) ).
thf(f1321,plain,
! [X2: option_fml,X0: option_trm,X1: option_trm > option_fml > $o] :
( ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5107,plain,
spl291_294,
inference(avatar_split_clause,[],[f2142,f5105]) ).
thf(f5105,plain,
( spl291_294
<=> ! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,trm)),sK200,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_294])]) ).
thf(f2142,plain,
! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,trm)),sK200,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1591]) ).
thf(f5103,plain,
spl291_293,
inference(avatar_split_clause,[],[f2136,f5101]) ).
thf(f5101,plain,
( spl291_293
<=> ! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_trm,sTfun(option_game,game),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,game)),sK199,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_293])]) ).
thf(f2136,plain,
! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_trm,sTfun(option_game,game),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,game)),sK199,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1587]) ).
thf(f1587,plain,
! [X0: option_game,X1: option_trm,X2: option_trm > option_game > $o] :
( ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_trm,sTfun(option_game,game),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,game)),sK199,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_game,trm,vAPP(option_trm,sTfun(option_game,trm),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,trm)),sK198,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199])],[f1585,f1586]) ).
thf(f1586,plain,
! [X0: option_game,X1: option_trm,X2: option_trm > option_game > $o] :
( ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
=> ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_trm,sTfun(option_game,game),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,game)),sK199,X2),X1),X0)) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_game,trm,vAPP(option_trm,sTfun(option_game,trm),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,trm)),sK198,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1585,plain,
! [X0: option_game,X1: option_trm,X2: option_trm > option_game > $o] :
( ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(trm,option_trm,some_trm,X3) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ),
inference(rectify,[],[f1584]) ).
thf(f1584,plain,
! [X2: option_game,X0: option_trm,X1: option_trm > option_game > $o] :
( ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1319]) ).
thf(f1319,plain,
! [X2: option_game,X0: option_trm,X1: option_trm > option_game > $o] :
( ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5099,plain,
spl291_292,
inference(avatar_split_clause,[],[f2135,f5097]) ).
thf(f5097,plain,
( spl291_292
<=> ! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_game,trm,vAPP(option_trm,sTfun(option_game,trm),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,trm)),sK198,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_292])]) ).
thf(f2135,plain,
! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_game,trm,vAPP(option_trm,sTfun(option_game,trm),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,trm)),sK198,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1587]) ).
thf(f5095,plain,
spl291_291,
inference(avatar_split_clause,[],[f2129,f5093]) ).
thf(f5093,plain,
( spl291_291
<=> ! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_fml,sTfun(option_trm,trm),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,trm)),sK197,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_291])]) ).
thf(f2129,plain,
! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_fml,sTfun(option_trm,trm),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,trm)),sK197,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1583]) ).
thf(f1583,plain,
! [X0: option_trm,X1: option_fml,X2: option_fml > option_trm > $o] :
( ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_fml,sTfun(option_trm,trm),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,trm)),sK197,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_trm,fml,vAPP(option_fml,sTfun(option_trm,fml),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,fml)),sK196,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196,sK197])],[f1581,f1582]) ).
thf(f1582,plain,
! [X0: option_trm,X1: option_fml,X2: option_fml > option_trm > $o] :
( ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
=> ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_fml,sTfun(option_trm,trm),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,trm)),sK197,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_trm,fml,vAPP(option_fml,sTfun(option_trm,fml),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,fml)),sK196,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1581,plain,
! [X0: option_trm,X1: option_fml,X2: option_fml > option_trm > $o] :
( ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ),
inference(rectify,[],[f1580]) ).
thf(f1580,plain,
! [X2: option_trm,X0: option_fml,X1: option_fml > option_trm > $o] :
( ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1317]) ).
thf(f1317,plain,
! [X2: option_trm,X0: option_fml,X1: option_fml > option_trm > $o] :
( ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5091,plain,
spl291_290,
inference(avatar_split_clause,[],[f2128,f5089]) ).
thf(f5089,plain,
( spl291_290
<=> ! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_trm,fml,vAPP(option_fml,sTfun(option_trm,fml),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,fml)),sK196,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_290])]) ).
thf(f2128,plain,
! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_trm,fml,vAPP(option_fml,sTfun(option_trm,fml),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,fml)),sK196,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1583]) ).
thf(f5087,plain,
( spl291_289
| ~ spl291_2
| ~ spl291_273 ),
inference(avatar_split_clause,[],[f5019,f4959,f2910,f5085]) ).
thf(f5085,plain,
( spl291_289
<=> ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),theta)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_289])]) ).
thf(f4959,plain,
( spl291_273
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_273])]) ).
thf(f5019,plain,
( ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),theta)) )
| ~ spl291_2
| ~ spl291_273 ),
inference(trivial_inequality_removal,[],[f5015]) ).
thf(f5015,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),theta)) ) )
| ~ spl291_2
| ~ spl291_273 ),
inference(superposition,[],[f4960,f2912]) ).
thf(f4960,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) )
| ~ spl291_273 ),
inference(avatar_component_clause,[],[f4959]) ).
thf(f5083,plain,
spl291_288,
inference(avatar_split_clause,[],[f2122,f5081]) ).
thf(f5081,plain,
( spl291_288
<=> ! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK195,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_288])]) ).
thf(f2122,plain,
! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK195,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1579]) ).
thf(f1579,plain,
! [X0: option_fml,X1: option_fml,X2: option_fml > option_fml > $o] :
( ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK195,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK194,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194,sK195])],[f1577,f1578]) ).
thf(f1578,plain,
! [X0: option_fml,X1: option_fml,X2: option_fml > option_fml > $o] :
( ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
=> ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK195,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK194,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1577,plain,
! [X0: option_fml,X1: option_fml,X2: option_fml > option_fml > $o] :
( ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ),
inference(rectify,[],[f1576]) ).
thf(f1576,plain,
! [X2: option_fml,X0: option_fml,X1: option_fml > option_fml > $o] :
( ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1315]) ).
thf(f1315,plain,
! [X2: option_fml,X0: option_fml,X1: option_fml > option_fml > $o] :
( ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5079,plain,
spl291_287,
inference(avatar_split_clause,[],[f2121,f5077]) ).
thf(f5077,plain,
( spl291_287
<=> ! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK194,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_287])]) ).
thf(f2121,plain,
! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_fml,sTfun(option_fml,fml),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,fml)),sK194,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1579]) ).
thf(f5075,plain,
spl291_286,
inference(avatar_split_clause,[],[f2115,f5073]) ).
thf(f5073,plain,
( spl291_286
<=> ! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_fml,sTfun(option_game,game),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,game)),sK193,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_286])]) ).
thf(f2115,plain,
! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_fml,sTfun(option_game,game),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,game)),sK193,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1575]) ).
thf(f1575,plain,
! [X0: option_game,X1: option_fml,X2: option_fml > option_game > $o] :
( ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_fml,sTfun(option_game,game),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,game)),sK193,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,fml)),sK192,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192,sK193])],[f1573,f1574]) ).
thf(f1574,plain,
! [X0: option_game,X1: option_fml,X2: option_fml > option_game > $o] :
( ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
=> ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_fml,sTfun(option_game,game),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,game)),sK193,X2),X1),X0)) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,fml)),sK192,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1573,plain,
! [X0: option_game,X1: option_fml,X2: option_fml > option_game > $o] :
( ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(fml,option_fml,some_fml,X3) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ),
inference(rectify,[],[f1572]) ).
thf(f1572,plain,
! [X2: option_game,X0: option_fml,X1: option_fml > option_game > $o] :
( ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1313]) ).
thf(f1313,plain,
! [X2: option_game,X0: option_fml,X1: option_fml > option_game > $o] :
( ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5071,plain,
spl291_285,
inference(avatar_split_clause,[],[f2114,f5069]) ).
thf(f5069,plain,
( spl291_285
<=> ! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,fml)),sK192,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_285])]) ).
thf(f2114,plain,
! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,fml)),sK192,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1575]) ).
thf(f5067,plain,
spl291_284,
inference(avatar_split_clause,[],[f2108,f5065]) ).
thf(f5065,plain,
( spl291_284
<=> ! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_game,sTfun(option_trm,trm),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,trm)),sK191,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_284])]) ).
thf(f2108,plain,
! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_game,sTfun(option_trm,trm),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,trm)),sK191,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1571]) ).
thf(f1571,plain,
! [X0: option_trm,X1: option_game,X2: option_game > option_trm > $o] :
( ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_game,sTfun(option_trm,trm),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,trm)),sK191,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_trm,game,vAPP(option_game,sTfun(option_trm,game),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,game)),sK190,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191])],[f1569,f1570]) ).
thf(f1570,plain,
! [X0: option_trm,X1: option_game,X2: option_game > option_trm > $o] :
( ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
=> ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_game,sTfun(option_trm,trm),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,trm)),sK191,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_trm,game,vAPP(option_game,sTfun(option_trm,game),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,game)),sK190,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1569,plain,
! [X0: option_trm,X1: option_game,X2: option_game > option_trm > $o] :
( ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
& ( vAPP(trm,option_trm,some_trm,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ),
inference(rectify,[],[f1568]) ).
thf(f1568,plain,
! [X2: option_trm,X0: option_game,X1: option_game > option_trm > $o] :
( ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1311]) ).
thf(f1311,plain,
! [X2: option_trm,X0: option_game,X1: option_game > option_trm > $o] :
( ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5063,plain,
spl291_283,
inference(avatar_split_clause,[],[f2107,f5061]) ).
thf(f5061,plain,
( spl291_283
<=> ! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_trm,game,vAPP(option_game,sTfun(option_trm,game),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,game)),sK190,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_283])]) ).
thf(f2107,plain,
! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_trm,game,vAPP(option_game,sTfun(option_trm,game),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,game)),sK190,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1571]) ).
thf(f5059,plain,
spl291_282,
inference(avatar_split_clause,[],[f2101,f5057]) ).
thf(f5057,plain,
( spl291_282
<=> ! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,fml)),sK189,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_282])]) ).
thf(f2101,plain,
! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,fml)),sK189,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1567]) ).
thf(f1567,plain,
! [X0: option_fml,X1: option_game,X2: option_game > option_fml > $o] :
( ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,fml)),sK189,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_fml,game,vAPP(option_game,sTfun(option_fml,game),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,game)),sK188,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188,sK189])],[f1565,f1566]) ).
thf(f1566,plain,
! [X0: option_fml,X1: option_game,X2: option_game > option_fml > $o] :
( ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
=> ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,fml)),sK189,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_fml,game,vAPP(option_game,sTfun(option_fml,game),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,game)),sK188,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1565,plain,
! [X0: option_fml,X1: option_game,X2: option_game > option_fml > $o] :
( ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
& ( vAPP(fml,option_fml,some_fml,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ),
inference(rectify,[],[f1564]) ).
thf(f1564,plain,
! [X2: option_fml,X0: option_game,X1: option_game > option_fml > $o] :
( ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1309]) ).
thf(f1309,plain,
! [X2: option_fml,X0: option_game,X1: option_game > option_fml > $o] :
( ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5055,plain,
spl291_281,
inference(avatar_split_clause,[],[f2100,f5053]) ).
thf(f5053,plain,
( spl291_281
<=> ! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_fml,game,vAPP(option_game,sTfun(option_fml,game),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,game)),sK188,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_281])]) ).
thf(f2100,plain,
! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_fml,game,vAPP(option_game,sTfun(option_fml,game),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,game)),sK188,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1567]) ).
thf(f5051,plain,
spl291_280,
inference(avatar_split_clause,[],[f2094,f5049]) ).
thf(f5049,plain,
( spl291_280
<=> ! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK187,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_280])]) ).
thf(f2094,plain,
! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK187,X2),X1),X0)) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1563]) ).
thf(f1563,plain,
! [X0: option_game,X1: option_game,X2: option_game > option_game > $o] :
( ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK187,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK186,X2),X1),X0)) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186,sK187])],[f1561,f1562]) ).
thf(f1562,plain,
! [X0: option_game,X1: option_game,X2: option_game > option_game > $o] :
( ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
=> ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK187,X2),X1),X0)) = X0 )
& ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK186,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1561,plain,
! [X0: option_game,X1: option_game,X2: option_game > option_game > $o] :
( ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
& ( vAPP(game,option_game,some_game,X4) = X0 )
& ( vAPP(game,option_game,some_game,X3) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ),
inference(rectify,[],[f1560]) ).
thf(f1560,plain,
! [X2: option_game,X0: option_game,X1: option_game > option_game > $o] :
( ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1307]) ).
thf(f1307,plain,
! [X2: option_game,X0: option_game,X1: option_game > option_game > $o] :
( ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5047,plain,
spl291_279,
inference(avatar_split_clause,[],[f2093,f5045]) ).
thf(f5045,plain,
( spl291_279
<=> ! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK186,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_279])]) ).
thf(f2093,plain,
! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,vAPP(option_game,sTfun(option_game,game),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,game)),sK186,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1563]) ).
thf(f5043,plain,
( spl291_278
| ~ spl291_2
| ~ spl291_272 ),
inference(avatar_split_clause,[],[f5014,f4955,f2910,f5041]) ).
thf(f5041,plain,
( spl291_278
<=> ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,theta),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_278])]) ).
thf(f4955,plain,
( spl291_272
<=> ! [X0: produc1418842292n_game,X3: trm,X2: trm,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_272])]) ).
thf(f5014,plain,
( ! [X0: trm] : ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,theta),X0)) )
| ~ spl291_2
| ~ spl291_272 ),
inference(trivial_inequality_removal,[],[f5010]) ).
thf(f5010,plain,
( ! [X0: trm] :
( ( none_trm != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,theta),X0)) ) )
| ~ spl291_2
| ~ spl291_272 ),
inference(superposition,[],[f4956,f2912]) ).
thf(f4956,plain,
( ! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) )
| ~ spl291_272 ),
inference(avatar_component_clause,[],[f4955]) ).
thf(f4988,plain,
spl291_277,
inference(avatar_split_clause,[],[f2279,f4986]) ).
thf(f2279,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) ),
inference(cnf_transformation,[],[f1215]) ).
thf(f1215,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f2,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) != none_fml )
=> ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_usubstappf__geq__conv) ).
thf(f4984,plain,
spl291_276,
inference(avatar_split_clause,[],[f2278,f4982]) ).
thf(f2278,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,X0),X1),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) = none_fml ) ),
inference(cnf_transformation,[],[f1215]) ).
thf(f4980,plain,
spl291_275,
inference(avatar_split_clause,[],[f2276,f4978]) ).
thf(f2276,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) ),
inference(cnf_transformation,[],[f1213]) ).
thf(f1213,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) )
=> ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_usubstappt__times__conv) ).
thf(f4976,plain,
spl291_274,
inference(avatar_split_clause,[],[f2275,f4974]) ).
thf(f2275,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ) ),
inference(cnf_transformation,[],[f1213]) ).
thf(f4961,plain,
spl291_273,
inference(avatar_split_clause,[],[f2274,f4959]) ).
thf(f2274,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) ),
inference(cnf_transformation,[],[f1212]) ).
thf(f1212,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X2: trm,X3: trm] :
( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) )
=> ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X3) )
& ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_usubstappt__plus__conv) ).
thf(f4957,plain,
spl291_272,
inference(avatar_split_clause,[],[f2273,f4955]) ).
thf(f2273,plain,
! [X2: trm,X3: trm,X0: produc1418842292n_game,X1: set_variable] :
( ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),X2) != none_trm )
| ( none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ) ),
inference(cnf_transformation,[],[f1212]) ).
thf(f4953,plain,
spl291_271,
inference(avatar_split_clause,[],[f1944,f4951]) ).
thf(f4951,plain,
( spl291_271
<=> ! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_271])]) ).
thf(f1944,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)) ) ),
inference(cnf_transformation,[],[f1454]) ).
thf(f1454,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f1033,f1453]) ).
thf(f1453,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ? [X2: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1033,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ? [X2: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f568]) ).
thf(f568,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ! [X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(fool_elimination,[],[f567]) ).
thf(f567,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ! [X2: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ),
inference(rectify,[],[f204]) ).
thf(f204,axiom,
! [X86: option_trm > option_trm > $o,X23: option_trm] :
( ! [X41: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X41),X23)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X41) )
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_accp_Ointros) ).
thf(f4949,plain,
spl291_270,
inference(avatar_split_clause,[],[f1942,f4947]) ).
thf(f4947,plain,
( spl291_270
<=> ! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_270])]) ).
thf(f1942,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)) ) ),
inference(cnf_transformation,[],[f1452]) ).
thf(f1452,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f1032,f1451]) ).
thf(f1451,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ? [X2: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1032,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ? [X2: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f566]) ).
thf(f566,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ! [X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(fool_elimination,[],[f565]) ).
thf(f565,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ! [X2: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X86: option_fml > option_fml > $o,X23: option_fml] :
( ! [X41: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X41),X23)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X41) )
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_accp_Ointros) ).
thf(f4945,plain,
spl291_269,
inference(avatar_split_clause,[],[f1940,f4943]) ).
thf(f4943,plain,
( spl291_269
<=> ! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_269])]) ).
thf(f1940,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)) ) ),
inference(cnf_transformation,[],[f1450]) ).
thf(f1450,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f1031,f1449]) ).
thf(f1449,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ? [X2: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1031,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ? [X2: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f564]) ).
thf(f564,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ! [X2: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(fool_elimination,[],[f563]) ).
thf(f563,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ! [X2: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X86: produc1072747943on_trm > produc1072747943on_trm > $o,X23: produc1072747943on_trm] :
( ! [X41: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X41),X23)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X41) )
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_accp_Ointros) ).
thf(f4941,plain,
spl291_268,
inference(avatar_split_clause,[],[f1938,f4939]) ).
thf(f4939,plain,
( spl291_268
<=> ! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_268])]) ).
thf(f1938,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)) ) ),
inference(cnf_transformation,[],[f1448]) ).
thf(f1448,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f1030,f1447]) ).
thf(f1447,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ? [X2: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1030,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ? [X2: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f562]) ).
thf(f562,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ! [X2: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(fool_elimination,[],[f561]) ).
thf(f561,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ! [X2: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X86: produc464795408on_trm > produc464795408on_trm > $o,X23: produc464795408on_trm] :
( ! [X41: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X41),X23)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X41) )
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_accp_Ointros) ).
thf(f4937,plain,
spl291_267,
inference(avatar_split_clause,[],[f1936,f4935]) ).
thf(f4935,plain,
( spl291_267
<=> ! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_267])]) ).
thf(f1936,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)) ) ),
inference(cnf_transformation,[],[f1446]) ).
thf(f1446,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f1029,f1445]) ).
thf(f1445,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ? [X2: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1029,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ? [X2: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f560]) ).
thf(f560,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ! [X2: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(fool_elimination,[],[f559]) ).
thf(f559,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ! [X2: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X86: produc1024976764on_trm > produc1024976764on_trm > $o,X23: produc1024976764on_trm] :
( ! [X41: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X41),X23)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X41) )
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_accp_Ointros) ).
thf(f4933,plain,
spl291_266,
inference(avatar_split_clause,[],[f1924,f4931]) ).
thf(f4931,plain,
( spl291_266
<=> ! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_266])]) ).
thf(f1924,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1432]) ).
thf(f1432,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)),X1) ) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125])],[f1022,f1431]) ).
thf(f1431,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ? [X2: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1022,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ? [X2: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) ) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ~ ! [X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) ) ),
inference(flattening,[],[f550]) ).
thf(f550,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ~ ! [X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f549]) ).
thf(f549,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1)
=> ~ ! [X2: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
! [X49: option_trm > option_trm > $o,X23: option_trm] :
( ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X49),X23)
=> ~ ! [X80: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X49,X80),X23)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X49),X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_not__accp__down) ).
thf(f4929,plain,
spl291_265,
inference(avatar_split_clause,[],[f1922,f4927]) ).
thf(f4927,plain,
( spl291_265
<=> ! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_265])]) ).
thf(f1922,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1430]) ).
thf(f1430,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)),X1) ) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124])],[f1021,f1429]) ).
thf(f1429,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ? [X2: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1021,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ? [X2: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) ) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(ennf_transformation,[],[f929]) ).
thf(f929,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ~ ! [X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) ) ),
inference(flattening,[],[f548]) ).
thf(f548,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ~ ! [X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) ) ),
inference(fool_elimination,[],[f547]) ).
thf(f547,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1)
=> ~ ! [X2: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) ),
inference(rectify,[],[f225]) ).
thf(f225,axiom,
! [X49: option_fml > option_fml > $o,X23: option_fml] :
( ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X49),X23)
=> ~ ! [X80: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X49,X80),X23)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X49),X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__accp__down) ).
thf(f4925,plain,
spl291_264,
inference(avatar_split_clause,[],[f1920,f4923]) ).
thf(f4923,plain,
( spl291_264
<=> ! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_264])]) ).
thf(f1920,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1428]) ).
thf(f1428,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)),X1) ) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK123])],[f1020,f1427]) ).
thf(f1427,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ? [X2: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1020,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ? [X2: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) ) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f928]) ).
thf(f928,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ~ ! [X2: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) ) ),
inference(flattening,[],[f546]) ).
thf(f546,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ~ ! [X2: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f545]) ).
thf(f545,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ~ vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1)
=> ~ ! [X2: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) ),
inference(rectify,[],[f222]) ).
thf(f222,axiom,
! [X49: produc1072747943on_trm > produc1072747943on_trm > $o,X23: produc1072747943on_trm] :
( ~ vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X49),X23)
=> ~ ! [X80: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X49,X80),X23)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X49),X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_not__accp__down) ).
thf(f4920,plain,
spl291_263,
inference(avatar_split_clause,[],[f1918,f4918]) ).
thf(f4918,plain,
( spl291_263
<=> ! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_263])]) ).
thf(f1918,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1426]) ).
thf(f1426,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)),X1) ) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122])],[f1019,f1425]) ).
thf(f1425,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ? [X2: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1019,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ? [X2: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) ) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f927]) ).
thf(f927,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ~ ! [X2: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) ) ),
inference(flattening,[],[f544]) ).
thf(f544,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ~ ! [X2: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f543]) ).
thf(f543,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1)
=> ~ ! [X2: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) ),
inference(rectify,[],[f223]) ).
thf(f223,axiom,
! [X49: produc464795408on_trm > produc464795408on_trm > $o,X23: produc464795408on_trm] :
( ~ vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X49),X23)
=> ~ ! [X80: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X49,X80),X23)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X49),X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_not__accp__down) ).
thf(f4916,plain,
spl291_262,
inference(avatar_split_clause,[],[f1916,f4914]) ).
thf(f4914,plain,
( spl291_262
<=> ! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_262])]) ).
thf(f1916,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1424]) ).
thf(f1424,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)),X1) ) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121])],[f1018,f1423]) ).
thf(f1423,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ? [X2: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1018,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ? [X2: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) ) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f926]) ).
thf(f926,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ~ ! [X2: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) ) ),
inference(flattening,[],[f542]) ).
thf(f542,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ~ ! [X2: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f541]) ).
thf(f541,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1)
=> ~ ! [X2: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) ),
inference(rectify,[],[f221]) ).
thf(f221,axiom,
! [X49: produc1024976764on_trm > produc1024976764on_trm > $o,X23: produc1024976764on_trm] :
( ~ vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X49),X23)
=> ~ ! [X80: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X49,X80),X23)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X49),X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_not__accp__down) ).
thf(f4751,plain,
( spl291_260
| spl291_261 ),
inference(avatar_split_clause,[],[f2372,f4748,f4745]) ).
thf(f4745,plain,
( spl291_260
<=> ! [X0: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_260])]) ).
thf(f4748,plain,
( spl291_261
<=> ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_261])]) ).
thf(f2372,plain,
! [X0: option_trm] :
( ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ),
inference(equality_resolution,[],[f1905]) ).
thf(f1905,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1281]) ).
thf(f1281,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true )
& ( none_trm = X1 )
& ( none_trm = X0 ) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(definition_folding,[],[f1011,f1280]) ).
thf(f1280,plain,
! [X1: option_trm,X0: option_trm] :
( ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1011,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true )
& ( none_trm = X1 )
& ( none_trm = X0 ) )
| ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(flattening,[],[f1010]) ).
thf(f1010,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) = $true )
& ( none_trm = X1 )
& ( none_trm = X0 ) )
| ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(ennf_transformation,[],[f925]) ).
thf(f925,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = X1 )
=> ( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
=> ( ! [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,X2) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
=> ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) ) ) )
=> ~ ( ( none_trm = X0 )
=> ( ( none_trm = X1 )
=> ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) != $true ) ) ) ) ) ),
inference(flattening,[],[f534]) ).
thf(f534,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = X1 )
=> ( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
=> ( ! [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,X2) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
=> ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) ) ) )
=> ~ ( ( none_trm = X0 )
=> ( ( none_trm = X1 )
=> ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) != $true ) ) ) ) ) ),
inference(fool_elimination,[],[f533]) ).
thf(f533,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = X1 )
=> ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0)
=> ( ! [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,X2) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
=> ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) ) )
=> ~ ( ( none_trm = X0 )
=> ( ( none_trm = X1 )
=> ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) ) ) ) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X23: option_trm,X36: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X23) = X36 )
=> ( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X23)
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X23 )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X54)) = X36 )
=> ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X54)) ) )
=> ~ ( ( none_trm = X23 )
=> ( ( none_trm = X36 )
=> ~ vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),none_trm) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Differentialo_Opelims) ).
thf(f4737,plain,
( spl291_258
| spl291_259 ),
inference(avatar_split_clause,[],[f2364,f4734,f4731]) ).
thf(f4731,plain,
( spl291_258
<=> ! [X0: option_fml] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_258])]) ).
thf(f4734,plain,
( spl291_259
<=> ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_259])]) ).
thf(f2364,plain,
! [X0: option_fml] :
( ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ),
inference(equality_resolution,[],[f1894]) ).
thf(f1894,plain,
! [X0: option_fml,X1: option_game] :
( ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1279]) ).
thf(f1279,plain,
! [X0: option_fml,X1: option_game] :
( ( ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true )
& ( none_game = X1 )
& ( none_fml = X0 ) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(definition_folding,[],[f1006,f1278]) ).
thf(f1278,plain,
! [X1: option_game,X0: option_fml] :
( ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1006,plain,
! [X0: option_fml,X1: option_game] :
( ( ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true )
& ( none_game = X1 )
& ( none_fml = X0 ) )
| ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(flattening,[],[f1005]) ).
thf(f1005,plain,
! [X0: option_fml,X1: option_game] :
( ( ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) = $true )
& ( none_game = X1 )
& ( none_fml = X0 ) )
| ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(ennf_transformation,[],[f922]) ).
thf(f922,plain,
! [X0: option_fml,X1: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = X1 )
=> ( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
=> ( ! [X2: fml] :
( ( vAPP(fml,option_fml,some_fml,X2) = X0 )
=> ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
=> ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) ) ) )
=> ~ ( ( none_fml = X0 )
=> ( ( none_game = X1 )
=> ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) != $true ) ) ) ) ) ),
inference(flattening,[],[f532]) ).
thf(f532,plain,
! [X0: option_fml,X1: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = X1 )
=> ( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
=> ( ! [X2: fml] :
( ( vAPP(fml,option_fml,some_fml,X2) = X0 )
=> ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
=> ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) ) ) )
=> ~ ( ( none_fml = X0 )
=> ( ( none_game = X1 )
=> ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) != $true ) ) ) ) ) ),
inference(fool_elimination,[],[f531]) ).
thf(f531,plain,
! [X0: option_fml,X1: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = X1 )
=> ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0)
=> ( ! [X2: fml] :
( ( vAPP(fml,option_fml,some_fml,X2) = X0 )
=> ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
=> ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) ) )
=> ~ ( ( none_fml = X0 )
=> ( ( none_game = X1 )
=> ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) ) ) ) ) ),
inference(rectify,[],[f338]) ).
thf(f338,axiom,
! [X23: option_fml,X36: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X23) = X36 )
=> ( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X23)
=> ( ! [X74: fml] :
( ( vAPP(fml,option_fml,some_fml,X74) = X23 )
=> ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X74)) = X36 )
=> ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X74)) ) )
=> ~ ( ( none_fml = X23 )
=> ( ( none_game = X36 )
=> ~ vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),none_fml) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_Testo_Opelims) ).
thf(f4729,plain,
spl291_257,
inference(avatar_split_clause,[],[f2237,f4727]) ).
thf(f4727,plain,
( spl291_257
<=> ! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_257])]) ).
thf(f2237,plain,
! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK262,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1685]) ).
thf(f4725,plain,
spl291_256,
inference(avatar_split_clause,[],[f2234,f4723]) ).
thf(f4723,plain,
( spl291_256
<=> ! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_256])]) ).
thf(f2234,plain,
! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK261,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1683]) ).
thf(f4721,plain,
spl291_255,
inference(avatar_split_clause,[],[f2231,f4719]) ).
thf(f4719,plain,
( spl291_255
<=> ! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_255])]) ).
thf(f2231,plain,
! [X2: option_trm > $o,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1681]) ).
thf(f1681,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) ) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) ) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK260])],[f1679,f1680]) ).
thf(f1680,plain,
! [X0: option_trm > option_trm > $o,X2: option_trm > $o] :
( ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3) ) ) )
=> ( ( $true != vAPP(option_trm,$o,X2,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) ) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(sTfun(option_trm,$o),sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK260,X2),X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1679,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3) ) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(rectify,[],[f1186]) ).
thf(f1186,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3) ) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(flattening,[],[f1185]) ).
thf(f1185,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X2,X1) )
| ? [X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X2,X3) )
& ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,X2,X5) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3) ) )
& ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X4) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f748]) ).
thf(f748,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ( ! [X3: option_trm] :
( ! [X4: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X4) ) )
=> ( ! [X5: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3) )
=> ( $true = vAPP(option_trm,$o,X2,X5) ) )
=> ( $true = vAPP(option_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f747]) ).
thf(f747,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm,X2: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1)
=> ( ! [X3: option_trm] :
( ! [X4: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X4),X3)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X4) )
=> ( ! [X5: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X5),X3)
=> vAPP(option_trm,$o,X2,X5) )
=> vAPP(option_trm,$o,X2,X3) ) )
=> vAPP(option_trm,$o,X2,X1) ) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X86: option_trm > option_trm > $o,X23: option_trm,X26: option_trm > $o] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X23)
=> ( ! [X22: option_trm] :
( ! [X72: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X72),X22)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X72) )
=> ( ! [X72: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X72),X22)
=> vAPP(option_trm,$o,X26,X72) )
=> vAPP(option_trm,$o,X26,X22) ) )
=> vAPP(option_trm,$o,X26,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_accp_Oinducts) ).
thf(f4717,plain,
spl291_254,
inference(avatar_split_clause,[],[f2227,f4715]) ).
thf(f4715,plain,
( spl291_254
<=> ! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_254])]) ).
thf(f2227,plain,
! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK259,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1678]) ).
thf(f4713,plain,
spl291_253,
inference(avatar_split_clause,[],[f2224,f4711]) ).
thf(f4711,plain,
( spl291_253
<=> ! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_253])]) ).
thf(f2224,plain,
! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK258,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1676]) ).
thf(f4709,plain,
spl291_252,
inference(avatar_split_clause,[],[f2221,f4707]) ).
thf(f4707,plain,
( spl291_252
<=> ! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_252])]) ).
thf(f2221,plain,
! [X2: option_fml > $o,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1674]) ).
thf(f1674,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) ) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) ) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK257])],[f1672,f1673]) ).
thf(f1673,plain,
! [X0: option_fml > option_fml > $o,X2: option_fml > $o] :
( ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3) ) ) )
=> ( ( $true != vAPP(option_fml,$o,X2,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) ) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(sTfun(option_fml,$o),sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK257,X2),X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1672,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3) ) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(rectify,[],[f1178]) ).
thf(f1178,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3) ) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(flattening,[],[f1177]) ).
thf(f1177,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X2,X1) )
| ? [X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X2,X3) )
& ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,X2,X5) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3) ) )
& ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X4) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(ennf_transformation,[],[f740]) ).
thf(f740,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ( ! [X3: option_fml] :
( ! [X4: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X4) ) )
=> ( ! [X5: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3) )
=> ( $true = vAPP(option_fml,$o,X2,X5) ) )
=> ( $true = vAPP(option_fml,$o,X2,X3) ) ) )
=> ( $true = vAPP(option_fml,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f739]) ).
thf(f739,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml,X2: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1)
=> ( ! [X3: option_fml] :
( ! [X4: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X4),X3)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X4) )
=> ( ! [X5: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X5),X3)
=> vAPP(option_fml,$o,X2,X5) )
=> vAPP(option_fml,$o,X2,X3) ) )
=> vAPP(option_fml,$o,X2,X1) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X86: option_fml > option_fml > $o,X23: option_fml,X26: option_fml > $o] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X23)
=> ( ! [X22: option_fml] :
( ! [X72: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X72),X22)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X72) )
=> ( ! [X72: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X72),X22)
=> vAPP(option_fml,$o,X26,X72) )
=> vAPP(option_fml,$o,X26,X22) ) )
=> vAPP(option_fml,$o,X26,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_accp_Oinducts) ).
thf(f4705,plain,
spl291_251,
inference(avatar_split_clause,[],[f2217,f4703]) ).
thf(f4703,plain,
( spl291_251
<=> ! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_251])]) ).
thf(f2217,plain,
! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK256,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1671]) ).
thf(f4701,plain,
spl291_250,
inference(avatar_split_clause,[],[f2214,f4699]) ).
thf(f4699,plain,
( spl291_250
<=> ! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_250])]) ).
thf(f2214,plain,
! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK255,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1669]) ).
thf(f4696,plain,
spl291_249,
inference(avatar_split_clause,[],[f2211,f4694]) ).
thf(f4694,plain,
( spl291_249
<=> ! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_249])]) ).
thf(f2211,plain,
! [X2: produc1072747943on_trm > $o,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1667]) ).
thf(f1667,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) ) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) ) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK254])],[f1665,f1666]) ).
thf(f1666,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm > $o] :
( ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3) ) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,X2,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) ) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,$o),sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK254,X2),X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1665,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3) ) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(rectify,[],[f1170]) ).
thf(f1170,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(flattening,[],[f1169]) ).
thf(f1169,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) )
| ? [X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X2,X3) )
& ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,X2,X5) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X4) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f732]) ).
thf(f732,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ( ! [X3: produc1072747943on_trm] :
( ! [X4: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X4) ) )
=> ( ! [X5: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X5) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1072747943on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f731]) ).
thf(f731,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm,X2: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1)
=> ( ! [X3: produc1072747943on_trm] :
( ! [X4: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X4),X3)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X4) )
=> ( ! [X5: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X5),X3)
=> vAPP(produc1072747943on_trm,$o,X2,X5) )
=> vAPP(produc1072747943on_trm,$o,X2,X3) ) )
=> vAPP(produc1072747943on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X86: produc1072747943on_trm > produc1072747943on_trm > $o,X23: produc1072747943on_trm,X26: produc1072747943on_trm > $o] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X23)
=> ( ! [X22: produc1072747943on_trm] :
( ! [X72: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X72),X22)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X72) )
=> ( ! [X72: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X72),X22)
=> vAPP(produc1072747943on_trm,$o,X26,X72) )
=> vAPP(produc1072747943on_trm,$o,X26,X22) ) )
=> vAPP(produc1072747943on_trm,$o,X26,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_accp_Oinducts) ).
thf(f4692,plain,
spl291_248,
inference(avatar_split_clause,[],[f2207,f4690]) ).
thf(f4690,plain,
( spl291_248
<=> ! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_248])]) ).
thf(f2207,plain,
! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK253,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1664]) ).
thf(f4688,plain,
spl291_247,
inference(avatar_split_clause,[],[f2204,f4686]) ).
thf(f4686,plain,
( spl291_247
<=> ! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_247])]) ).
thf(f2204,plain,
! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK252,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1662]) ).
thf(f4684,plain,
spl291_246,
inference(avatar_split_clause,[],[f2201,f4682]) ).
thf(f4682,plain,
( spl291_246
<=> ! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_246])]) ).
thf(f2201,plain,
! [X2: produc464795408on_trm > $o,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1660]) ).
thf(f1660,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) ) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) ) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK251])],[f1658,f1659]) ).
thf(f1659,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm > $o] :
( ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3) ) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,X2,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) ) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,$o),sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK251,X2),X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1658,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3) ) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(rectify,[],[f1162]) ).
thf(f1162,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(flattening,[],[f1161]) ).
thf(f1161,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X1) )
| ? [X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X2,X3) )
& ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,X2,X5) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X4) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f724]) ).
thf(f724,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ( ! [X3: produc464795408on_trm] :
( ! [X4: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X4) ) )
=> ( ! [X5: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X5) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc464795408on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f723]) ).
thf(f723,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm,X2: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1)
=> ( ! [X3: produc464795408on_trm] :
( ! [X4: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X4),X3)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X4) )
=> ( ! [X5: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X5),X3)
=> vAPP(produc464795408on_trm,$o,X2,X5) )
=> vAPP(produc464795408on_trm,$o,X2,X3) ) )
=> vAPP(produc464795408on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X86: produc464795408on_trm > produc464795408on_trm > $o,X23: produc464795408on_trm,X26: produc464795408on_trm > $o] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X23)
=> ( ! [X22: produc464795408on_trm] :
( ! [X72: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X72),X22)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X72) )
=> ( ! [X72: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X72),X22)
=> vAPP(produc464795408on_trm,$o,X26,X72) )
=> vAPP(produc464795408on_trm,$o,X26,X22) ) )
=> vAPP(produc464795408on_trm,$o,X26,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_accp_Oinducts) ).
thf(f4680,plain,
spl291_245,
inference(avatar_split_clause,[],[f2197,f4678]) ).
thf(f4678,plain,
( spl291_245
<=> ! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_245])]) ).
thf(f2197,plain,
! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK250,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1657]) ).
thf(f4676,plain,
spl291_244,
inference(avatar_split_clause,[],[f2194,f4674]) ).
thf(f4674,plain,
( spl291_244
<=> ! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_244])]) ).
thf(f2194,plain,
! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK249,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1655]) ).
thf(f4672,plain,
spl291_243,
inference(avatar_split_clause,[],[f2191,f4670]) ).
thf(f4670,plain,
( spl291_243
<=> ! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_243])]) ).
thf(f2191,plain,
! [X2: produc1024976764on_trm > $o,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1653]) ).
thf(f1653,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) ) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) ) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK248])],[f1651,f1652]) ).
thf(f1652,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm > $o] :
( ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3) ) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,X2,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) ) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,$o),sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK248,X2),X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1651,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3) ) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(rectify,[],[f1154]) ).
thf(f1154,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(flattening,[],[f1153]) ).
thf(f1153,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) )
| ? [X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X2,X3) )
& ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,X2,X5) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3) ) )
& ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X4) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) ) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f716]) ).
thf(f716,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ( ! [X3: produc1024976764on_trm] :
( ! [X4: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X4) ) )
=> ( ! [X5: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X5) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X3) ) ) )
=> ( $true = vAPP(produc1024976764on_trm,$o,X2,X1) ) ) ),
inference(fool_elimination,[],[f715]) ).
thf(f715,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm,X2: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1)
=> ( ! [X3: produc1024976764on_trm] :
( ! [X4: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X4),X3)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X4) )
=> ( ! [X5: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X5),X3)
=> vAPP(produc1024976764on_trm,$o,X2,X5) )
=> vAPP(produc1024976764on_trm,$o,X2,X3) ) )
=> vAPP(produc1024976764on_trm,$o,X2,X1) ) ),
inference(rectify,[],[f211]) ).
thf(f211,axiom,
! [X86: produc1024976764on_trm > produc1024976764on_trm > $o,X23: produc1024976764on_trm,X26: produc1024976764on_trm > $o] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X23)
=> ( ! [X22: produc1024976764on_trm] :
( ! [X72: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X72),X22)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X72) )
=> ( ! [X72: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X72),X22)
=> vAPP(produc1024976764on_trm,$o,X26,X72) )
=> vAPP(produc1024976764on_trm,$o,X26,X22) ) )
=> vAPP(produc1024976764on_trm,$o,X26,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_accp_Oinducts) ).
thf(f4643,plain,
spl291_242,
inference(avatar_split_clause,[],[f2250,f4641]) ).
thf(f4641,plain,
( spl291_242
<=> ! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_242])]) ).
thf(f2250,plain,
! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1691]) ).
thf(f1691,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( ( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 ) )
| ( ( $true = X0 )
& ( none_trm = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK265])],[f1198,f1690]) ).
thf(f1690,plain,
! [X1: trm > $o,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(trm,$o,X1,X3) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1198,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(trm,$o,X1,X3) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_trm = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(flattening,[],[f1197]) ).
thf(f1197,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(trm,$o,X1,X3) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_trm = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(ennf_transformation,[],[f962]) ).
thf(f962,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) )
=> ( ( ( none_trm = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ( $true != vAPP(trm,$o,X1,X3) ) ) ) ),
inference(flattening,[],[f760]) ).
thf(f760,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) )
=> ( ( ( none_trm = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ( $true != vAPP(trm,$o,X1,X3) ) ) ) ),
inference(fool_elimination,[],[f759]) ).
thf(f759,plain,
! [X0: $o,X1: trm > $o,X2: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2)
=> ( ( ( none_trm = X2 )
=> ~ X0 )
=> ~ ! [X3: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ~ vAPP(trm,$o,X1,X3) ) ) ),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
! [X26: $o,X38: trm > $o,X23: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X26),X38),X23)
=> ( ( ( none_trm = X23 )
=> ~ X26 )
=> ~ ! [X41: trm] :
( ( vAPP(trm,option_trm,some_trm,X41) = X23 )
=> ~ vAPP(trm,$o,X38,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_case__optionE) ).
thf(f4638,plain,
spl291_241,
inference(avatar_split_clause,[],[f2249,f4636]) ).
thf(f4636,plain,
( spl291_241
<=> ! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
| ( none_trm = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_241])]) ).
thf(f2249,plain,
! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( $true = vAPP(trm,$o,X1,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) )
| ( none_trm = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1691]) ).
thf(f4634,plain,
spl291_240,
inference(avatar_split_clause,[],[f2248,f4632]) ).
thf(f4632,plain,
( spl291_240
<=> ! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_240])]) ).
thf(f2248,plain,
! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1691]) ).
thf(f4630,plain,
spl291_239,
inference(avatar_split_clause,[],[f2247,f4628]) ).
thf(f4628,plain,
( spl291_239
<=> ! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 )
| ( none_trm = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_239])]) ).
thf(f2247,plain,
! [X2: option_trm,X0: $o,X1: trm > $o] :
( ( vAPP(trm,option_trm,some_trm,vAPP(sTfun(trm,$o),trm,vAPP(option_trm,sTfun(sTfun(trm,$o),trm),sK265,X2),X1)) = X2 )
| ( none_trm = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(trm,$o),sTfun(option_trm,$o),vAPP($o,sTfun(sTfun(trm,$o),sTfun(option_trm,$o)),case_option_o_trm,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1691]) ).
thf(f4626,plain,
spl291_238,
inference(avatar_split_clause,[],[f2246,f4624]) ).
thf(f4624,plain,
( spl291_238
<=> ! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_238])]) ).
thf(f2246,plain,
! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1689]) ).
thf(f1689,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( ( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
& ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 ) )
| ( ( $true = X0 )
& ( none_fml = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK264])],[f1196,f1688]) ).
thf(f1688,plain,
! [X1: fml > $o,X2: option_fml] :
( ? [X3: fml] :
( ( $true = vAPP(fml,$o,X1,X3) )
& ( vAPP(fml,option_fml,some_fml,X3) = X2 ) )
=> ( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
& ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1196,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( ? [X3: fml] :
( ( $true = vAPP(fml,$o,X1,X3) )
& ( vAPP(fml,option_fml,some_fml,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_fml = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(flattening,[],[f1195]) ).
thf(f1195,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( ? [X3: fml] :
( ( $true = vAPP(fml,$o,X1,X3) )
& ( vAPP(fml,option_fml,some_fml,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_fml = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(ennf_transformation,[],[f961]) ).
thf(f961,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) )
=> ( ( ( none_fml = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: fml] :
( ( vAPP(fml,option_fml,some_fml,X3) = X2 )
=> ( $true != vAPP(fml,$o,X1,X3) ) ) ) ),
inference(flattening,[],[f758]) ).
thf(f758,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) )
=> ( ( ( none_fml = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: fml] :
( ( vAPP(fml,option_fml,some_fml,X3) = X2 )
=> ( $true != vAPP(fml,$o,X1,X3) ) ) ) ),
inference(fool_elimination,[],[f757]) ).
thf(f757,plain,
! [X0: $o,X1: fml > $o,X2: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2)
=> ( ( ( none_fml = X2 )
=> ~ X0 )
=> ~ ! [X3: fml] :
( ( vAPP(fml,option_fml,some_fml,X3) = X2 )
=> ~ vAPP(fml,$o,X1,X3) ) ) ),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
! [X26: $o,X38: fml > $o,X23: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X26),X38),X23)
=> ( ( ( none_fml = X23 )
=> ~ X26 )
=> ~ ! [X41: fml] :
( ( vAPP(fml,option_fml,some_fml,X41) = X23 )
=> ~ vAPP(fml,$o,X38,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_case__optionE) ).
thf(f4622,plain,
spl291_237,
inference(avatar_split_clause,[],[f2245,f4620]) ).
thf(f4620,plain,
( spl291_237
<=> ! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
| ( none_fml = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_237])]) ).
thf(f2245,plain,
! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( $true = vAPP(fml,$o,X1,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) )
| ( none_fml = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1689]) ).
thf(f4618,plain,
spl291_236,
inference(avatar_split_clause,[],[f2244,f4616]) ).
thf(f4616,plain,
( spl291_236
<=> ! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_236])]) ).
thf(f2244,plain,
! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1689]) ).
thf(f4614,plain,
spl291_235,
inference(avatar_split_clause,[],[f2243,f4612]) ).
thf(f4612,plain,
( spl291_235
<=> ! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 )
| ( none_fml = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_235])]) ).
thf(f2243,plain,
! [X2: option_fml,X0: $o,X1: fml > $o] :
( ( vAPP(fml,option_fml,some_fml,vAPP(sTfun(fml,$o),fml,vAPP(option_fml,sTfun(sTfun(fml,$o),fml),sK264,X2),X1)) = X2 )
| ( none_fml = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(fml,$o),sTfun(option_fml,$o),vAPP($o,sTfun(sTfun(fml,$o),sTfun(option_fml,$o)),case_option_o_fml,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1689]) ).
thf(f4610,plain,
spl291_234,
inference(avatar_split_clause,[],[f2242,f4608]) ).
thf(f4608,plain,
( spl291_234
<=> ! [X2: option_game,X0: $o,X1: game > $o] :
( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_234])]) ).
thf(f2242,plain,
! [X2: option_game,X0: $o,X1: game > $o] :
( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
| ( $true = X0 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1687]) ).
thf(f1687,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( ( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
& ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 ) )
| ( ( $true = X0 )
& ( none_game = X2 ) )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK263])],[f1194,f1686]) ).
thf(f1686,plain,
! [X1: game > $o,X2: option_game] :
( ? [X3: game] :
( ( $true = vAPP(game,$o,X1,X3) )
& ( vAPP(game,option_game,some_game,X3) = X2 ) )
=> ( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
& ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1194,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( ? [X3: game] :
( ( $true = vAPP(game,$o,X1,X3) )
& ( vAPP(game,option_game,some_game,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_game = X2 ) )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(flattening,[],[f1193]) ).
thf(f1193,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( ? [X3: game] :
( ( $true = vAPP(game,$o,X1,X3) )
& ( vAPP(game,option_game,some_game,X3) = X2 ) )
| ( ( $true = X0 )
& ( none_game = X2 ) )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(ennf_transformation,[],[f960]) ).
thf(f960,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) )
=> ( ( ( none_game = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: game] :
( ( vAPP(game,option_game,some_game,X3) = X2 )
=> ( $true != vAPP(game,$o,X1,X3) ) ) ) ),
inference(flattening,[],[f756]) ).
thf(f756,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) )
=> ( ( ( none_game = X2 )
=> ( $true != X0 ) )
=> ~ ! [X3: game] :
( ( vAPP(game,option_game,some_game,X3) = X2 )
=> ( $true != vAPP(game,$o,X1,X3) ) ) ) ),
inference(fool_elimination,[],[f755]) ).
thf(f755,plain,
! [X0: $o,X1: game > $o,X2: option_game] :
( vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2)
=> ( ( ( none_game = X2 )
=> ~ X0 )
=> ~ ! [X3: game] :
( ( vAPP(game,option_game,some_game,X3) = X2 )
=> ~ vAPP(game,$o,X1,X3) ) ) ),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
! [X26: $o,X38: game > $o,X23: option_game] :
( vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X26),X38),X23)
=> ( ( ( none_game = X23 )
=> ~ X26 )
=> ~ ! [X41: game] :
( ( vAPP(game,option_game,some_game,X41) = X23 )
=> ~ vAPP(game,$o,X38,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_case__optionE) ).
thf(f4606,plain,
spl291_233,
inference(avatar_split_clause,[],[f2241,f4604]) ).
thf(f4604,plain,
( spl291_233
<=> ! [X2: option_game,X0: $o,X1: game > $o] :
( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
| ( none_game = X2 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_233])]) ).
thf(f2241,plain,
! [X2: option_game,X0: $o,X1: game > $o] :
( ( $true = vAPP(game,$o,X1,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) )
| ( none_game = X2 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1687]) ).
thf(f4602,plain,
spl291_232,
inference(avatar_split_clause,[],[f2240,f4600]) ).
thf(f4600,plain,
( spl291_232
<=> ! [X2: option_game,X0: $o,X1: game > $o] :
( ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_232])]) ).
thf(f2240,plain,
! [X2: option_game,X0: $o,X1: game > $o] :
( ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 )
| ( $true = X0 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1687]) ).
thf(f4597,plain,
spl291_231,
inference(avatar_split_clause,[],[f2239,f4595]) ).
thf(f4595,plain,
( spl291_231
<=> ! [X2: option_game,X0: $o,X1: game > $o] :
( ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 )
| ( none_game = X2 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_231])]) ).
thf(f2239,plain,
! [X2: option_game,X0: $o,X1: game > $o] :
( ( vAPP(game,option_game,some_game,vAPP(sTfun(game,$o),game,vAPP(option_game,sTfun(sTfun(game,$o),game),sK263,X2),X1)) = X2 )
| ( none_game = X2 )
| ( $true != vAPP(option_game,$o,vAPP(sTfun(game,$o),sTfun(option_game,$o),vAPP($o,sTfun(sTfun(game,$o),sTfun(option_game,$o)),case_option_o_game,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1687]) ).
thf(f4382,plain,
spl291_230,
inference(avatar_split_clause,[],[f2390,f4380]) ).
thf(f4380,plain,
( spl291_230
<=> ! [X0: char,X1: option_trm] :
( ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_230])]) ).
thf(f2390,plain,
! [X0: char,X1: option_trm] :
( ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0)) = X1 ) ),
inference(equality_resolution,[],[f2027]) ).
thf(f2027,plain,
! [X2: option_game,X0: char,X1: option_trm] :
( ( none_game = X2 )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0)) = X1 )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f4378,plain,
spl291_229,
inference(avatar_split_clause,[],[f2383,f4376]) ).
thf(f4376,plain,
( spl291_229
<=> ! [X0: variable,X1: option_trm] :
( ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_229])]) ).
thf(f2383,plain,
! [X0: variable,X1: option_trm] :
( ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0)) = X1 ) ),
inference(equality_resolution,[],[f2017]) ).
thf(f2017,plain,
! [X2: option_game,X0: variable,X1: option_trm] :
( ( none_game = X2 )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0)) = X1 )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1495]) ).
thf(f4374,plain,
spl291_228,
inference(avatar_split_clause,[],[f1943,f4372]) ).
thf(f4372,plain,
( spl291_228
<=> ! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_228])]) ).
thf(f1943,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK136,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1454]) ).
thf(f4369,plain,
spl291_227,
inference(avatar_split_clause,[],[f1941,f4367]) ).
thf(f4367,plain,
( spl291_227
<=> ! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_227])]) ).
thf(f1941,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK135,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1452]) ).
thf(f4365,plain,
spl291_226,
inference(avatar_split_clause,[],[f1939,f4363]) ).
thf(f4363,plain,
( spl291_226
<=> ! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_226])]) ).
thf(f1939,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK134,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1450]) ).
thf(f4361,plain,
spl291_225,
inference(avatar_split_clause,[],[f1937,f4359]) ).
thf(f4359,plain,
( spl291_225
<=> ! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_225])]) ).
thf(f1937,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK133,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1448]) ).
thf(f4357,plain,
spl291_224,
inference(avatar_split_clause,[],[f1935,f4355]) ).
thf(f4355,plain,
( spl291_224
<=> ! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_224])]) ).
thf(f1935,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK132,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1446]) ).
thf(f4353,plain,
spl291_223,
inference(avatar_split_clause,[],[f1930,f4351]) ).
thf(f4351,plain,
( spl291_223
<=> ! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ( $true != vAPP(char,$o,X1,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_223])]) ).
thf(f1930,plain,
! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ( $true != vAPP(char,$o,X1,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ),
inference(cnf_transformation,[],[f1440]) ).
thf(f1440,plain,
! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ( ( $true != vAPP(char,$o,X1,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) )
& ( $true = vAPP(char,$o,X0,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129])],[f1026,f1439]) ).
thf(f1439,plain,
! [X0: char > $o,X1: char > $o] :
( ? [X2: char] :
( ( $true != vAPP(char,$o,X1,X2) )
& ( $true = vAPP(char,$o,X0,X2) ) )
=> ( ( $true != vAPP(char,$o,X1,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) )
& ( $true = vAPP(char,$o,X0,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1026,plain,
! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ? [X2: char] :
( ( $true != vAPP(char,$o,X1,X2) )
& ( $true = vAPP(char,$o,X0,X2) ) ) ),
inference(ennf_transformation,[],[f554]) ).
thf(f554,plain,
! [X0: char > $o,X1: char > $o] :
( ! [X2: char] :
( ( $true = vAPP(char,$o,X0,X2) )
=> ( $true = vAPP(char,$o,X1,X2) ) )
=> ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) ) ),
inference(fool_elimination,[],[f553]) ).
thf(f553,plain,
! [X0: char > $o,X1: char > $o] :
( ! [X2: char] :
( vAPP(char,$o,X0,X2)
=> vAPP(char,$o,X1,X2) )
=> vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X26: char > $o,X38: char > $o] :
( ! [X22: char] :
( vAPP(char,$o,X26,X22)
=> vAPP(char,$o,X38,X22) )
=> vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X26)),vAPP(sTfun(char,$o),set_char,collect_char,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Collect__mono) ).
thf(f4349,plain,
spl291_222,
inference(avatar_split_clause,[],[f1929,f4347]) ).
thf(f4347,plain,
( spl291_222
<=> ! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ( $true = vAPP(char,$o,X0,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_222])]) ).
thf(f1929,plain,
! [X0: char > $o,X1: char > $o] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,vAPP(sTfun(char,$o),set_char,collect_char,X0)),vAPP(sTfun(char,$o),set_char,collect_char,X1)) )
| ( $true = vAPP(char,$o,X0,vAPP(sTfun(char,$o),char,vAPP(sTfun(char,$o),sTfun(sTfun(char,$o),char),sK129,X1),X0)) ) ),
inference(cnf_transformation,[],[f1440]) ).
thf(f4345,plain,
spl291_221,
inference(avatar_split_clause,[],[f1928,f4343]) ).
thf(f4343,plain,
( spl291_221
<=> ! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ( $true != vAPP(variable,$o,X1,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_221])]) ).
thf(f1928,plain,
! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ( $true != vAPP(variable,$o,X1,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ),
inference(cnf_transformation,[],[f1438]) ).
thf(f1438,plain,
! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ( ( $true != vAPP(variable,$o,X1,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) )
& ( $true = vAPP(variable,$o,X0,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128])],[f1025,f1437]) ).
thf(f1437,plain,
! [X0: variable > $o,X1: variable > $o] :
( ? [X2: variable] :
( ( $true != vAPP(variable,$o,X1,X2) )
& ( $true = vAPP(variable,$o,X0,X2) ) )
=> ( ( $true != vAPP(variable,$o,X1,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) )
& ( $true = vAPP(variable,$o,X0,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1025,plain,
! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ? [X2: variable] :
( ( $true != vAPP(variable,$o,X1,X2) )
& ( $true = vAPP(variable,$o,X0,X2) ) ) ),
inference(ennf_transformation,[],[f552]) ).
thf(f552,plain,
! [X0: variable > $o,X1: variable > $o] :
( ! [X2: variable] :
( ( $true = vAPP(variable,$o,X0,X2) )
=> ( $true = vAPP(variable,$o,X1,X2) ) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) ) ),
inference(fool_elimination,[],[f551]) ).
thf(f551,plain,
! [X0: variable > $o,X1: variable > $o] :
( ! [X2: variable] :
( vAPP(variable,$o,X0,X2)
=> vAPP(variable,$o,X1,X2) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
! [X26: variable > $o,X38: variable > $o] :
( ! [X22: variable] :
( vAPP(variable,$o,X26,X22)
=> vAPP(variable,$o,X38,X22) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X26)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Collect__mono) ).
thf(f4341,plain,
spl291_220,
inference(avatar_split_clause,[],[f1927,f4339]) ).
thf(f4339,plain,
( spl291_220
<=> ! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ( $true = vAPP(variable,$o,X0,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_220])]) ).
thf(f1927,plain,
! [X0: variable > $o,X1: variable > $o] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(variable,$o),set_variable,collect_variable,X0)),vAPP(sTfun(variable,$o),set_variable,collect_variable,X1)) )
| ( $true = vAPP(variable,$o,X0,vAPP(sTfun(variable,$o),variable,vAPP(sTfun(variable,$o),sTfun(sTfun(variable,$o),variable),sK128,X1),X0)) ) ),
inference(cnf_transformation,[],[f1438]) ).
thf(f4337,plain,
spl291_219,
inference(avatar_split_clause,[],[f1923,f4335]) ).
thf(f4335,plain,
( spl291_219
<=> ! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)),X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_219])]) ).
thf(f1923,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),option_trm,vAPP(option_trm,sTfun(sTfun(option_trm,sTfun(option_trm,$o)),option_trm),sK125,X1),X0)),X1) )
| ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1432]) ).
thf(f4333,plain,
spl291_218,
inference(avatar_split_clause,[],[f1921,f4331]) ).
thf(f4331,plain,
( spl291_218
<=> ! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)),X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_218])]) ).
thf(f1921,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),option_fml,vAPP(option_fml,sTfun(sTfun(option_fml,sTfun(option_fml,$o)),option_fml),sK124,X1),X0)),X1) )
| ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1430]) ).
thf(f4329,plain,
( spl291_217
| ~ spl291_11
| ~ spl291_36 ),
inference(avatar_split_clause,[],[f3094,f3077,f2977,f4327]) ).
thf(f4327,plain,
( spl291_217
<=> ! [X0: option_trm] :
( ( vAPP(option_trm,trm,the_trm,X0) = vAPP(option_trm,trm,sK50,X0) )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_217])]) ).
thf(f2977,plain,
( spl291_11
<=> ! [X0: trm] : ( vAPP(option_trm,trm,the_trm,vAPP(trm,option_trm,some_trm,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_11])]) ).
thf(f3077,plain,
( spl291_36
<=> ! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK50,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_36])]) ).
thf(f3094,plain,
( ! [X0: option_trm] :
( ( vAPP(option_trm,trm,the_trm,X0) = vAPP(option_trm,trm,sK50,X0) )
| ( none_trm = X0 ) )
| ~ spl291_11
| ~ spl291_36 ),
inference(superposition,[],[f2978,f3078]) ).
thf(f3078,plain,
( ! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK50,X0)) = X0 )
| ( none_trm = X0 ) )
| ~ spl291_36 ),
inference(avatar_component_clause,[],[f3077]) ).
thf(f2978,plain,
( ! [X0: trm] : ( vAPP(option_trm,trm,the_trm,vAPP(trm,option_trm,some_trm,X0)) = X0 )
| ~ spl291_11 ),
inference(avatar_component_clause,[],[f2977]) ).
thf(f4325,plain,
spl291_216,
inference(avatar_split_clause,[],[f1919,f4323]) ).
thf(f4323,plain,
( spl291_216
<=> ! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)),X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_216])]) ).
thf(f1919,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm,vAPP(produc1072747943on_trm,sTfun(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),produc1072747943on_trm),sK123,X1),X0)),X1) )
| ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1428]) ).
thf(f4321,plain,
spl291_215,
inference(avatar_split_clause,[],[f1917,f4319]) ).
thf(f4319,plain,
( spl291_215
<=> ! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)),X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_215])]) ).
thf(f1917,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm,vAPP(produc464795408on_trm,sTfun(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),produc464795408on_trm),sK122,X1),X0)),X1) )
| ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1426]) ).
thf(f4317,plain,
spl291_214,
inference(avatar_split_clause,[],[f1915,f4315]) ).
thf(f4315,plain,
( spl291_214
<=> ! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)),X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_214])]) ).
thf(f1915,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm,vAPP(produc1024976764on_trm,sTfun(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),produc1024976764on_trm),sK121,X1),X0)),X1) )
| ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1424]) ).
thf(f4303,plain,
spl291_213,
inference(avatar_split_clause,[],[f1982,f4301]) ).
thf(f4301,plain,
( spl291_213
<=> ! [X2: option_trm,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_213])]) ).
thf(f1982,plain,
! [X2: option_trm,X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1068]) ).
thf(f1068,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ! [X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) ) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f614]) ).
thf(f614,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1) )
=> ! [X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f613]) ).
thf(f613,plain,
! [X0: option_trm > option_trm > $o,X1: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X1)
=> ! [X2: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X0,X2),X1)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X0),X2) ) ),
inference(rectify,[],[f194]) ).
thf(f194,axiom,
! [X86: option_trm > option_trm > $o,X30: option_trm] :
( vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X30)
=> ! [X72: option_trm] :
( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X86,X72),X30)
=> vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,X86),X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_accp_Ocases) ).
thf(f4299,plain,
spl291_212,
inference(avatar_split_clause,[],[f1981,f4297]) ).
thf(f4297,plain,
( spl291_212
<=> ! [X2: option_fml,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_212])]) ).
thf(f1981,plain,
! [X2: option_fml,X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(cnf_transformation,[],[f1067]) ).
thf(f1067,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ! [X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) ) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) ) ),
inference(ennf_transformation,[],[f612]) ).
thf(f612,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1) )
=> ! [X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1) )
=> ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) ) ),
inference(fool_elimination,[],[f611]) ).
thf(f611,plain,
! [X0: option_fml > option_fml > $o,X1: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X1)
=> ! [X2: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X0,X2),X1)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X0),X2) ) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X86: option_fml > option_fml > $o,X30: option_fml] :
( vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X30)
=> ! [X72: option_fml] :
( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X86,X72),X30)
=> vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,X86),X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_accp_Ocases) ).
thf(f4295,plain,
( spl291_211
| ~ spl291_10
| ~ spl291_35 ),
inference(avatar_split_clause,[],[f3091,f3073,f2973,f4293]) ).
thf(f4293,plain,
( spl291_211
<=> ! [X0: option_fml] :
( ( vAPP(option_fml,fml,the_fml,X0) = vAPP(option_fml,fml,sK39,X0) )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_211])]) ).
thf(f2973,plain,
( spl291_10
<=> ! [X0: fml] : ( vAPP(option_fml,fml,the_fml,vAPP(fml,option_fml,some_fml,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_10])]) ).
thf(f3073,plain,
( spl291_35
<=> ! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK39,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_35])]) ).
thf(f3091,plain,
( ! [X0: option_fml] :
( ( vAPP(option_fml,fml,the_fml,X0) = vAPP(option_fml,fml,sK39,X0) )
| ( none_fml = X0 ) )
| ~ spl291_10
| ~ spl291_35 ),
inference(superposition,[],[f2974,f3074]) ).
thf(f3074,plain,
( ! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK39,X0)) = X0 )
| ( none_fml = X0 ) )
| ~ spl291_35 ),
inference(avatar_component_clause,[],[f3073]) ).
thf(f2974,plain,
( ! [X0: fml] : ( vAPP(option_fml,fml,the_fml,vAPP(fml,option_fml,some_fml,X0)) = X0 )
| ~ spl291_10 ),
inference(avatar_component_clause,[],[f2973]) ).
thf(f4291,plain,
spl291_210,
inference(avatar_split_clause,[],[f1980,f4289]) ).
thf(f4289,plain,
( spl291_210
<=> ! [X2: produc1072747943on_trm,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_210])]) ).
thf(f1980,plain,
! [X2: produc1072747943on_trm,X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1066]) ).
thf(f1066,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ! [X2: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) ) )
| ( $true != vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f610]) ).
thf(f610,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1) )
=> ! [X2: produc1072747943on_trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f609]) ).
thf(f609,plain,
! [X0: produc1072747943on_trm > produc1072747943on_trm > $o,X1: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X1)
=> ! [X2: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X0,X2),X1)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X0),X2) ) ),
inference(rectify,[],[f192]) ).
thf(f192,axiom,
! [X86: produc1072747943on_trm > produc1072747943on_trm > $o,X30: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X30)
=> ! [X72: produc1072747943on_trm] :
( vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X86,X72),X30)
=> vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,X86),X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_accp_Ocases) ).
thf(f4287,plain,
spl291_209,
inference(avatar_split_clause,[],[f1979,f4285]) ).
thf(f4285,plain,
( spl291_209
<=> ! [X2: produc464795408on_trm,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_209])]) ).
thf(f1979,plain,
! [X2: produc464795408on_trm,X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1065]) ).
thf(f1065,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ! [X2: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) ) )
| ( $true != vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f608]) ).
thf(f608,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1) )
=> ! [X2: produc464795408on_trm] :
( ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f607]) ).
thf(f607,plain,
! [X0: produc464795408on_trm > produc464795408on_trm > $o,X1: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X1)
=> ! [X2: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X0,X2),X1)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X0),X2) ) ),
inference(rectify,[],[f193]) ).
thf(f193,axiom,
! [X86: produc464795408on_trm > produc464795408on_trm > $o,X30: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X30)
=> ! [X72: produc464795408on_trm] :
( vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X86,X72),X30)
=> vAPP(produc464795408on_trm,$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(produc464795408on_trm,$o),accp_P419951815on_trm,X86),X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_accp_Ocases) ).
thf(f4283,plain,
spl291_208,
inference(avatar_split_clause,[],[f1978,f4281]) ).
thf(f4281,plain,
( spl291_208
<=> ! [X2: produc1024976764on_trm,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_208])]) ).
thf(f1978,plain,
! [X2: produc1024976764on_trm,X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(cnf_transformation,[],[f1064]) ).
thf(f1064,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ! [X2: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) ) )
| ( $true != vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) ) ),
inference(ennf_transformation,[],[f606]) ).
thf(f606,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1) )
=> ! [X2: produc1024976764on_trm] :
( ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1) )
=> ( $true = vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) ) ),
inference(fool_elimination,[],[f605]) ).
thf(f605,plain,
! [X0: produc1024976764on_trm > produc1024976764on_trm > $o,X1: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X1)
=> ! [X2: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X0,X2),X1)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X0),X2) ) ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X86: produc1024976764on_trm > produc1024976764on_trm > $o,X30: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X30)
=> ! [X72: produc1024976764on_trm] :
( vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X86,X72),X30)
=> vAPP(produc1024976764on_trm,$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(produc1024976764on_trm,$o),accp_P394694195on_trm,X86),X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_accp_Ocases) ).
thf(f4237,plain,
( spl291_207
| ~ spl291_9
| ~ spl291_33 ),
inference(avatar_split_clause,[],[f3089,f3065,f2969,f4235]) ).
thf(f4235,plain,
( spl291_207
<=> ! [X0: option_game] :
( ( vAPP(option_game,game,the_game,X0) = vAPP(option_game,game,sK38,X0) )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_207])]) ).
thf(f2969,plain,
( spl291_9
<=> ! [X0: game] : ( vAPP(option_game,game,the_game,vAPP(game,option_game,some_game,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_9])]) ).
thf(f3065,plain,
( spl291_33
<=> ! [X0: option_game] :
( ( none_game = X0 )
| ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK38,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_33])]) ).
thf(f3089,plain,
( ! [X0: option_game] :
( ( vAPP(option_game,game,the_game,X0) = vAPP(option_game,game,sK38,X0) )
| ( none_game = X0 ) )
| ~ spl291_9
| ~ spl291_33 ),
inference(superposition,[],[f2970,f3066]) ).
thf(f3066,plain,
( ! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK38,X0)) = X0 )
| ( none_game = X0 ) )
| ~ spl291_33 ),
inference(avatar_component_clause,[],[f3065]) ).
thf(f2970,plain,
( ! [X0: game] : ( vAPP(option_game,game,the_game,vAPP(game,option_game,some_game,X0)) = X0 )
| ~ spl291_9 ),
inference(avatar_component_clause,[],[f2969]) ).
thf(f4209,plain,
( spl291_206
| ~ spl291_11
| ~ spl291_32 ),
inference(avatar_split_clause,[],[f3087,f3061,f2977,f4207]) ).
thf(f4207,plain,
( spl291_206
<=> ! [X0: option_trm] :
( ( vAPP(option_trm,trm,the_trm,X0) = vAPP(option_trm,trm,sK37,X0) )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_206])]) ).
thf(f3061,plain,
( spl291_32
<=> ! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK37,X0)) = X0 )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_32])]) ).
thf(f3087,plain,
( ! [X0: option_trm] :
( ( vAPP(option_trm,trm,the_trm,X0) = vAPP(option_trm,trm,sK37,X0) )
| ( none_trm = X0 ) )
| ~ spl291_11
| ~ spl291_32 ),
inference(superposition,[],[f2978,f3062]) ).
thf(f3062,plain,
( ! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK37,X0)) = X0 )
| ( none_trm = X0 ) )
| ~ spl291_32 ),
inference(avatar_component_clause,[],[f3061]) ).
thf(f4185,plain,
( spl291_205
| ~ spl291_10
| ~ spl291_30 ),
inference(avatar_split_clause,[],[f3084,f3053,f2973,f4183]) ).
thf(f4183,plain,
( spl291_205
<=> ! [X0: option_fml] :
( ( vAPP(option_fml,fml,the_fml,X0) = vAPP(option_fml,fml,sK36,X0) )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_205])]) ).
thf(f3053,plain,
( spl291_30
<=> ! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK36,X0)) = X0 )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_30])]) ).
thf(f3084,plain,
( ! [X0: option_fml] :
( ( vAPP(option_fml,fml,the_fml,X0) = vAPP(option_fml,fml,sK36,X0) )
| ( none_fml = X0 ) )
| ~ spl291_10
| ~ spl291_30 ),
inference(superposition,[],[f2974,f3054]) ).
thf(f3054,plain,
( ! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK36,X0)) = X0 )
| ( none_fml = X0 ) )
| ~ spl291_30 ),
inference(avatar_component_clause,[],[f3053]) ).
thf(f4181,plain,
spl291_204,
inference(avatar_split_clause,[],[f2328,f4179]) ).
thf(f4179,plain,
( spl291_204
<=> ! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ( $true != vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_204])]) ).
thf(f2328,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ( $true != vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
inference(cnf_transformation,[],[f1735]) ).
thf(f1735,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ( ( $true != vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)),vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) )
& ( $true = vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) ) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK288,sK289])],[f1733,f1734]) ).
thf(f1734,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ? [X2: option_trm,X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X0,X3) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X3),X2) )
& ( $true = vAPP(option_trm,$o,X0,X2) ) )
=> ( ( $true != vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK289,X1),X0)),vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) )
& ( $true = vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1733,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ? [X2: option_trm,X3: option_trm] :
( ( $true != vAPP(option_trm,$o,X0,X3) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X3),X2) )
& ( $true = vAPP(option_trm,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
inference(rectify,[],[f1732]) ).
thf(f1732,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ? [X4: option_trm,X5: option_trm] :
( ( $true != vAPP(option_trm,$o,X0,X5) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X5),X4) )
& ( $true = vAPP(option_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
inference(nnf_transformation,[],[f1338]) ).
thf(f1338,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ? [X4: option_trm,X5: option_trm] :
( ( $true != vAPP(option_trm,$o,X0,X5) )
& ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X5),X4) )
& ( $true = vAPP(option_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4177,plain,
spl291_203,
inference(avatar_split_clause,[],[f2326,f4175]) ).
thf(f4175,plain,
( spl291_203
<=> ! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_203])]) ).
thf(f2326,plain,
! [X0: option_trm > $o,X1: option_trm > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,X0,vAPP(sTfun(option_trm,$o),option_trm,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),option_trm),sK288,X1),X0)) )
| ( $true != vAPP(sTfun(option_trm,$o),$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(sTfun(option_trm,$o),$o),sP34,X1),X0) ) ),
inference(cnf_transformation,[],[f1735]) ).
thf(f4173,plain,
spl291_202,
inference(avatar_split_clause,[],[f2322,f4171]) ).
thf(f4171,plain,
( spl291_202
<=> ! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ( $true != vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_202])]) ).
thf(f2322,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ( $true != vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
inference(cnf_transformation,[],[f1728]) ).
thf(f1728,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ( ( $true != vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)),vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) )
& ( $true = vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) ) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK285,sK286])],[f1726,f1727]) ).
thf(f1727,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ? [X2: option_fml,X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X0,X3) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X3),X2) )
& ( $true = vAPP(option_fml,$o,X0,X2) ) )
=> ( ( $true != vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK286,X1),X0)),vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) )
& ( $true = vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1726,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ? [X2: option_fml,X3: option_fml] :
( ( $true != vAPP(option_fml,$o,X0,X3) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X3),X2) )
& ( $true = vAPP(option_fml,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
inference(rectify,[],[f1725]) ).
thf(f1725,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ? [X4: option_fml,X5: option_fml] :
( ( $true != vAPP(option_fml,$o,X0,X5) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X5),X4) )
& ( $true = vAPP(option_fml,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
inference(nnf_transformation,[],[f1336]) ).
thf(f1336,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ? [X4: option_fml,X5: option_fml] :
( ( $true != vAPP(option_fml,$o,X0,X5) )
& ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X5),X4) )
& ( $true = vAPP(option_fml,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4169,plain,
spl291_201,
inference(avatar_split_clause,[],[f2320,f4167]) ).
thf(f4167,plain,
( spl291_201
<=> ! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_201])]) ).
thf(f2320,plain,
! [X0: option_fml > $o,X1: option_fml > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,X0,vAPP(sTfun(option_fml,$o),option_fml,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),option_fml),sK285,X1),X0)) )
| ( $true != vAPP(sTfun(option_fml,$o),$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(sTfun(option_fml,$o),$o),sP33,X1),X0) ) ),
inference(cnf_transformation,[],[f1728]) ).
thf(f4165,plain,
spl291_200,
inference(avatar_split_clause,[],[f2316,f4163]) ).
thf(f4163,plain,
( spl291_200
<=> ! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_200])]) ).
thf(f2316,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
inference(cnf_transformation,[],[f1721]) ).
thf(f1721,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( ( $true != vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)),vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) ) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK282,sK283])],[f1719,f1720]) ).
thf(f1720,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ? [X2: produc1072747943on_trm,X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,X3) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,X2) ) )
=> ( ( $true != vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK283,X1),X0)),vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1719,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ? [X2: produc1072747943on_trm,X3: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,X3) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
inference(rectify,[],[f1718]) ).
thf(f1718,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ? [X4: produc1072747943on_trm,X5: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,X5) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
inference(nnf_transformation,[],[f1334]) ).
thf(f1334,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ? [X4: produc1072747943on_trm,X5: produc1072747943on_trm] :
( ( $true != vAPP(produc1072747943on_trm,$o,X0,X5) )
& ( $true = vAPP(produc1072747943on_trm,$o,vAPP(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc1072747943on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4161,plain,
spl291_199,
inference(avatar_split_clause,[],[f2314,f4159]) ).
thf(f4159,plain,
( spl291_199
<=> ! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_199])]) ).
thf(f2314,plain,
! [X0: produc1072747943on_trm > $o,X1: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( $true = vAPP(produc1072747943on_trm,$o,X0,vAPP(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),produc1072747943on_trm),sK282,X1),X0)) )
| ( $true != vAPP(sTfun(produc1072747943on_trm,$o),$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(sTfun(produc1072747943on_trm,$o),$o),sP32,X1),X0) ) ),
inference(cnf_transformation,[],[f1721]) ).
thf(f4157,plain,
spl291_198,
inference(avatar_split_clause,[],[f2310,f4155]) ).
thf(f4155,plain,
( spl291_198
<=> ! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_198])]) ).
thf(f2310,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
inference(cnf_transformation,[],[f1714]) ).
thf(f1714,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ( ( $true != vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)),vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) ) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK279,sK280])],[f1712,f1713]) ).
thf(f1713,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ? [X2: produc464795408on_trm,X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,X3) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,X2) ) )
=> ( ( $true != vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK280,X1),X0)),vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1712,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ? [X2: produc464795408on_trm,X3: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,X3) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
inference(rectify,[],[f1711]) ).
thf(f1711,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ? [X4: produc464795408on_trm,X5: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,X5) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
inference(nnf_transformation,[],[f1332]) ).
thf(f1332,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ? [X4: produc464795408on_trm,X5: produc464795408on_trm] :
( ( $true != vAPP(produc464795408on_trm,$o,X0,X5) )
& ( $true = vAPP(produc464795408on_trm,$o,vAPP(produc464795408on_trm,sTfun(produc464795408on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc464795408on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4153,plain,
spl291_197,
inference(avatar_split_clause,[],[f2308,f4151]) ).
thf(f4151,plain,
( spl291_197
<=> ! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_197])]) ).
thf(f2308,plain,
! [X0: produc464795408on_trm > $o,X1: produc464795408on_trm > produc464795408on_trm > $o] :
( ( $true = vAPP(produc464795408on_trm,$o,X0,vAPP(sTfun(produc464795408on_trm,$o),produc464795408on_trm,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),produc464795408on_trm),sK279,X1),X0)) )
| ( $true != vAPP(sTfun(produc464795408on_trm,$o),$o,vAPP(sTfun(produc464795408on_trm,sTfun(produc464795408on_trm,$o)),sTfun(sTfun(produc464795408on_trm,$o),$o),sP31,X1),X0) ) ),
inference(cnf_transformation,[],[f1714]) ).
thf(f4149,plain,
spl291_196,
inference(avatar_split_clause,[],[f2304,f4147]) ).
thf(f4147,plain,
( spl291_196
<=> ! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_196])]) ).
thf(f2304,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
inference(cnf_transformation,[],[f1707]) ).
thf(f1707,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( ( $true != vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)),vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) ) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK276,sK277])],[f1705,f1706]) ).
thf(f1706,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ? [X2: produc1024976764on_trm,X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,X3) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,X2) ) )
=> ( ( $true != vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK277,X1),X0)),vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1705,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ? [X2: produc1024976764on_trm,X3: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,X3) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,X3),X2) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
inference(rectify,[],[f1704]) ).
thf(f1704,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ? [X4: produc1024976764on_trm,X5: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,X5) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
inference(nnf_transformation,[],[f1330]) ).
thf(f1330,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ? [X4: produc1024976764on_trm,X5: produc1024976764on_trm] :
( ( $true != vAPP(produc1024976764on_trm,$o,X0,X5) )
& ( $true = vAPP(produc1024976764on_trm,$o,vAPP(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o),X1,X5),X4) )
& ( $true = vAPP(produc1024976764on_trm,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4145,plain,
( spl291_195
| ~ spl291_9
| ~ spl291_28 ),
inference(avatar_split_clause,[],[f3081,f3045,f2969,f4143]) ).
thf(f4143,plain,
( spl291_195
<=> ! [X0: option_game] :
( ( vAPP(option_game,game,the_game,X0) = vAPP(option_game,game,sK35,X0) )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_195])]) ).
thf(f3045,plain,
( spl291_28
<=> ! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK35,X0)) = X0 )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_28])]) ).
thf(f3081,plain,
( ! [X0: option_game] :
( ( vAPP(option_game,game,the_game,X0) = vAPP(option_game,game,sK35,X0) )
| ( none_game = X0 ) )
| ~ spl291_9
| ~ spl291_28 ),
inference(superposition,[],[f2970,f3046]) ).
thf(f3046,plain,
( ! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK35,X0)) = X0 )
| ( none_game = X0 ) )
| ~ spl291_28 ),
inference(avatar_component_clause,[],[f3045]) ).
thf(f4141,plain,
spl291_194,
inference(avatar_split_clause,[],[f2302,f4139]) ).
thf(f4139,plain,
( spl291_194
<=> ! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_194])]) ).
thf(f2302,plain,
! [X0: produc1024976764on_trm > $o,X1: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( $true = vAPP(produc1024976764on_trm,$o,X0,vAPP(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),produc1024976764on_trm),sK276,X1),X0)) )
| ( $true != vAPP(sTfun(produc1024976764on_trm,$o),$o,vAPP(sTfun(produc1024976764on_trm,sTfun(produc1024976764on_trm,$o)),sTfun(sTfun(produc1024976764on_trm,$o),$o),sP30,X1),X0) ) ),
inference(cnf_transformation,[],[f1707]) ).
thf(f4137,plain,
spl291_193,
inference(avatar_split_clause,[],[f2086,f4135]) ).
thf(f4135,plain,
( spl291_193
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_193])]) ).
thf(f2086,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1559]) ).
thf(f1559,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK184,sK185])],[f1556,f1558,f1557]) ).
thf(f1557,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1558,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK185,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1556,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ),
inference(rectify,[],[f1555]) ).
thf(f1555,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1304]) ).
thf(f1304,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4133,plain,
spl291_192,
inference(avatar_split_clause,[],[f2085,f4131]) ).
thf(f4131,plain,
( spl291_192
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_192])]) ).
thf(f2085,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK184,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP16,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1559]) ).
thf(f4129,plain,
spl291_191,
inference(avatar_split_clause,[],[f2081,f4127]) ).
thf(f4127,plain,
( spl291_191
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_191])]) ).
thf(f2081,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1554]) ).
thf(f1554,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0))),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f1552,f1553]) ).
thf(f1553,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0))),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK183,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1552,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ),
inference(rectify,[],[f1551]) ).
thf(f1551,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_trm = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1305]) ).
thf(f1305,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst924844285so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_trm = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4125,plain,
spl291_190,
inference(avatar_split_clause,[],[f2075,f4123]) ).
thf(f4123,plain,
( spl291_190
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_190])]) ).
thf(f2075,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1550]) ).
thf(f1550,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181,sK182])],[f1547,f1549,f1548]) ).
thf(f1548,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1549,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK182,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1547,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ),
inference(rectify,[],[f1546]) ).
thf(f1546,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1301]) ).
thf(f1301,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4121,plain,
spl291_189,
inference(avatar_split_clause,[],[f2074,f4119]) ).
thf(f4119,plain,
( spl291_189
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_189])]) ).
thf(f2074,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK181,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1550]) ).
thf(f4117,plain,
spl291_188,
inference(avatar_split_clause,[],[f2070,f4115]) ).
thf(f4115,plain,
( spl291_188
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_188])]) ).
thf(f2070,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1545]) ).
thf(f1545,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0))),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f1543,f1544]) ).
thf(f1544,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0))),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK180,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1543,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ),
inference(rectify,[],[f1542]) ).
thf(f1542,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_trm = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1302]) ).
thf(f1302,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst691094423so_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_trm = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4113,plain,
spl291_187,
inference(avatar_split_clause,[],[f2066,f4111]) ).
thf(f4111,plain,
( spl291_187
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_187])]) ).
thf(f2066,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1541]) ).
thf(f1541,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178,sK179])],[f1538,f1540,f1539]) ).
thf(f1539,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1540,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK179,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1538,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ),
inference(rectify,[],[f1537]) ).
thf(f1537,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1298]) ).
thf(f1298,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4109,plain,
spl291_186,
inference(avatar_split_clause,[],[f2065,f4107]) ).
thf(f4107,plain,
( spl291_186
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_186])]) ).
thf(f2065,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK178,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1541]) ).
thf(f4105,plain,
spl291_185,
inference(avatar_split_clause,[],[f2058,f4103]) ).
thf(f4103,plain,
( spl291_185
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_185])]) ).
thf(f2058,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1532]) ).
thf(f1532,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176])],[f1529,f1531,f1530]) ).
thf(f1530,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1531,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)),vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK176,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1529,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ),
inference(rectify,[],[f1528]) ).
thf(f1528,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1295]) ).
thf(f1295,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4101,plain,
spl291_184,
inference(avatar_split_clause,[],[f2791,f4099]) ).
thf(f4099,plain,
( spl291_184
<=> ! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) = vAPP(real,trm,number,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_184])]) ).
thf(f2791,plain,
! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) = vAPP(real,trm,number,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2790]) ).
thf(f2790,plain,
! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) = vAPP(real,trm,number,X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2786]) ).
thf(f2786,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(real,trm,number,X0)),vAPP(real,trm,number,X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1851]) ).
thf(f1851,plain,
! [X0: real,X1: real] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(real,trm,number,X0)),vAPP(real,trm,number,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ),
inference(cnf_transformation,[],[f470]) ).
thf(f470,plain,
! [X0: real,X1: real] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(real,trm,number,X0)),vAPP(real,trm,number,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ),
inference(fool_elimination,[],[f469]) ).
thf(f469,plain,
! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) = vAPP(real,trm,number,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f282]) ).
thf(f282,axiom,
! [X57: real,X58: real] :
( ( vAPP(real,trm,number,X57) = vAPP(real,trm,number,X58) )
= ( X57 = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_trm_Oinject_I2_J) ).
thf(f4097,plain,
spl291_183,
inference(avatar_split_clause,[],[f2057,f4095]) ).
thf(f4095,plain,
( spl291_183
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_183])]) ).
thf(f2057,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,trm)),sK175,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP10,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1532]) ).
thf(f4093,plain,
spl291_182,
inference(avatar_split_clause,[],[f2048,f4091]) ).
thf(f4091,plain,
( spl291_182
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_182])]) ).
thf(f2048,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1523]) ).
thf(f1523,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)),vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172,sK173])],[f1520,f1522,f1521]) ).
thf(f1521,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1522,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0))),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0))),vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)),vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK173,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1520,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ),
inference(rectify,[],[f1519]) ).
thf(f1519,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1292]) ).
thf(f1292,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),vAPP(trm,option_trm,some_trm,X4))) )
& ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4089,plain,
spl291_181,
inference(avatar_split_clause,[],[f2047,f4087]) ).
thf(f4087,plain,
( spl291_181
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_181])]) ).
thf(f2047,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK172,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1523]) ).
thf(f4085,plain,
spl291_180,
inference(avatar_split_clause,[],[f2043,f4083]) ).
thf(f4083,plain,
( spl291_180
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_180])]) ).
thf(f2043,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1518]) ).
thf(f1518,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0))),none_trm)) )
& ( none_fml = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f1516,f1517]) ).
thf(f1517,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_fml = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0))),none_trm)) )
& ( none_fml = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK171,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1516,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X3)),none_trm)) )
& ( none_fml = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ),
inference(rectify,[],[f1515]) ).
thf(f1515,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_fml = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1293]) ).
thf(f1293,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X5: trm] :
( ( $true = vAPP(produc1072747943on_trm,$o,vAPP(sTfun(produc1072747943on_trm,sTfun(produc1072747943on_trm,$o)),sTfun(produc1072747943on_trm,$o),accp_P758790320on_trm,uSubst1304144938qo_rel),vAPP(option_trm,produc1072747943on_trm,vAPP(option_trm,sTfun(option_trm,produc1072747943on_trm),produc709594775on_trm,vAPP(trm,option_trm,some_trm,X5)),none_trm)) )
& ( none_fml = X2 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4081,plain,
spl291_179,
inference(avatar_split_clause,[],[f2039,f4079]) ).
thf(f4079,plain,
( spl291_179
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_179])]) ).
thf(f2039,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0)) = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1514]) ).
thf(f1514,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)),vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0)) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170])],[f1511,f1513,f1512]) ).
thf(f1512,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
=> ( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1513,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
=> ( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)),vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK170,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1511,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ),
inference(rectify,[],[f1510]) ).
thf(f1510,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1289]) ).
thf(f1289,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ? [X3: trm] :
( ? [X4: trm] :
( ( vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X3),X4)) = X2 )
& ( vAPP(trm,option_trm,some_trm,X4) = X1 ) )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f4077,plain,
spl291_178,
inference(avatar_split_clause,[],[f2038,f4075]) ).
thf(f4075,plain,
( spl291_178
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_178])]) ).
thf(f2038,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_fml,trm,vAPP(option_trm,sTfun(option_fml,trm),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,trm)),sK169,X2),X1),X0)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1514]) ).
thf(f4073,plain,
spl291_177,
inference(avatar_split_clause,[],[f2029,f4071]) ).
thf(f4071,plain,
( spl291_177
<=> ! [X2: option_trm,X0: char,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)) = X2 )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_177])]) ).
thf(f2029,plain,
! [X2: option_trm,X0: char,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_game,sTfun(char,trm),vAPP(option_trm,sTfun(option_game,sTfun(char,trm)),sK167,X2),X1),X0)) = X2 )
| ( $true != vAPP(char,$o,vAPP(option_game,sTfun(char,$o),vAPP(option_trm,sTfun(option_game,sTfun(char,$o)),sP5,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1505]) ).
thf(f4069,plain,
spl291_176,
inference(avatar_split_clause,[],[f2019,f4067]) ).
thf(f4067,plain,
( spl291_176
<=> ! [X2: option_trm,X0: variable,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)) = X2 )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_176])]) ).
thf(f2019,plain,
! [X2: option_trm,X0: variable,X1: option_game] :
( ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_game,sTfun(variable,trm),vAPP(option_trm,sTfun(option_game,sTfun(variable,trm)),sK165,X2),X1),X0)) = X2 )
| ( $true != vAPP(variable,$o,vAPP(option_game,sTfun(variable,$o),vAPP(option_trm,sTfun(option_game,sTfun(variable,$o)),sP4,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1499]) ).
thf(f4065,plain,
spl291_175,
inference(avatar_split_clause,[],[f1766,f4062]) ).
thf(f4062,plain,
( spl291_175
<=> ( denota1419872369iation = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),cCOMB,denota1419872369iation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_175])]) ).
thf(f1766,plain,
denota1419872369iation = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),cCOMB,denota1419872369iation),
inference(cnf_transformation,[],[f400]) ).
thf(f400,plain,
denota1419872369iation = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o))),cCOMB,denota1419872369iation),
inference(fool_elimination,[],[f399]) ).
thf(f399,plain,
( denota1419872369iation
= ( ^ [X0: variable > real,X1: variable > real] : vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X1),X0) ) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
( denota1419872369iation
= ( ^ [X44: variable > real,X45: variable > real] : vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X45),X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Uvariation__sym) ).
thf(f4055,plain,
spl291_174,
inference(avatar_split_clause,[],[f2789,f4053]) ).
thf(f4053,plain,
( spl291_174
<=> ! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) != vAPP(real,trm,number,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_174])]) ).
thf(f2789,plain,
! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) != vAPP(real,trm,number,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2788]) ).
thf(f2788,plain,
! [X0: real,X1: real] :
( ( vAPP(real,trm,number,X0) != vAPP(real,trm,number,X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2787]) ).
thf(f2787,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(real,trm,number,X0)),vAPP(real,trm,number,X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1851]) ).
thf(f4007,plain,
spl291_173,
inference(avatar_split_clause,[],[f2785,f4005]) ).
thf(f4005,plain,
( spl291_173
<=> ! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) = vAPP(game,option_game,some_game,X0) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_173])]) ).
thf(f2785,plain,
! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) = vAPP(game,option_game,some_game,X0) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2784]) ).
thf(f2784,plain,
! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) = vAPP(game,option_game,some_game,X0) )
| ( $false = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2780]) ).
thf(f2780,plain,
! [X0: game,X1: game] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),vAPP(game,option_game,some_game,X1)),vAPP(game,option_game,some_game,X0)) )
| ( $false = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1852]) ).
thf(f1852,plain,
! [X0: game,X1: game] : ( vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),vAPP(game,option_game,some_game,X1)),vAPP(game,option_game,some_game,X0)) = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ),
inference(cnf_transformation,[],[f472]) ).
thf(f472,plain,
! [X0: game,X1: game] : ( vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),vAPP(game,option_game,some_game,X1)),vAPP(game,option_game,some_game,X0)) = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ),
inference(fool_elimination,[],[f471]) ).
thf(f471,plain,
! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) = vAPP(game,option_game,some_game,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X57: game,X58: game] :
( ( vAPP(game,option_game,some_game,X57) = vAPP(game,option_game,some_game,X58) )
= ( X57 = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_option_Oinject) ).
thf(f4003,plain,
spl291_172,
inference(avatar_split_clause,[],[f2152,f4001]) ).
thf(f4001,plain,
( spl291_172
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_172])]) ).
thf(f2152,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_trm = X0 ) ),
inference(cnf_transformation,[],[f1324]) ).
thf(f1324,plain,
! [X0: option_trm,X1: option_trm > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X1),X0),X2) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(definition_folding,[],[f1114,f1323]) ).
thf(f1114,plain,
! [X0: option_trm,X1: option_trm > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(flattening,[],[f1113]) ).
thf(f1113,plain,
! [X0: option_trm,X1: option_trm > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: trm,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(ennf_transformation,[],[f674]) ).
thf(f674,plain,
! [X0: option_trm,X1: option_trm > option_trm > $o,X2: option_trm] :
( ( ( none_trm = X0 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ( ( none_trm = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ! [X3: trm,X4: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f673]) ).
thf(f673,plain,
! [X0: option_trm,X1: option_trm > option_trm > $o,X2: option_trm] :
( ( ( none_trm = X0 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ( ( none_trm = X2 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ! [X3: trm,X4: trm] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X23: option_trm,X26: option_trm > option_trm > $o,X36: option_trm] :
( ( ( none_trm = X23 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ( ( none_trm = X36 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ! [X61: trm,X62: trm] :
( ( vAPP(trm,option_trm,some_trm,X61) = X23 )
=> ( ( vAPP(trm,option_trm,some_trm,X62) = X36 )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X26,X23),X36) ) )
=> vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_combine__options__cases) ).
thf(f3999,plain,
spl291_171,
inference(avatar_split_clause,[],[f2145,f3997]) ).
thf(f3997,plain,
( spl291_171
<=> ! [X2: option_fml,X0: option_trm,X1: option_trm > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_171])]) ).
thf(f2145,plain,
! [X2: option_fml,X0: option_trm,X1: option_trm > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_trm = X0 ) ),
inference(cnf_transformation,[],[f1322]) ).
thf(f1322,plain,
! [X0: option_trm,X1: option_trm > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X1),X0),X2) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(definition_folding,[],[f1112,f1321]) ).
thf(f1112,plain,
! [X0: option_trm,X1: option_trm > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(flattening,[],[f1111]) ).
thf(f1111,plain,
! [X0: option_trm,X1: option_trm > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: trm,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(ennf_transformation,[],[f672]) ).
thf(f672,plain,
! [X0: option_trm,X1: option_trm > option_fml > $o,X2: option_fml] :
( ( ( none_trm = X0 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ( ( none_fml = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ! [X3: trm,X4: fml] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f671]) ).
thf(f671,plain,
! [X0: option_trm,X1: option_trm > option_fml > $o,X2: option_fml] :
( ( ( none_trm = X0 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ( ( none_fml = X2 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ! [X3: trm,X4: fml] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f111]) ).
thf(f111,axiom,
! [X23: option_trm,X26: option_trm > option_fml > $o,X36: option_fml] :
( ( ( none_trm = X23 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ( ( none_fml = X36 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ! [X61: trm,X62: fml] :
( ( vAPP(trm,option_trm,some_trm,X61) = X23 )
=> ( ( vAPP(fml,option_fml,some_fml,X62) = X36 )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X26,X23),X36) ) )
=> vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_combine__options__cases) ).
thf(f3995,plain,
spl291_170,
inference(avatar_split_clause,[],[f2138,f3993]) ).
thf(f3993,plain,
( spl291_170
<=> ! [X2: option_game,X0: option_trm,X1: option_trm > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X1),X0),X2) )
| ( none_game = X2 )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_170])]) ).
thf(f2138,plain,
! [X2: option_game,X0: option_trm,X1: option_trm > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X1),X0),X2) )
| ( none_game = X2 )
| ( none_trm = X0 ) ),
inference(cnf_transformation,[],[f1320]) ).
thf(f1320,plain,
! [X0: option_trm,X1: option_trm > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X1),X0),X2) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(definition_folding,[],[f1110,f1319]) ).
thf(f1110,plain,
! [X0: option_trm,X1: option_trm > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(flattening,[],[f1109]) ).
thf(f1109,plain,
! [X0: option_trm,X1: option_trm > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: trm,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(trm,option_trm,some_trm,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
& ( none_trm = X0 ) ) ),
inference(ennf_transformation,[],[f670]) ).
thf(f670,plain,
! [X0: option_trm,X1: option_trm > option_game > $o,X2: option_game] :
( ( ( none_trm = X0 )
=> ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ( ( none_game = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ! [X3: trm,X4: game] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f669]) ).
thf(f669,plain,
! [X0: option_trm,X1: option_trm > option_game > $o,X2: option_game] :
( ( ( none_trm = X0 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
=> ( ( ( none_game = X2 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) )
=> ( ! [X3: trm,X4: game] :
( ( vAPP(trm,option_trm,some_trm,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X23: option_trm,X26: option_trm > option_game > $o,X36: option_game] :
( ( ( none_trm = X23 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X26,X23),X36) )
=> ( ( ( none_game = X36 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X26,X23),X36) )
=> ( ! [X61: trm,X62: game] :
( ( vAPP(trm,option_trm,some_trm,X61) = X23 )
=> ( ( vAPP(game,option_game,some_game,X62) = X36 )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X26,X23),X36) ) )
=> vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_combine__options__cases) ).
thf(f3991,plain,
spl291_169,
inference(avatar_split_clause,[],[f2131,f3989]) ).
thf(f3989,plain,
( spl291_169
<=> ! [X2: option_trm,X0: option_fml,X1: option_fml > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_169])]) ).
thf(f2131,plain,
! [X2: option_trm,X0: option_fml,X1: option_fml > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_fml = X0 ) ),
inference(cnf_transformation,[],[f1318]) ).
thf(f1318,plain,
! [X0: option_fml,X1: option_fml > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X1),X0),X2) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(definition_folding,[],[f1108,f1317]) ).
thf(f1108,plain,
! [X0: option_fml,X1: option_fml > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(flattening,[],[f1107]) ).
thf(f1107,plain,
! [X0: option_fml,X1: option_fml > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: fml,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(ennf_transformation,[],[f668]) ).
thf(f668,plain,
! [X0: option_fml,X1: option_fml > option_trm > $o,X2: option_trm] :
( ( ( none_fml = X0 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ( ( none_trm = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ! [X3: fml,X4: trm] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f667]) ).
thf(f667,plain,
! [X0: option_fml,X1: option_fml > option_trm > $o,X2: option_trm] :
( ( ( none_fml = X0 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ( ( none_trm = X2 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ! [X3: fml,X4: trm] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X23: option_fml,X26: option_fml > option_trm > $o,X36: option_trm] :
( ( ( none_fml = X23 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ( ( none_trm = X36 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ! [X61: fml,X62: trm] :
( ( vAPP(fml,option_fml,some_fml,X61) = X23 )
=> ( ( vAPP(trm,option_trm,some_trm,X62) = X36 )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X26,X23),X36) ) )
=> vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_combine__options__cases) ).
thf(f3987,plain,
spl291_168,
inference(avatar_split_clause,[],[f2124,f3985]) ).
thf(f3985,plain,
( spl291_168
<=> ! [X2: option_fml,X0: option_fml,X1: option_fml > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_168])]) ).
thf(f2124,plain,
! [X2: option_fml,X0: option_fml,X1: option_fml > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_fml = X0 ) ),
inference(cnf_transformation,[],[f1316]) ).
thf(f1316,plain,
! [X0: option_fml,X1: option_fml > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X1),X0),X2) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(definition_folding,[],[f1106,f1315]) ).
thf(f1106,plain,
! [X0: option_fml,X1: option_fml > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(flattening,[],[f1105]) ).
thf(f1105,plain,
! [X0: option_fml,X1: option_fml > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: fml,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(ennf_transformation,[],[f666]) ).
thf(f666,plain,
! [X0: option_fml,X1: option_fml > option_fml > $o,X2: option_fml] :
( ( ( none_fml = X0 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ( ( none_fml = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ! [X3: fml,X4: fml] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f665]) ).
thf(f665,plain,
! [X0: option_fml,X1: option_fml > option_fml > $o,X2: option_fml] :
( ( ( none_fml = X0 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ( ( none_fml = X2 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ! [X3: fml,X4: fml] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f114]) ).
thf(f114,axiom,
! [X23: option_fml,X26: option_fml > option_fml > $o,X36: option_fml] :
( ( ( none_fml = X23 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ( ( none_fml = X36 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ! [X61: fml,X62: fml] :
( ( vAPP(fml,option_fml,some_fml,X61) = X23 )
=> ( ( vAPP(fml,option_fml,some_fml,X62) = X36 )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X26,X23),X36) ) )
=> vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_combine__options__cases) ).
thf(f3983,plain,
spl291_167,
inference(avatar_split_clause,[],[f2117,f3981]) ).
thf(f3981,plain,
( spl291_167
<=> ! [X2: option_game,X0: option_fml,X1: option_fml > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X1),X0),X2) )
| ( none_game = X2 )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_167])]) ).
thf(f2117,plain,
! [X2: option_game,X0: option_fml,X1: option_fml > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X1),X0),X2) )
| ( none_game = X2 )
| ( none_fml = X0 ) ),
inference(cnf_transformation,[],[f1314]) ).
thf(f1314,plain,
! [X0: option_fml,X1: option_fml > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X1),X0),X2) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(definition_folding,[],[f1104,f1313]) ).
thf(f1104,plain,
! [X0: option_fml,X1: option_fml > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(flattening,[],[f1103]) ).
thf(f1103,plain,
! [X0: option_fml,X1: option_fml > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: fml,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(fml,option_fml,some_fml,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
& ( none_fml = X0 ) ) ),
inference(ennf_transformation,[],[f664]) ).
thf(f664,plain,
! [X0: option_fml,X1: option_fml > option_game > $o,X2: option_game] :
( ( ( none_fml = X0 )
=> ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ( ( none_game = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ! [X3: fml,X4: game] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f663]) ).
thf(f663,plain,
! [X0: option_fml,X1: option_fml > option_game > $o,X2: option_game] :
( ( ( none_fml = X0 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
=> ( ( ( none_game = X2 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) )
=> ( ! [X3: fml,X4: game] :
( ( vAPP(fml,option_fml,some_fml,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f115]) ).
thf(f115,axiom,
! [X23: option_fml,X26: option_fml > option_game > $o,X36: option_game] :
( ( ( none_fml = X23 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X26,X23),X36) )
=> ( ( ( none_game = X36 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X26,X23),X36) )
=> ( ! [X61: fml,X62: game] :
( ( vAPP(fml,option_fml,some_fml,X61) = X23 )
=> ( ( vAPP(game,option_game,some_game,X62) = X36 )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X26,X23),X36) ) )
=> vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_combine__options__cases) ).
thf(f3979,plain,
spl291_166,
inference(avatar_split_clause,[],[f2110,f3977]) ).
thf(f3977,plain,
( spl291_166
<=> ! [X2: option_trm,X0: option_game,X1: option_game > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_166])]) ).
thf(f2110,plain,
! [X2: option_trm,X0: option_game,X1: option_game > option_trm > $o] :
( ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X1),X0),X2) )
| ( none_trm = X2 )
| ( none_game = X0 ) ),
inference(cnf_transformation,[],[f1312]) ).
thf(f1312,plain,
! [X0: option_game,X1: option_game > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
| ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X1),X0),X2) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(definition_folding,[],[f1102,f1311]) ).
thf(f1102,plain,
! [X0: option_game,X1: option_game > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(flattening,[],[f1101]) ).
thf(f1101,plain,
! [X0: option_game,X1: option_game > option_trm > $o,X2: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
| ? [X3: game,X4: trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( vAPP(trm,option_trm,some_trm,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_trm = X2 ) )
| ( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(ennf_transformation,[],[f662]) ).
thf(f662,plain,
! [X0: option_game,X1: option_game > option_trm > $o,X2: option_trm] :
( ( ( none_game = X0 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ( ( none_trm = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) )
=> ( ! [X3: game,X4: trm] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f661]) ).
thf(f661,plain,
! [X0: option_game,X1: option_game > option_trm > $o,X2: option_trm] :
( ( ( none_game = X0 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ( ( none_trm = X2 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) )
=> ( ! [X3: game,X4: trm] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(trm,option_trm,some_trm,X4) = X2 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f116]) ).
thf(f116,axiom,
! [X23: option_game,X26: option_game > option_trm > $o,X36: option_trm] :
( ( ( none_game = X23 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ( ( none_trm = X36 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X26,X23),X36) )
=> ( ! [X61: game,X62: trm] :
( ( vAPP(game,option_game,some_game,X61) = X23 )
=> ( ( vAPP(trm,option_trm,some_trm,X62) = X36 )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X26,X23),X36) ) )
=> vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_combine__options__cases) ).
thf(f3975,plain,
spl291_165,
inference(avatar_split_clause,[],[f2103,f3973]) ).
thf(f3973,plain,
( spl291_165
<=> ! [X2: option_fml,X0: option_game,X1: option_game > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_165])]) ).
thf(f2103,plain,
! [X2: option_fml,X0: option_game,X1: option_game > option_fml > $o] :
( ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X1),X0),X2) )
| ( none_fml = X2 )
| ( none_game = X0 ) ),
inference(cnf_transformation,[],[f1310]) ).
thf(f1310,plain,
! [X0: option_game,X1: option_game > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
| ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X1),X0),X2) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(definition_folding,[],[f1100,f1309]) ).
thf(f1100,plain,
! [X0: option_game,X1: option_game > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(flattening,[],[f1099]) ).
thf(f1099,plain,
! [X0: option_game,X1: option_game > option_fml > $o,X2: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
| ? [X3: game,X4: fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( vAPP(fml,option_fml,some_fml,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_fml = X2 ) )
| ( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(ennf_transformation,[],[f660]) ).
thf(f660,plain,
! [X0: option_game,X1: option_game > option_fml > $o,X2: option_fml] :
( ( ( none_game = X0 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ( ( none_fml = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) )
=> ( ! [X3: game,X4: fml] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f659]) ).
thf(f659,plain,
! [X0: option_game,X1: option_game > option_fml > $o,X2: option_fml] :
( ( ( none_game = X0 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ( ( none_fml = X2 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) )
=> ( ! [X3: game,X4: fml] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(fml,option_fml,some_fml,X4) = X2 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f117]) ).
thf(f117,axiom,
! [X23: option_game,X26: option_game > option_fml > $o,X36: option_fml] :
( ( ( none_game = X23 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ( ( none_fml = X36 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X26,X23),X36) )
=> ( ! [X61: game,X62: fml] :
( ( vAPP(game,option_game,some_game,X61) = X23 )
=> ( ( vAPP(fml,option_fml,some_fml,X62) = X36 )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X26,X23),X36) ) )
=> vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_combine__options__cases) ).
thf(f3971,plain,
spl291_164,
inference(avatar_split_clause,[],[f2096,f3969]) ).
thf(f3969,plain,
( spl291_164
<=> ! [X2: option_game,X0: option_game,X1: option_game > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X1),X0),X2) )
| ( none_game = X2 )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_164])]) ).
thf(f2096,plain,
! [X2: option_game,X0: option_game,X1: option_game > option_game > $o] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X1),X0),X2) )
| ( none_game = X2 )
| ( none_game = X0 ) ),
inference(cnf_transformation,[],[f1308]) ).
thf(f1308,plain,
! [X0: option_game,X1: option_game > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
| ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X1),X0),X2) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(definition_folding,[],[f1098,f1307]) ).
thf(f1098,plain,
! [X0: option_game,X1: option_game > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(flattening,[],[f1097]) ).
thf(f1097,plain,
! [X0: option_game,X1: option_game > option_game > $o,X2: option_game] :
( ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
| ? [X3: game,X4: game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( vAPP(game,option_game,some_game,X4) = X2 )
& ( vAPP(game,option_game,some_game,X3) = X0 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X2 ) )
| ( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
& ( none_game = X0 ) ) ),
inference(ennf_transformation,[],[f658]) ).
thf(f658,plain,
! [X0: option_game,X1: option_game > option_game > $o,X2: option_game] :
( ( ( none_game = X0 )
=> ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ( ( none_game = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) )
=> ( ! [X3: game,X4: game] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) ) )
=> ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) ) ) ),
inference(fool_elimination,[],[f657]) ).
thf(f657,plain,
! [X0: option_game,X1: option_game > option_game > $o,X2: option_game] :
( ( ( none_game = X0 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
=> ( ( ( none_game = X2 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) )
=> ( ! [X3: game,X4: game] :
( ( vAPP(game,option_game,some_game,X3) = X0 )
=> ( ( vAPP(game,option_game,some_game,X4) = X2 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X1,X0),X2) ) ) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X23: option_game,X26: option_game > option_game > $o,X36: option_game] :
( ( ( none_game = X23 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X26,X23),X36) )
=> ( ( ( none_game = X36 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X26,X23),X36) )
=> ( ! [X61: game,X62: game] :
( ( vAPP(game,option_game,some_game,X61) = X23 )
=> ( ( vAPP(game,option_game,some_game,X62) = X36 )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X26,X23),X36) ) )
=> vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X26,X23),X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_combine__options__cases) ).
thf(f3967,plain,
spl291_163,
inference(avatar_split_clause,[],[f1902,f3965]) ).
thf(f3965,plain,
( spl291_163
<=> ! [X0: option_trm,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_163])]) ).
thf(f1902,plain,
! [X0: option_trm,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1422]) ).
thf(f1422,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0)) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120])],[f1420,f1421]) ).
thf(f1421,plain,
! [X0: option_trm,X1: option_trm] :
( ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X2) = X1 ) )
=> ( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) = X0 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1420,plain,
! [X0: option_trm,X1: option_trm] :
( ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X0 )
& ( vAPP(trm,option_trm,some_trm,X2) = X1 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ),
inference(rectify,[],[f1419]) ).
thf(f1419,plain,
! [X1: option_trm,X0: option_trm] :
( ? [X2: trm] :
( ( $true = vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),vAPP(trm,option_trm,some_trm,X2)) )
& ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) ) ),
inference(nnf_transformation,[],[f1280]) ).
thf(f3963,plain,
spl291_162,
inference(avatar_split_clause,[],[f2783,f3961]) ).
thf(f3961,plain,
( spl291_162
<=> ! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) != vAPP(game,option_game,some_game,X0) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_162])]) ).
thf(f2783,plain,
! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) != vAPP(game,option_game,some_game,X0) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2782]) ).
thf(f2782,plain,
! [X0: game,X1: game] :
( ( vAPP(game,option_game,some_game,X1) != vAPP(game,option_game,some_game,X0) )
| ( $true = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2781]) ).
thf(f2781,plain,
! [X0: game,X1: game] :
( ( $false = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),vAPP(game,option_game,some_game,X1)),vAPP(game,option_game,some_game,X0)) )
| ( $true = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1852]) ).
thf(f3959,plain,
spl291_161,
inference(avatar_split_clause,[],[f1891,f3957]) ).
thf(f3957,plain,
( spl291_161
<=> ! [X0: option_game,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_161])]) ).
thf(f1891,plain,
! [X0: option_game,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1416]) ).
thf(f1416,plain,
! [X0: option_game,X1: option_fml] :
( ( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0)) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118])],[f1414,f1415]) ).
thf(f1415,plain,
! [X0: option_game,X1: option_fml] :
( ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X0 )
& ( vAPP(fml,option_fml,some_fml,X2) = X1 ) )
=> ( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) = X0 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1414,plain,
! [X0: option_game,X1: option_fml] :
( ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X0 )
& ( vAPP(fml,option_fml,some_fml,X2) = X1 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ),
inference(rectify,[],[f1413]) ).
thf(f1413,plain,
! [X1: option_game,X0: option_fml] :
( ? [X2: fml] :
( ( $true = vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),vAPP(fml,option_fml,some_fml,X2)) )
& ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) ) ),
inference(nnf_transformation,[],[f1278]) ).
thf(f3953,plain,
spl291_160,
inference(avatar_split_clause,[],[f2010,f3951]) ).
thf(f3951,plain,
( spl291_160
<=> ! [X2: char,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(char,trm,const,X2)) = vAPP(char,option_trm,vAPP(set_variable,sTfun(char,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(char,option_trm)),uSubst1559070963pconst,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_160])]) ).
thf(f2010,plain,
! [X2: char,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(char,trm,const,X2)) = vAPP(char,option_trm,vAPP(set_variable,sTfun(char,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(char,option_trm)),uSubst1559070963pconst,X0),X1),X2) ),
inference(cnf_transformation,[],[f949]) ).
thf(f949,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: char] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(char,trm,const,X2)) = vAPP(char,option_trm,vAPP(set_variable,sTfun(char,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(char,option_trm)),uSubst1559070963pconst,X0),X1),X2) ),
inference(rectify,[],[f314]) ).
thf(f314,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X40: char] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(char,trm,const,X40)) = vAPP(char,option_trm,vAPP(set_variable,sTfun(char,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(char,option_trm)),uSubst1559070963pconst,X0),X1),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_usubstappt_Osimps_I3_J) ).
thf(f3949,plain,
spl291_159,
inference(avatar_split_clause,[],[f1972,f3947]) ).
thf(f3947,plain,
( spl291_159
<=> ! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)),X1) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_159])]) ).
thf(f1972,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)),X1) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1493]) ).
thf(f1493,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f1054,f1492]) ).
thf(f1492,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ? [X2: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X1) )
& ( $true = vAPP(set_variable,$o,X0,X2) ) )
=> ( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1054,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ? [X2: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X1) )
& ( $true = vAPP(set_variable,$o,X0,X2) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(flattening,[],[f1053]) ).
thf(f1053,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ? [X2: set_variable] :
( ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X1) )
& ( $true = vAPP(set_variable,$o,X0,X2) ) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f594]) ).
thf(f594,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,X0,X1) )
=> ( ! [X2: set_variable] :
( ( $true = vAPP(set_variable,$o,X0,X2) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X1) ) )
=> ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 ) ) ),
inference(fool_elimination,[],[f593]) ).
thf(f593,plain,
! [X0: set_variable > $o,X1: set_variable] :
( vAPP(set_variable,$o,X0,X1)
=> ( ! [X2: set_variable] :
( vAPP(set_variable,$o,X0,X2)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X2),X1) )
=> ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 ) ) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X26: set_variable > $o,X23: set_variable] :
( vAPP(set_variable,$o,X26,X23)
=> ( ! [X41: set_variable] :
( vAPP(set_variable,$o,X26,X41)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X41),X23) )
=> ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X26) = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Greatest__equality) ).
thf(f3935,plain,
spl291_158,
inference(avatar_split_clause,[],[f2779,f3933]) ).
thf(f3933,plain,
( spl291_158
<=> ! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) = vAPP(fml,game,test,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_158])]) ).
thf(f2779,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) = vAPP(fml,game,test,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2778]) ).
thf(f2778,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) = vAPP(fml,game,test,X1) )
| ( $false = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2774]) ).
thf(f2774,plain,
! [X0: fml,X1: fml] :
( ( $true = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),vAPP(fml,game,test,X0)),vAPP(fml,game,test,X1)) )
| ( $false = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1853]) ).
thf(f1853,plain,
! [X0: fml,X1: fml] : ( vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),vAPP(fml,game,test,X0)),vAPP(fml,game,test,X1)) = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ),
inference(cnf_transformation,[],[f474]) ).
thf(f474,plain,
! [X0: fml,X1: fml] : ( vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),vAPP(fml,game,test,X0)),vAPP(fml,game,test,X1)) = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ),
inference(fool_elimination,[],[f473]) ).
thf(f473,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) = vAPP(fml,game,test,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f326]) ).
thf(f326,axiom,
! [X103: fml,X104: fml] :
( ( vAPP(fml,game,test,X103) = vAPP(fml,game,test,X104) )
= ( X103 = X104 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_game_Oinject_I3_J) ).
thf(f3931,plain,
spl291_157,
inference(avatar_split_clause,[],[f2175,f3929]) ).
thf(f3929,plain,
( spl291_157
<=> ! [X0: set_variable > $o,X1: set_variable > $o] :
( ( $true != vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_157])]) ).
thf(f2175,plain,
! [X0: set_variable > $o,X1: set_variable > $o] :
( ( $true != vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ),
inference(cnf_transformation,[],[f1648]) ).
thf(f3927,plain,
spl291_156,
inference(avatar_split_clause,[],[f2173,f3925]) ).
thf(f3925,plain,
( spl291_156
<=> ! [X0: set_variable > $o,X1: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X1,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_156])]) ).
thf(f2173,plain,
! [X0: set_variable > $o,X1: set_variable > $o] :
( ( $true = vAPP(set_variable,$o,X1,vAPP(sTfun(set_variable,$o),set_variable,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),set_variable),sK246,X1),X0)) )
| ( $true != vAPP(sTfun(set_variable,$o),$o,vAPP(sTfun(set_variable,$o),sTfun(sTfun(set_variable,$o),$o),sP29,X1),X0) ) ),
inference(cnf_transformation,[],[f1648]) ).
thf(f3923,plain,
spl291_155,
inference(avatar_split_clause,[],[f1830,f3921]) ).
thf(f3921,plain,
( spl291_155
<=> ! [X0: produc464795408on_trm] :
( ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK74,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK75,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc464795408on_trm,trm,sK76,X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_155])]) ).
thf(f1830,plain,
! [X0: produc464795408on_trm] :
( ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK74,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK75,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc464795408on_trm,trm,sK76,X0))) = X0 ) ),
inference(cnf_transformation,[],[f1381]) ).
thf(f1381,plain,
! [X0: produc464795408on_trm] :
( ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK74,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK75,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc464795408on_trm,trm,sK76,X0))) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76])],[f1378,f1380,f1379]) ).
thf(f1379,plain,
! [X0: produc464795408on_trm] :
( ? [X1: char] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X1),none_trm) = X0 )
=> ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK74,X0)),none_trm) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1380,plain,
! [X0: produc464795408on_trm] :
( ? [X2: char,X3: trm] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),vAPP(trm,option_trm,some_trm,X3)) = X0 )
=> ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,vAPP(produc464795408on_trm,char,sK75,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc464795408on_trm,trm,sK76,X0))) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1378,plain,
! [X0: produc464795408on_trm] :
( ? [X1: char] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X1),none_trm) = X0 )
| ? [X2: char,X3: trm] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X2),vAPP(trm,option_trm,some_trm,X3)) = X0 ) ),
inference(rectify,[],[f986]) ).
thf(f986,plain,
! [X0: produc464795408on_trm] :
( ? [X3: char] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X3),none_trm) = X0 )
| ? [X1: char,X2: trm] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X1),vAPP(trm,option_trm,some_trm,X2)) = X0 ) ),
inference(ennf_transformation,[],[f900]) ).
thf(f900,plain,
! [X0: produc464795408on_trm] :
( ! [X1: char,X2: trm] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X1),vAPP(trm,option_trm,some_trm,X2)) != X0 )
=> ~ ! [X3: char] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X3),none_trm) != X0 ) ),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
! [X23: produc464795408on_trm] :
( ! [X22: char,X54: trm] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X22),vAPP(trm,option_trm,some_trm,X54)) != X23 )
=> ~ ! [X22: char] : ( vAPP(option_trm,produc464795408on_trm,vAPP(char,sTfun(option_trm,produc464795408on_trm),produc1500300866on_trm,X22),none_trm) != X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_ODEo_Ocases) ).
thf(f3919,plain,
spl291_154,
inference(avatar_split_clause,[],[f1829,f3917]) ).
thf(f3917,plain,
( spl291_154
<=> ! [X0: produc1024976764on_trm] :
( ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK71,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK72,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc1024976764on_trm,trm,sK73,X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_154])]) ).
thf(f1829,plain,
! [X0: produc1024976764on_trm] :
( ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK71,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK72,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc1024976764on_trm,trm,sK73,X0))) = X0 ) ),
inference(cnf_transformation,[],[f1377]) ).
thf(f1377,plain,
! [X0: produc1024976764on_trm] :
( ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK71,X0)),none_trm) = X0 )
| ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK72,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc1024976764on_trm,trm,sK73,X0))) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72,sK73])],[f1374,f1376,f1375]) ).
thf(f1375,plain,
! [X0: produc1024976764on_trm] :
( ? [X1: variable] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X1),none_trm) = X0 )
=> ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK71,X0)),none_trm) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1376,plain,
! [X0: produc1024976764on_trm] :
( ? [X2: variable,X3: trm] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X2),vAPP(trm,option_trm,some_trm,X3)) = X0 )
=> ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,vAPP(produc1024976764on_trm,variable,sK72,X0)),vAPP(trm,option_trm,some_trm,vAPP(produc1024976764on_trm,trm,sK73,X0))) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1374,plain,
! [X0: produc1024976764on_trm] :
( ? [X1: variable] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X1),none_trm) = X0 )
| ? [X2: variable,X3: trm] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X2),vAPP(trm,option_trm,some_trm,X3)) = X0 ) ),
inference(rectify,[],[f985]) ).
thf(f985,plain,
! [X0: produc1024976764on_trm] :
( ? [X3: variable] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X3),none_trm) = X0 )
| ? [X1: variable,X2: trm] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X1),vAPP(trm,option_trm,some_trm,X2)) = X0 ) ),
inference(ennf_transformation,[],[f899]) ).
thf(f899,plain,
! [X0: produc1024976764on_trm] :
( ! [X1: variable,X2: trm] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X1),vAPP(trm,option_trm,some_trm,X2)) != X0 )
=> ~ ! [X3: variable] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X3),none_trm) != X0 ) ),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
! [X23: produc1024976764on_trm] :
( ! [X22: variable,X54: trm] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X22),vAPP(trm,option_trm,some_trm,X54)) != X23 )
=> ~ ! [X22: variable] : ( vAPP(option_trm,produc1024976764on_trm,vAPP(variable,sTfun(option_trm,produc1024976764on_trm),produc1743721902on_trm,X22),none_trm) != X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_Assigno_Ocases) ).
thf(f3915,plain,
spl291_153,
inference(avatar_split_clause,[],[f1827,f3913]) ).
thf(f3913,plain,
( spl291_153
<=> ! [X0: produc1408538418on_fml] :
( ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK51,X0)),none_fml) = X0 )
| ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK52,X0)),vAPP(fml,option_fml,some_fml,vAPP(produc1408538418on_fml,fml,sK53,X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_153])]) ).
thf(f1827,plain,
! [X0: produc1408538418on_fml] :
( ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK51,X0)),none_fml) = X0 )
| ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK52,X0)),vAPP(fml,option_fml,some_fml,vAPP(produc1408538418on_fml,fml,sK53,X0))) = X0 ) ),
inference(cnf_transformation,[],[f1364]) ).
thf(f1364,plain,
! [X0: produc1408538418on_fml] :
( ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK51,X0)),none_fml) = X0 )
| ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK52,X0)),vAPP(fml,option_fml,some_fml,vAPP(produc1408538418on_fml,fml,sK53,X0))) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53])],[f1361,f1363,f1362]) ).
thf(f1362,plain,
! [X0: produc1408538418on_fml] :
( ? [X1: variable] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X1),none_fml) = X0 )
=> ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK51,X0)),none_fml) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1363,plain,
! [X0: produc1408538418on_fml] :
( ? [X2: variable,X3: fml] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X2),vAPP(fml,option_fml,some_fml,X3)) = X0 )
=> ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,vAPP(produc1408538418on_fml,variable,sK52,X0)),vAPP(fml,option_fml,some_fml,vAPP(produc1408538418on_fml,fml,sK53,X0))) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1361,plain,
! [X0: produc1408538418on_fml] :
( ? [X1: variable] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X1),none_fml) = X0 )
| ? [X2: variable,X3: fml] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X2),vAPP(fml,option_fml,some_fml,X3)) = X0 ) ),
inference(rectify,[],[f982]) ).
thf(f982,plain,
! [X0: produc1408538418on_fml] :
( ? [X3: variable] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X3),none_fml) = X0 )
| ? [X1: variable,X2: fml] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X1),vAPP(fml,option_fml,some_fml,X2)) = X0 ) ),
inference(ennf_transformation,[],[f897]) ).
thf(f897,plain,
! [X0: produc1408538418on_fml] :
( ! [X1: variable,X2: fml] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X1),vAPP(fml,option_fml,some_fml,X2)) != X0 )
=> ~ ! [X3: variable] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X3),none_fml) != X0 ) ),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
! [X23: produc1408538418on_fml] :
( ! [X22: variable,X74: fml] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X22),vAPP(fml,option_fml,some_fml,X74)) != X23 )
=> ~ ! [X22: variable] : ( vAPP(option_fml,produc1408538418on_fml,vAPP(variable,sTfun(option_fml,produc1408538418on_fml),produc1205977188on_fml,X22),none_fml) != X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_Existso_Ocases) ).
thf(f3900,plain,
spl291_152,
inference(avatar_split_clause,[],[f2373,f3898]) ).
thf(f3898,plain,
( spl291_152
<=> ! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_152])]) ).
thf(f2373,plain,
! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ),
inference(equality_resolution,[],[f1904]) ).
thf(f1904,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1281]) ).
thf(f3896,plain,
spl291_151,
inference(avatar_split_clause,[],[f2365,f3894]) ).
thf(f3894,plain,
( spl291_151
<=> ! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_151])]) ).
thf(f2365,plain,
! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ),
inference(equality_resolution,[],[f1893]) ).
thf(f1893,plain,
! [X0: option_fml,X1: option_game] :
( ( none_game = X1 )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1279]) ).
thf(f3892,plain,
spl291_150,
inference(avatar_split_clause,[],[f2777,f3890]) ).
thf(f3890,plain,
( spl291_150
<=> ! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) != vAPP(fml,game,test,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_150])]) ).
thf(f2777,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) != vAPP(fml,game,test,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2776]) ).
thf(f2776,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,game,test,X0) != vAPP(fml,game,test,X1) )
| ( $true = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2775]) ).
thf(f2775,plain,
! [X0: fml,X1: fml] :
( ( $false = vAPP(game,$o,vAPP(game,sTfun(game,$o),vEQ(game),vAPP(fml,game,test,X0)),vAPP(fml,game,test,X1)) )
| ( $true = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1853]) ).
thf(f3888,plain,
spl291_149,
inference(avatar_split_clause,[],[f1991,f3886]) ).
thf(f3886,plain,
( spl291_149
<=> ! [X0: variable > real,X1: variable > real] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_149])]) ).
thf(f1991,plain,
! [X0: variable > real,X1: variable > real] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))) ),
inference(cnf_transformation,[],[f632]) ).
thf(f632,plain,
! [X0: variable > real,X1: variable > real] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP($o,sTfun(variable,$o),kCOMB,$true))) ),
inference(fool_elimination,[],[f631]) ).
thf(f631,plain,
! [X0: variable > real,X1: variable > real] :
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X1),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X2: variable] : $true)),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X19: variable > real,X24: variable > real] :
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X19),X24),
vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X25: variable] : $true)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Uvariation__univ) ).
thf(f3876,plain,
spl291_148,
inference(avatar_split_clause,[],[f2161,f3874]) ).
thf(f3874,plain,
( spl291_148
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_148])]) ).
thf(f2161,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK212,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(cnf_transformation,[],[f1609]) ).
thf(f3872,plain,
spl291_147,
inference(avatar_split_clause,[],[f2160,f3870]) ).
thf(f3870,plain,
( spl291_147
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_147])]) ).
thf(f2160,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK210,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK211,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP27,X0) ) ),
inference(cnf_transformation,[],[f1609]) ).
thf(f3868,plain,
spl291_146,
inference(avatar_split_clause,[],[f2158,f3866]) ).
thf(f3866,plain,
( spl291_146
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_146])]) ).
thf(f2158,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK209,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(cnf_transformation,[],[f1604]) ).
thf(f3864,plain,
spl291_145,
inference(avatar_split_clause,[],[f2157,f3862]) ).
thf(f3862,plain,
( spl291_145
<=> ! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_145])]) ).
thf(f2157,plain,
! [X0: denotational_interp > trm > $o] :
( ( $true = vAPP(trm,$o,vAPP(denotational_interp,sTfun(trm,$o),X0,vAPP(sTfun(denotational_interp,sTfun(trm,$o)),denotational_interp,sK207,X0)),vAPP(sTfun(denotational_interp,sTfun(trm,$o)),trm,sK208,X0)) )
| ( $true != vAPP(sTfun(denotational_interp,sTfun(trm,$o)),$o,sP28,X0) ) ),
inference(cnf_transformation,[],[f1604]) ).
thf(f3857,plain,
spl291_144,
inference(avatar_split_clause,[],[f2773,f3855]) ).
thf(f3855,plain,
( spl291_144
<=> ! [X0: fml,X1: fml] :
( ( X0 = X1 )
| ( vAPP(fml,option_fml,some_fml,X1) != vAPP(fml,option_fml,some_fml,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_144])]) ).
thf(f2773,plain,
! [X0: fml,X1: fml] :
( ( X0 = X1 )
| ( vAPP(fml,option_fml,some_fml,X1) != vAPP(fml,option_fml,some_fml,X0) ) ),
inference(equality_proxy_clausification,[],[f2772]) ).
thf(f2772,plain,
! [X0: fml,X1: fml] :
( ( X0 = X1 )
| ( $false = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ) ),
inference(equality_proxy_clausification,[],[f2768]) ).
thf(f2768,plain,
! [X0: fml,X1: fml] :
( ( $true = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) )
| ( $false = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ) ),
inference(binary_proxy_clausification,[],[f1854]) ).
thf(f1854,plain,
! [X0: fml,X1: fml] : ( vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ),
inference(cnf_transformation,[],[f476]) ).
thf(f476,plain,
! [X0: fml,X1: fml] : ( vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ),
inference(fool_elimination,[],[f475]) ).
thf(f475,plain,
! [X0: fml,X1: fml] :
( ( vAPP(fml,option_fml,some_fml,X1) = vAPP(fml,option_fml,some_fml,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X57: fml,X58: fml] :
( ( vAPP(fml,option_fml,some_fml,X57) = vAPP(fml,option_fml,some_fml,X58) )
= ( X57 = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_option_Oinject) ).
thf(f3845,plain,
spl291_143,
inference(avatar_split_clause,[],[f2185,f3843]) ).
thf(f3843,plain,
( spl291_143
<=> ! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_143])]) ).
thf(f2185,plain,
! [X2: set_variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(cnf_transformation,[],[f1146]) ).
thf(f1146,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(flattening,[],[f1145]) ).
thf(f1145,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(ennf_transformation,[],[f708]) ).
thf(f708,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
=> ( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) ) ) ),
inference(fool_elimination,[],[f707]) ).
thf(f707,plain,
! [X0: set_variable,X1: set_variable,X2: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1)
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X2)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X2) ) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X30: set_variable,X29: set_variable,X35: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X30),X29)
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X29),X35)
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X30),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Otrans) ).
thf(f3841,plain,
spl291_142,
inference(avatar_split_clause,[],[f2183,f3839]) ).
thf(f3839,plain,
( spl291_142
<=> ! [X2: variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_142])]) ).
thf(f2183,plain,
! [X2: variable,X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(cnf_transformation,[],[f1142]) ).
thf(f1142,plain,
! [X0: set_variable,X1: set_variable,X2: variable] :
( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(flattening,[],[f1141]) ).
thf(f1141,plain,
! [X0: set_variable,X1: set_variable,X2: variable] :
( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(ennf_transformation,[],[f704]) ).
thf(f704,plain,
! [X0: set_variable,X1: set_variable,X2: variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
=> ( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
=> ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) ) ) ),
inference(fool_elimination,[],[f703]) ).
thf(f703,plain,
! [X0: set_variable,X1: set_variable,X2: variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1)
=> ( vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0)
=> vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) ) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X20: set_variable,X21: set_variable,X23: variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X20),X21)
=> ( vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X23),X20)
=> vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X23),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_in__mono) ).
thf(f3837,plain,
spl291_141,
inference(avatar_split_clause,[],[f2179,f3835]) ).
thf(f3835,plain,
( spl291_141
<=> ! [X2: char,X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
| ( $true != vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_141])]) ).
thf(f2179,plain,
! [X2: char,X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
| ( $true != vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) ),
inference(cnf_transformation,[],[f1135]) ).
thf(f1135,plain,
! [X0: set_char,X1: set_char,X2: char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
| ( $true != vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) ),
inference(flattening,[],[f1134]) ).
thf(f1134,plain,
! [X0: set_char,X1: set_char,X2: char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
| ( $true != vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) ),
inference(ennf_transformation,[],[f696]) ).
thf(f696,plain,
! [X0: set_char,X1: set_char,X2: char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
=> ( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
=> ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) ) ) ),
inference(fool_elimination,[],[f695]) ).
thf(f695,plain,
! [X0: set_char,X1: set_char,X2: char] :
( vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1)
=> ( vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0)
=> vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) ) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X20: set_char,X21: set_char,X23: char] :
( vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X20),X21)
=> ( vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X23),X20)
=> vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X23),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_in__mono) ).
thf(f3801,plain,
spl291_140,
inference(avatar_split_clause,[],[f2771,f3799]) ).
thf(f3799,plain,
( spl291_140
<=> ! [X0: fml,X1: fml] :
( ( X0 != X1 )
| ( vAPP(fml,option_fml,some_fml,X1) = vAPP(fml,option_fml,some_fml,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_140])]) ).
thf(f2771,plain,
! [X0: fml,X1: fml] :
( ( X0 != X1 )
| ( vAPP(fml,option_fml,some_fml,X1) = vAPP(fml,option_fml,some_fml,X0) ) ),
inference(equality_proxy_clausification,[],[f2770]) ).
thf(f2770,plain,
! [X0: fml,X1: fml] :
( ( X0 != X1 )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ) ),
inference(equality_proxy_clausification,[],[f2769]) ).
thf(f2769,plain,
! [X0: fml,X1: fml] :
( ( $false = vAPP(fml,$o,vAPP(fml,sTfun(fml,$o),vEQ(fml),X0),X1) )
| ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),vAPP(fml,option_fml,some_fml,X1)),vAPP(fml,option_fml,some_fml,X0)) ) ),
inference(binary_proxy_clausification,[],[f1854]) ).
thf(f3773,plain,
spl291_139,
inference(avatar_split_clause,[],[f2392,f3771]) ).
thf(f3771,plain,
( spl291_139
<=> ! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_139])]) ).
thf(f2392,plain,
! [X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1)),X1),X0)) = X1 ) ),
inference(equality_resolution,[],[f2025]) ).
thf(f2025,plain,
! [X2: option_game,X0: char,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(char,trm,vAPP(option_trm,sTfun(char,trm),vAPP(option_game,sTfun(option_trm,sTfun(char,trm)),sK166,X2),X1),X0)) = X1 )
| ( vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f3769,plain,
spl291_138,
inference(avatar_split_clause,[],[f2385,f3767]) ).
thf(f3767,plain,
( spl291_138
<=> ! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_138])]) ).
thf(f2385,plain,
! [X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1)),X1),X0)) = X1 ) ),
inference(equality_resolution,[],[f2015]) ).
thf(f2015,plain,
! [X2: option_game,X0: variable,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(variable,trm,vAPP(option_trm,sTfun(variable,trm),vAPP(option_game,sTfun(option_trm,sTfun(variable,trm)),sK164,X2),X1),X0)) = X1 )
| ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1495]) ).
thf(f3765,plain,
spl291_137,
inference(avatar_split_clause,[],[f2767,f3763]) ).
thf(f3763,plain,
( spl291_137
<=> ! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) = vAPP(variable,trm,var,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_137])]) ).
thf(f2767,plain,
! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) = vAPP(variable,trm,var,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2766]) ).
thf(f2766,plain,
! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) = vAPP(variable,trm,var,X1) )
| ( $false = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2762]) ).
thf(f2762,plain,
! [X0: variable,X1: variable] :
( ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(variable,trm,var,X0)),vAPP(variable,trm,var,X1)) )
| ( $false = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1855]) ).
thf(f1855,plain,
! [X0: variable,X1: variable] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(variable,trm,var,X0)),vAPP(variable,trm,var,X1)) = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ),
inference(cnf_transformation,[],[f478]) ).
thf(f478,plain,
! [X0: variable,X1: variable] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(variable,trm,var,X0)),vAPP(variable,trm,var,X1)) = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ),
inference(fool_elimination,[],[f477]) ).
thf(f477,plain,
! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) = vAPP(variable,trm,var,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
! [X93: variable,X94: variable] :
( ( vAPP(variable,trm,var,X93) = vAPP(variable,trm,var,X94) )
= ( X93 = X94 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_trm_Oinject_I1_J) ).
thf(f3761,plain,
spl291_136,
inference(avatar_split_clause,[],[f2151,f3759]) ).
thf(f3759,plain,
( spl291_136
<=> ! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_136])]) ).
thf(f2151,plain,
! [X2: option_trm > option_trm > $o,X0: option_trm,X1: option_trm] :
( ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,sTfun(option_trm,$o)),sP26,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1595]) ).
thf(f3757,plain,
spl291_135,
inference(avatar_split_clause,[],[f2144,f3755]) ).
thf(f3755,plain,
( spl291_135
<=> ! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_135])]) ).
thf(f2144,plain,
! [X2: option_trm > option_fml > $o,X0: option_fml,X1: option_trm] :
( ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(sTfun(option_trm,sTfun(option_fml,$o)),sTfun(option_trm,sTfun(option_fml,$o)),sP25,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1591]) ).
thf(f3753,plain,
spl291_134,
inference(avatar_split_clause,[],[f2137,f3751]) ).
thf(f3751,plain,
( spl291_134
<=> ! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_134])]) ).
thf(f2137,plain,
! [X2: option_trm > option_game > $o,X0: option_game,X1: option_trm] :
( ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_trm,sTfun(option_game,$o),vAPP(sTfun(option_trm,sTfun(option_game,$o)),sTfun(option_trm,sTfun(option_game,$o)),sP24,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1587]) ).
thf(f3749,plain,
spl291_133,
inference(avatar_split_clause,[],[f2130,f3747]) ).
thf(f3747,plain,
( spl291_133
<=> ! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_133])]) ).
thf(f2130,plain,
! [X2: option_fml > option_trm > $o,X0: option_trm,X1: option_fml] :
( ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_fml,sTfun(option_trm,$o),vAPP(sTfun(option_fml,sTfun(option_trm,$o)),sTfun(option_fml,sTfun(option_trm,$o)),sP23,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1583]) ).
thf(f3745,plain,
spl291_132,
inference(avatar_split_clause,[],[f2123,f3743]) ).
thf(f3743,plain,
( spl291_132
<=> ! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_132])]) ).
thf(f2123,plain,
! [X2: option_fml > option_fml > $o,X0: option_fml,X1: option_fml] :
( ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,sTfun(option_fml,$o)),sP22,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1579]) ).
thf(f3741,plain,
spl291_131,
inference(avatar_split_clause,[],[f2116,f3739]) ).
thf(f3739,plain,
( spl291_131
<=> ! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_131])]) ).
thf(f2116,plain,
! [X2: option_fml > option_game > $o,X0: option_game,X1: option_fml] :
( ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),vAPP(sTfun(option_fml,sTfun(option_game,$o)),sTfun(option_fml,sTfun(option_game,$o)),sP21,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1575]) ).
thf(f3737,plain,
spl291_130,
inference(avatar_split_clause,[],[f2109,f3735]) ).
thf(f3735,plain,
( spl291_130
<=> ! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_130])]) ).
thf(f2109,plain,
! [X2: option_game > option_trm > $o,X0: option_trm,X1: option_game] :
( ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),X2,X1),X0) )
| ( $true != vAPP(option_trm,$o,vAPP(option_game,sTfun(option_trm,$o),vAPP(sTfun(option_game,sTfun(option_trm,$o)),sTfun(option_game,sTfun(option_trm,$o)),sP20,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1571]) ).
thf(f3733,plain,
spl291_129,
inference(avatar_split_clause,[],[f2102,f3731]) ).
thf(f3731,plain,
( spl291_129
<=> ! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_129])]) ).
thf(f2102,plain,
! [X2: option_game > option_fml > $o,X0: option_fml,X1: option_game] :
( ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),X2,X1),X0) )
| ( $true != vAPP(option_fml,$o,vAPP(option_game,sTfun(option_fml,$o),vAPP(sTfun(option_game,sTfun(option_fml,$o)),sTfun(option_game,sTfun(option_fml,$o)),sP19,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1567]) ).
thf(f3729,plain,
spl291_128,
inference(avatar_split_clause,[],[f2095,f3727]) ).
thf(f3727,plain,
( spl291_128
<=> ! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_128])]) ).
thf(f2095,plain,
! [X2: option_game > option_game > $o,X0: option_game,X1: option_game] :
( ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),X2,X1),X0) )
| ( $true != vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vAPP(sTfun(option_game,sTfun(option_game,$o)),sTfun(option_game,sTfun(option_game,$o)),sP18,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1563]) ).
thf(f3725,plain,
spl291_127,
inference(avatar_split_clause,[],[f1952,f3723]) ).
thf(f3723,plain,
( spl291_127
<=> ! [X0: trm > $o] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(trm,$o),trm,sK141,X0)),vAPP(sTfun(trm,$o),trm,sK142,X0))) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_127])]) ).
thf(f1952,plain,
! [X0: trm > $o] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(trm,$o),trm,sK141,X0)),vAPP(sTfun(trm,$o),trm,sK142,X0))) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f1466,plain,
! [X0: trm > $o] :
( ( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(trm,$o),trm,sK141,X0)),vAPP(sTfun(trm,$o),trm,sK142,X0))) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK142,X0)) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK141,X0)) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142])],[f1464,f1465]) ).
thf(f1465,plain,
! [X0: trm > $o] :
( ? [X1: trm,X2: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2)) )
& ( $true = vAPP(trm,$o,X0,X2) )
& ( $true = vAPP(trm,$o,X0,X1) ) )
=> ( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,vAPP(sTfun(trm,$o),trm,sK141,X0)),vAPP(sTfun(trm,$o),trm,sK142,X0))) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK142,X0)) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK141,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1464,plain,
! [X0: trm > $o] :
( ? [X1: trm,X2: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2)) )
& ( $true = vAPP(trm,$o,X0,X2) )
& ( $true = vAPP(trm,$o,X0,X1) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(rectify,[],[f1463]) ).
thf(f1463,plain,
! [X0: trm > $o] :
( ? [X7: trm,X8: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X7),X8)) )
& ( $true = vAPP(trm,$o,X0,X8) )
& ( $true = vAPP(trm,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(nnf_transformation,[],[f1282]) ).
thf(f1282,plain,
! [X0: trm > $o] :
( ? [X7: trm,X8: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X7),X8)) )
& ( $true = vAPP(trm,$o,X0,X8) )
& ( $true = vAPP(trm,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3721,plain,
spl291_126,
inference(avatar_split_clause,[],[f1949,f3719]) ).
thf(f3719,plain,
( spl291_126
<=> ! [X0: trm > $o] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(trm,$o),trm,sK139,X0)),vAPP(sTfun(trm,$o),trm,sK140,X0))) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_126])]) ).
thf(f1949,plain,
! [X0: trm > $o] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(trm,$o),trm,sK139,X0)),vAPP(sTfun(trm,$o),trm,sK140,X0))) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1462]) ).
thf(f1462,plain,
! [X0: trm > $o] :
( ( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(trm,$o),trm,sK139,X0)),vAPP(sTfun(trm,$o),trm,sK140,X0))) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK140,X0)) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK139,X0)) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140])],[f1460,f1461]) ).
thf(f1461,plain,
! [X0: trm > $o] :
( ? [X1: trm,X2: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2)) )
& ( $true = vAPP(trm,$o,X0,X2) )
& ( $true = vAPP(trm,$o,X0,X1) ) )
=> ( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(sTfun(trm,$o),trm,sK139,X0)),vAPP(sTfun(trm,$o),trm,sK140,X0))) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK140,X0)) )
& ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK139,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1460,plain,
! [X0: trm > $o] :
( ? [X1: trm,X2: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2)) )
& ( $true = vAPP(trm,$o,X0,X2) )
& ( $true = vAPP(trm,$o,X0,X1) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(rectify,[],[f1459]) ).
thf(f1459,plain,
! [X0: trm > $o] :
( ? [X9: trm,X10: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X9),X10)) )
& ( $true = vAPP(trm,$o,X0,X10) )
& ( $true = vAPP(trm,$o,X0,X9) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(nnf_transformation,[],[f1283]) ).
thf(f1283,plain,
! [X0: trm > $o] :
( ? [X9: trm,X10: trm] :
( ( $true != vAPP(trm,$o,X0,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X9),X10)) )
& ( $true = vAPP(trm,$o,X0,X10) )
& ( $true = vAPP(trm,$o,X0,X9) ) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3695,plain,
spl291_125,
inference(avatar_split_clause,[],[f2374,f3693]) ).
thf(f3693,plain,
( spl291_125
<=> ! [X0: option_trm] :
( ( none_trm = X0 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_125])]) ).
thf(f2374,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) ) ),
inference(equality_resolution,[],[f1903]) ).
thf(f1903,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X0),X1) )
| ( $true != vAPP(option_trm,$o,vAPP(sTfun(option_trm,sTfun(option_trm,$o)),sTfun(option_trm,$o),accp_option_trm,uSubst2051024824lo_rel),X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1281]) ).
thf(f3691,plain,
spl291_124,
inference(avatar_split_clause,[],[f2366,f3689]) ).
thf(f3689,plain,
( spl291_124
<=> ! [X0: option_fml] :
( ( none_fml = X0 )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_124])]) ).
thf(f2366,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) ) ),
inference(equality_resolution,[],[f1892]) ).
thf(f1892,plain,
! [X0: option_fml,X1: option_game] :
( ( none_fml = X0 )
| ( $true = vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X0),X1) )
| ( $true != vAPP(option_fml,$o,vAPP(sTfun(option_fml,sTfun(option_fml,$o)),sTfun(option_fml,$o),accp_option_fml,uSubst954181007to_rel),X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1279]) ).
thf(f3687,plain,
spl291_123,
inference(avatar_split_clause,[],[f1971,f3685]) ).
thf(f3685,plain,
( spl291_123
<=> ! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_123])]) ).
thf(f1971,plain,
! [X0: set_variable > $o,X1: set_variable] :
( ( vAPP(sTfun(set_variable,$o),set_variable,order_272405634riable,X0) = X1 )
| ( $true = vAPP(set_variable,$o,X0,vAPP(sTfun(set_variable,$o),set_variable,vAPP(set_variable,sTfun(sTfun(set_variable,$o),set_variable),sK163,X1),X0)) )
| ( $true != vAPP(set_variable,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1493]) ).
thf(f3658,plain,
( spl291_122
| ~ spl291_116
| ~ spl291_117 ),
inference(avatar_split_clause,[],[f3654,f3631,f3627,f3656]) ).
thf(f3656,plain,
( spl291_122
<=> ! [X0: set_char] : ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_122])]) ).
thf(f3627,plain,
( spl291_116
<=> ! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_116])]) ).
thf(f3631,plain,
( spl291_117
<=> ! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_117])]) ).
thf(f3654,plain,
( ! [X0: set_char] : ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X0) )
| ~ spl291_116
| ~ spl291_117 ),
inference(trivial_inequality_removal,[],[f3653]) ).
thf(f3653,plain,
( ! [X0: set_char] :
( ( $true != $true )
| ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X0) ) )
| ~ spl291_116
| ~ spl291_117 ),
inference(duplicate_literal_removal,[],[f3650]) ).
thf(f3650,plain,
( ! [X0: set_char] :
( ( $true != $true )
| ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X0) )
| ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X0) ) )
| ~ spl291_116
| ~ spl291_117 ),
inference(superposition,[],[f3632,f3628]) ).
thf(f3628,plain,
( ! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X0) )
| ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) )
| ~ spl291_116 ),
inference(avatar_component_clause,[],[f3627]) ).
thf(f3632,plain,
( ! [X0: set_char,X1: set_char] :
( ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X1) )
| ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) )
| ~ spl291_117 ),
inference(avatar_component_clause,[],[f3631]) ).
thf(f3649,plain,
spl291_121,
inference(avatar_split_clause,[],[f2368,f3647]) ).
thf(f3647,plain,
( spl291_121
<=> ! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_121])]) ).
thf(f2368,plain,
! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0))) ) ),
inference(equality_resolution,[],[f1899]) ).
thf(f1899,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0))) = X1 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1418]) ).
thf(f1418,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( none_trm = X1 )
& ( none_trm = X0 ) )
| ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0)) = X0 ) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK119])],[f1009,f1417]) ).
thf(f1417,plain,
! [X0: option_trm,X1: option_trm] :
( ? [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
=> ( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0))) = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1009,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( none_trm = X1 )
& ( none_trm = X0 ) )
| ? [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(flattening,[],[f1008]) ).
thf(f1008,plain,
! [X0: option_trm,X1: option_trm] :
( ( ( none_trm = X1 )
& ( none_trm = X0 ) )
| ? [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) = X1 )
& ( vAPP(trm,option_trm,some_trm,X2) = X0 ) )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(ennf_transformation,[],[f924]) ).
thf(f924,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = X1 )
=> ( ! [X2: trm] :
( ( vAPP(trm,option_trm,some_trm,X2) = X0 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) != X1 ) )
=> ~ ( ( none_trm = X0 )
=> ( none_trm != X1 ) ) ) ),
inference(rectify,[],[f143]) ).
thf(f143,axiom,
! [X23: option_trm,X36: option_trm] :
( ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X23) = X36 )
=> ( ! [X54: trm] :
( ( vAPP(trm,option_trm,some_trm,X54) = X23 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X54)) != X36 ) )
=> ~ ( ( none_trm = X23 )
=> ( none_trm != X36 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Differentialo_Oelims) ).
thf(f3645,plain,
spl291_120,
inference(avatar_split_clause,[],[f2360,f3643]) ).
thf(f3643,plain,
( spl291_120
<=> ! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_120])]) ).
thf(f2360,plain,
! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0))) ) ),
inference(equality_resolution,[],[f1888]) ).
thf(f1888,plain,
! [X0: option_fml,X1: option_game] :
( ( none_game = X1 )
| ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0))) = X1 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1412]) ).
thf(f1412,plain,
! [X0: option_fml,X1: option_game] :
( ( ( none_game = X1 )
& ( none_fml = X0 ) )
| ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0))) = X1 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0)) = X0 ) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK117])],[f1004,f1411]) ).
thf(f1411,plain,
! [X0: option_fml,X1: option_game] :
( ? [X2: fml] :
( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
=> ( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0))) = X1 )
& ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1004,plain,
! [X0: option_fml,X1: option_game] :
( ( ( none_game = X1 )
& ( none_fml = X0 ) )
| ? [X2: fml] :
( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(flattening,[],[f1003]) ).
thf(f1003,plain,
! [X0: option_fml,X1: option_game] :
( ( ( none_game = X1 )
& ( none_fml = X0 ) )
| ? [X2: fml] :
( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) = X1 )
& ( vAPP(fml,option_fml,some_fml,X2) = X0 ) )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(ennf_transformation,[],[f921]) ).
thf(f921,plain,
! [X0: option_fml,X1: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = X1 )
=> ( ! [X2: fml] :
( ( vAPP(fml,option_fml,some_fml,X2) = X0 )
=> ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X2)) != X1 ) )
=> ~ ( ( none_fml = X0 )
=> ( none_game != X1 ) ) ) ),
inference(rectify,[],[f325]) ).
thf(f325,axiom,
! [X23: option_fml,X36: option_game] :
( ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X23) = X36 )
=> ( ! [X74: fml] :
( ( vAPP(fml,option_fml,some_fml,X74) = X23 )
=> ( vAPP(game,option_game,some_game,vAPP(fml,game,test,X74)) != X36 ) )
=> ~ ( ( none_fml = X23 )
=> ( none_game != X36 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Testo_Oelims) ).
thf(f3641,plain,
spl291_119,
inference(avatar_split_clause,[],[f1934,f3639]) ).
thf(f3639,plain,
( spl291_119
<=> ! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_119])]) ).
thf(f1934,plain,
! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1444]) ).
thf(f1444,plain,
! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ( ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK131])],[f1028,f1443]) ).
thf(f1443,plain,
! [X0: set_variable,X1: set_variable] :
( ? [X2: variable] :
( ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
& ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) ) )
=> ( ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X1) )
& ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1028,plain,
! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ? [X2: variable] :
( ( $true != vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
& ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) ) ) ),
inference(ennf_transformation,[],[f558]) ).
thf(f558,plain,
! [X0: set_variable,X1: set_variable] :
( ! [X2: variable] :
( ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0) )
=> ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) ) )
=> ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(fool_elimination,[],[f557]) ).
thf(f557,plain,
! [X0: set_variable,X1: set_variable] :
( ! [X2: variable] :
( vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X0)
=> vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X2),X1) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X20: set_variable,X21: set_variable] :
( ! [X22: variable] :
( vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X22),X20)
=> vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X22),X21) )
=> vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X20),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_subsetI) ).
thf(f3637,plain,
spl291_118,
inference(avatar_split_clause,[],[f1933,f3635]) ).
thf(f3635,plain,
( spl291_118
<=> ! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_118])]) ).
thf(f1933,plain,
! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
| ( $true = vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,vAPP(set_variable,variable,vAPP(set_variable,sTfun(set_variable,variable),sK131,X1),X0)),X0) ) ),
inference(cnf_transformation,[],[f1444]) ).
thf(f3633,plain,
spl291_117,
inference(avatar_split_clause,[],[f1932,f3631]) ).
thf(f1932,plain,
! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1442]) ).
thf(f1442,plain,
! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ( ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X1) )
& ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130])],[f1027,f1441]) ).
thf(f1441,plain,
! [X0: set_char,X1: set_char] :
( ? [X2: char] :
( ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
& ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) ) )
=> ( ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X1) )
& ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1027,plain,
! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ? [X2: char] :
( ( $true != vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
& ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) ) ) ),
inference(ennf_transformation,[],[f556]) ).
thf(f556,plain,
! [X0: set_char,X1: set_char] :
( ! [X2: char] :
( ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0) )
=> ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) ) )
=> ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ) ),
inference(fool_elimination,[],[f555]) ).
thf(f555,plain,
! [X0: set_char,X1: set_char] :
( ! [X2: char] :
( vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X0)
=> vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X2),X1) )
=> vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X20: set_char,X21: set_char] :
( ! [X22: char] :
( vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X22),X20)
=> vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X22),X21) )
=> vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X20),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_subsetI) ).
thf(f3629,plain,
spl291_116,
inference(avatar_split_clause,[],[f1931,f3627]) ).
thf(f1931,plain,
! [X0: set_char,X1: set_char] :
( ( $true = vAPP(set_char,$o,vAPP(set_char,sTfun(set_char,$o),ord_less_eq_set_char,X0),X1) )
| ( $true = vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,vAPP(set_char,char,vAPP(set_char,sTfun(set_char,char),sK130,X1),X0)),X0) ) ),
inference(cnf_transformation,[],[f1442]) ).
thf(f3611,plain,
spl291_115,
inference(avatar_split_clause,[],[f2765,f3609]) ).
thf(f3609,plain,
( spl291_115
<=> ! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) != vAPP(variable,trm,var,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_115])]) ).
thf(f2765,plain,
! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) != vAPP(variable,trm,var,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2764]) ).
thf(f2764,plain,
! [X0: variable,X1: variable] :
( ( vAPP(variable,trm,var,X0) != vAPP(variable,trm,var,X1) )
| ( $true = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2763]) ).
thf(f2763,plain,
! [X0: variable,X1: variable] :
( ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(variable,trm,var,X0)),vAPP(variable,trm,var,X1)) )
| ( $true = vAPP(variable,$o,vAPP(variable,sTfun(variable,$o),vEQ(variable),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1855]) ).
thf(f3579,plain,
spl291_114,
inference(avatar_split_clause,[],[f1850,f3577]) ).
thf(f3577,plain,
( spl291_114
<=> ! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_114])]) ).
thf(f1850,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1)) ),
inference(cnf_transformation,[],[f917]) ).
thf(f917,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1)) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X2: trm,X3: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X2)),vAPP(trm,option_trm,some_trm,X3)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Pluso_Osimps_I1_J) ).
thf(f3575,plain,
spl291_113,
inference(avatar_split_clause,[],[f1849,f3573]) ).
thf(f3573,plain,
( spl291_113
<=> ! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_113])]) ).
thf(f1849,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)) ),
inference(cnf_transformation,[],[f916]) ).
thf(f916,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X2: trm,X3: trm] : ( vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X2)),vAPP(trm,option_trm,some_trm,X3)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Timeso_Osimps_I1_J) ).
thf(f3571,plain,
spl291_112,
inference(avatar_split_clause,[],[f1848,f3569]) ).
thf(f3569,plain,
( spl291_112
<=> ! [X0: trm,X1: trm] : ( vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_112])]) ).
thf(f1848,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),X1)) ),
inference(cnf_transformation,[],[f915]) ).
thf(f915,plain,
! [X0: trm,X1: trm] : ( vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),vAPP(trm,option_trm,some_trm,X1)) = vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X0),X1)) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X2: trm,X3: trm] : ( vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X2)),vAPP(trm,option_trm,some_trm,X3)) = vAPP(fml,option_fml,some_fml,vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Geqo_Osimps_I1_J) ).
thf(f3563,plain,
spl291_111,
inference(avatar_split_clause,[],[f1901,f3561]) ).
thf(f3561,plain,
( spl291_111
<=> ! [X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_111])]) ).
thf(f1901,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0))) = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1422]) ).
thf(f3559,plain,
spl291_110,
inference(avatar_split_clause,[],[f1890,f3557]) ).
thf(f3557,plain,
( spl291_110
<=> ! [X0: option_game,X1: option_fml] :
( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_110])]) ).
thf(f1890,plain,
! [X0: option_game,X1: option_fml] :
( ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0))) = X0 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1416]) ).
thf(f3555,plain,
spl291_109,
inference(avatar_split_clause,[],[f2761,f3553]) ).
thf(f3553,plain,
( spl291_109
<=> ! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) = vAPP(char,trm,const,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_109])]) ).
thf(f2761,plain,
! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) = vAPP(char,trm,const,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2760]) ).
thf(f2760,plain,
! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) = vAPP(char,trm,const,X1) )
| ( $false = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2756]) ).
thf(f2756,plain,
! [X0: char,X1: char] :
( ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(char,trm,const,X0)),vAPP(char,trm,const,X1)) )
| ( $false = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1856]) ).
thf(f1856,plain,
! [X0: char,X1: char] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(char,trm,const,X0)),vAPP(char,trm,const,X1)) = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ),
inference(cnf_transformation,[],[f480]) ).
thf(f480,plain,
! [X0: char,X1: char] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(char,trm,const,X0)),vAPP(char,trm,const,X1)) = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ),
inference(fool_elimination,[],[f479]) ).
thf(f479,plain,
! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) = vAPP(char,trm,const,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f297]) ).
thf(f297,axiom,
! [X103: char,X104: char] :
( ( vAPP(char,trm,const,X103) = vAPP(char,trm,const,X104) )
= ( X103 = X104 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_trm_Oinject_I3_J) ).
thf(f3551,plain,
spl291_108,
inference(avatar_split_clause,[],[f2009,f3549]) ).
thf(f3549,plain,
( spl291_108
<=> ! [X2: variable,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(variable,trm,var,X2)) = vAPP(trm,option_trm,some_trm,vAPP(variable,trm,var,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_108])]) ).
thf(f2009,plain,
! [X2: variable,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(variable,trm,var,X2)) = vAPP(trm,option_trm,some_trm,vAPP(variable,trm,var,X2)) ),
inference(cnf_transformation,[],[f948]) ).
thf(f948,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(variable,trm,var,X2)) = vAPP(trm,option_trm,some_trm,vAPP(variable,trm,var,X2)) ),
inference(rectify,[],[f292]) ).
thf(f292,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X23: variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(variable,trm,var,X23)) = vAPP(trm,option_trm,some_trm,vAPP(variable,trm,var,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_usubstappt_Osimps_I1_J) ).
thf(f3547,plain,
spl291_107,
inference(avatar_split_clause,[],[f2008,f3545]) ).
thf(f3545,plain,
( spl291_107
<=> ! [X2: real,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(real,trm,number,X2)) = vAPP(trm,option_trm,some_trm,vAPP(real,trm,number,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_107])]) ).
thf(f2008,plain,
! [X2: real,X0: produc1418842292n_game,X1: set_variable] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(real,trm,number,X2)) = vAPP(trm,option_trm,some_trm,vAPP(real,trm,number,X2)) ),
inference(cnf_transformation,[],[f947]) ).
thf(f947,plain,
! [X0: produc1418842292n_game,X1: set_variable,X2: real] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(real,trm,number,X2)) = vAPP(trm,option_trm,some_trm,vAPP(real,trm,number,X2)) ),
inference(rectify,[],[f291]) ).
thf(f291,axiom,
! [X0: produc1418842292n_game,X1: set_variable,X86: real] : ( vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,X0),X1),vAPP(real,trm,number,X86)) = vAPP(trm,option_trm,some_trm,vAPP(real,trm,number,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_usubstappt_Osimps_I2_J) ).
thf(f3523,plain,
spl291_106,
inference(avatar_split_clause,[],[f2370,f3521]) ).
thf(f3521,plain,
( spl291_106
<=> ! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_106])]) ).
thf(f2370,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0))) ) ),
inference(equality_resolution,[],[f1897]) ).
thf(f1897,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0))) = X1 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1418]) ).
thf(f3519,plain,
spl291_105,
inference(avatar_split_clause,[],[f2362,f3517]) ).
thf(f3517,plain,
( spl291_105
<=> ! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_105])]) ).
thf(f2362,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) = vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0))) ) ),
inference(equality_resolution,[],[f1886]) ).
thf(f1886,plain,
! [X0: option_fml,X1: option_game] :
( ( none_fml = X0 )
| ( vAPP(game,option_game,some_game,vAPP(fml,game,test,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0))) = X1 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1412]) ).
thf(f3515,plain,
spl291_104,
inference(avatar_split_clause,[],[f2759,f3513]) ).
thf(f3513,plain,
( spl291_104
<=> ! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) != vAPP(char,trm,const,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_104])]) ).
thf(f2759,plain,
! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) != vAPP(char,trm,const,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2758]) ).
thf(f2758,plain,
! [X0: char,X1: char] :
( ( vAPP(char,trm,const,X0) != vAPP(char,trm,const,X1) )
| ( $true = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2757]) ).
thf(f2757,plain,
! [X0: char,X1: char] :
( ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(char,trm,const,X0)),vAPP(char,trm,const,X1)) )
| ( $true = vAPP(char,$o,vAPP(char,sTfun(char,$o),vEQ(char),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1856]) ).
thf(f3511,plain,
spl291_103,
inference(avatar_split_clause,[],[f2062,f3509]) ).
thf(f3509,plain,
( spl291_103
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK177,X2)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_103])]) ).
thf(f2062,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK177,X2)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1536]) ).
thf(f1536,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK177,X2)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f1534,f1535]) ).
thf(f1535,plain,
! [X2: option_trm] :
( ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK177,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f1534,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( none_trm = X0 )
& ( none_trm = X1 )
& ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ),
inference(rectify,[],[f1533]) ).
thf(f1533,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ( ( none_trm = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1299]) ).
thf(f1299,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ( ( none_trm = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3507,plain,
spl291_102,
inference(avatar_split_clause,[],[f2054,f3505]) ).
thf(f3505,plain,
( spl291_102
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK174,X2)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_102])]) ).
thf(f2054,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK174,X2)) = X2 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1527]) ).
thf(f1527,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( none_trm = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK174,X2)) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f1525,f1526]) ).
thf(f1526,plain,
! [X2: option_trm] :
( ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK174,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f1525,plain,
! [X0: option_trm,X1: option_trm,X2: option_trm] :
( ( ( none_trm = X0 )
& ( none_trm = X1 )
& ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ),
inference(rectify,[],[f1524]) ).
thf(f1524,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ( ( none_trm = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1296]) ).
thf(f1296,plain,
! [X2: option_trm,X1: option_trm,X0: option_trm] :
( ( ( none_trm = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3503,plain,
spl291_101,
inference(avatar_split_clause,[],[f2035,f3501]) ).
thf(f3501,plain,
( spl291_101
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK168,X2)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_101])]) ).
thf(f2035,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK168,X2)) = X2 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1509]) ).
thf(f1509,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ( ( none_fml = X0 )
& ( none_trm = X1 )
& ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK168,X2)) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f1507,f1508]) ).
thf(f1508,plain,
! [X2: option_trm] :
( ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK168,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f1507,plain,
! [X0: option_fml,X1: option_trm,X2: option_trm] :
( ( ( none_fml = X0 )
& ( none_trm = X1 )
& ? [X3: trm] : ( vAPP(trm,option_trm,some_trm,X3) = X2 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ),
inference(rectify,[],[f1506]) ).
thf(f1506,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ( ( none_fml = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1290]) ).
thf(f1290,plain,
! [X2: option_fml,X1: option_trm,X0: option_trm] :
( ( ( none_fml = X2 )
& ( none_trm = X1 )
& ? [X5: trm] : ( vAPP(trm,option_trm,some_trm,X5) = X0 ) )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3443,plain,
spl291_100,
inference(avatar_split_clause,[],[f2755,f3441]) ).
thf(f3441,plain,
( spl291_100
<=> ! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) = vAPP(trm,trm,differential,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_100])]) ).
thf(f2755,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) = vAPP(trm,trm,differential,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2754]) ).
thf(f2754,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) = vAPP(trm,trm,differential,X1) )
| ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2750]) ).
thf(f2750,plain,
! [X0: trm,X1: trm] :
( ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(trm,trm,differential,X0)),vAPP(trm,trm,differential,X1)) )
| ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1857]) ).
thf(f1857,plain,
! [X0: trm,X1: trm] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(trm,trm,differential,X0)),vAPP(trm,trm,differential,X1)) = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ),
inference(cnf_transformation,[],[f482]) ).
thf(f482,plain,
! [X0: trm,X1: trm] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(trm,trm,differential,X0)),vAPP(trm,trm,differential,X1)) = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ),
inference(fool_elimination,[],[f481]) ).
thf(f481,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) = vAPP(trm,trm,differential,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X59: trm,X60: trm] :
( ( vAPP(trm,trm,differential,X59) = vAPP(trm,trm,differential,X60) )
= ( X59 = X60 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_trm_Oinject_I7_J) ).
thf(f3439,plain,
spl291_99,
inference(avatar_split_clause,[],[f1970,f3437]) ).
thf(f3437,plain,
( spl291_99
<=> ! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK162,X0))) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_99])]) ).
thf(f1970,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK162,X0))) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) ) ),
inference(cnf_transformation,[],[f1491]) ).
thf(f1491,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK162,X0))) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f1052,f1490]) ).
thf(f1490,plain,
! [X0: option_trm > $o] :
( ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
=> ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK162,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1052,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) ) ),
inference(flattening,[],[f1051]) ).
thf(f1051,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) ) ),
inference(ennf_transformation,[],[f592]) ).
thf(f592,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,none_trm) )
=> ( ! [X2: trm] : ( $true = vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
=> ( $true = vAPP(option_trm,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f591]) ).
thf(f591,plain,
! [X0: option_trm > $o,X1: option_trm] :
( vAPP(option_trm,$o,X0,none_trm)
=> ( ! [X2: trm] : vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2))
=> vAPP(option_trm,$o,X0,X1) ) ),
inference(rectify,[],[f125]) ).
thf(f125,axiom,
! [X26: option_trm > $o,X66: option_trm] :
( vAPP(option_trm,$o,X26,none_trm)
=> ( ! [X22: trm] : vAPP(option_trm,$o,X26,vAPP(trm,option_trm,some_trm,X22))
=> vAPP(option_trm,$o,X26,X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_option_Oinducts) ).
thf(f3435,plain,
spl291_98,
inference(avatar_split_clause,[],[f1969,f3433]) ).
thf(f3433,plain,
( spl291_98
<=> ! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK161,X0))) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_98])]) ).
thf(f1969,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK161,X0))) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) ) ),
inference(cnf_transformation,[],[f1489]) ).
thf(f1489,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK161,X0))) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f1050,f1488]) ).
thf(f1488,plain,
! [X0: option_fml > $o] :
( ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
=> ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK161,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1050,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) ) ),
inference(flattening,[],[f1049]) ).
thf(f1049,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) ) ),
inference(ennf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,none_fml) )
=> ( ! [X2: fml] : ( $true = vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
=> ( $true = vAPP(option_fml,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f589]) ).
thf(f589,plain,
! [X0: option_fml > $o,X1: option_fml] :
( vAPP(option_fml,$o,X0,none_fml)
=> ( ! [X2: fml] : vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2))
=> vAPP(option_fml,$o,X0,X1) ) ),
inference(rectify,[],[f126]) ).
thf(f126,axiom,
! [X26: option_fml > $o,X66: option_fml] :
( vAPP(option_fml,$o,X26,none_fml)
=> ( ! [X22: fml] : vAPP(option_fml,$o,X26,vAPP(fml,option_fml,some_fml,X22))
=> vAPP(option_fml,$o,X26,X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_option_Oinducts) ).
thf(f3431,plain,
spl291_97,
inference(avatar_split_clause,[],[f1968,f3429]) ).
thf(f3429,plain,
( spl291_97
<=> ! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK160,X0))) )
| ( $true != vAPP(option_game,$o,X0,none_game) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_97])]) ).
thf(f1968,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK160,X0))) )
| ( $true != vAPP(option_game,$o,X0,none_game) ) ),
inference(cnf_transformation,[],[f1487]) ).
thf(f1487,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK160,X0))) )
| ( $true != vAPP(option_game,$o,X0,none_game) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f1048,f1486]) ).
thf(f1486,plain,
! [X0: option_game > $o] :
( ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
=> ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK160,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1048,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
| ( $true != vAPP(option_game,$o,X0,none_game) ) ),
inference(flattening,[],[f1047]) ).
thf(f1047,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
| ( $true != vAPP(option_game,$o,X0,none_game) ) ),
inference(ennf_transformation,[],[f588]) ).
thf(f588,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,none_game) )
=> ( ! [X2: game] : ( $true = vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
=> ( $true = vAPP(option_game,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f587]) ).
thf(f587,plain,
! [X0: option_game > $o,X1: option_game] :
( vAPP(option_game,$o,X0,none_game)
=> ( ! [X2: game] : vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2))
=> vAPP(option_game,$o,X0,X1) ) ),
inference(rectify,[],[f127]) ).
thf(f127,axiom,
! [X26: option_game > $o,X66: option_game] :
( vAPP(option_game,$o,X26,none_game)
=> ( ! [X22: game] : vAPP(option_game,$o,X26,vAPP(game,option_game,some_game,X22))
=> vAPP(option_game,$o,X26,X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_option_Oinducts) ).
thf(f3427,plain,
spl291_96,
inference(avatar_split_clause,[],[f1957,f3425]) ).
thf(f3425,plain,
( spl291_96
<=> ! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK149,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_96])]) ).
thf(f1957,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK149,X0))) ) ),
inference(cnf_transformation,[],[f1475]) ).
thf(f1475,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) )
| ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK149,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f1041,f1474]) ).
thf(f1474,plain,
! [X0: option_trm > $o] :
( ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
=> ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,vAPP(sTfun(option_trm,$o),trm,sK149,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1041,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) )
| ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) ) ),
inference(flattening,[],[f1040]) ).
thf(f1040,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ( $true = vAPP(option_trm,$o,X0,X1) )
| ( $true != vAPP(option_trm,$o,X0,none_trm) )
| ? [X2: trm] : ( $true != vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) ) ),
inference(ennf_transformation,[],[f576]) ).
thf(f576,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ! [X2: trm] : ( $true = vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2)) )
=> ( ( $true = vAPP(option_trm,$o,X0,none_trm) )
=> ( $true = vAPP(option_trm,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f575]) ).
thf(f575,plain,
! [X0: option_trm > $o,X1: option_trm] :
( ! [X2: trm] : vAPP(option_trm,$o,X0,vAPP(trm,option_trm,some_trm,X2))
=> ( vAPP(option_trm,$o,X0,none_trm)
=> vAPP(option_trm,$o,X0,X1) ) ),
inference(rectify,[],[f137]) ).
thf(f137,axiom,
! [X26: option_trm > $o,X68: option_trm] :
( ! [X54: trm] : vAPP(option_trm,$o,X26,vAPP(trm,option_trm,some_trm,X54))
=> ( vAPP(option_trm,$o,X26,none_trm)
=> vAPP(option_trm,$o,X26,X68) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Differentialo_Oinduct) ).
thf(f3423,plain,
spl291_95,
inference(avatar_split_clause,[],[f1946,f3421]) ).
thf(f3421,plain,
( spl291_95
<=> ! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK138,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_95])]) ).
thf(f1946,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK138,X0))) ) ),
inference(cnf_transformation,[],[f1458]) ).
thf(f1458,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) )
| ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK138,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138])],[f1037,f1457]) ).
thf(f1457,plain,
! [X0: option_fml > $o] :
( ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
=> ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,vAPP(sTfun(option_fml,$o),fml,sK138,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1037,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) )
| ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) ) ),
inference(flattening,[],[f1036]) ).
thf(f1036,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ( $true = vAPP(option_fml,$o,X0,X1) )
| ( $true != vAPP(option_fml,$o,X0,none_fml) )
| ? [X2: fml] : ( $true != vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) ) ),
inference(ennf_transformation,[],[f572]) ).
thf(f572,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ! [X2: fml] : ( $true = vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2)) )
=> ( ( $true = vAPP(option_fml,$o,X0,none_fml) )
=> ( $true = vAPP(option_fml,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f571]) ).
thf(f571,plain,
! [X0: option_fml > $o,X1: option_fml] :
( ! [X2: fml] : vAPP(option_fml,$o,X0,vAPP(fml,option_fml,some_fml,X2))
=> ( vAPP(option_fml,$o,X0,none_fml)
=> vAPP(option_fml,$o,X0,X1) ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X26: option_fml > $o,X68: option_fml] :
( ! [X74: fml] : vAPP(option_fml,$o,X26,vAPP(fml,option_fml,some_fml,X74))
=> ( vAPP(option_fml,$o,X26,none_fml)
=> vAPP(option_fml,$o,X26,X68) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Testo_Oinduct) ).
thf(f3419,plain,
spl291_94,
inference(avatar_split_clause,[],[f1945,f3417]) ).
thf(f3417,plain,
( spl291_94
<=> ! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,none_game) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK137,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_94])]) ).
thf(f1945,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,none_game) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK137,X0))) ) ),
inference(cnf_transformation,[],[f1456]) ).
thf(f1456,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,none_game) )
| ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK137,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f1035,f1455]) ).
thf(f1455,plain,
! [X0: option_game > $o] :
( ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
=> ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,vAPP(sTfun(option_game,$o),game,sK137,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1035,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,none_game) )
| ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) ) ),
inference(flattening,[],[f1034]) ).
thf(f1034,plain,
! [X0: option_game > $o,X1: option_game] :
( ( $true = vAPP(option_game,$o,X0,X1) )
| ( $true != vAPP(option_game,$o,X0,none_game) )
| ? [X2: game] : ( $true != vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) ) ),
inference(ennf_transformation,[],[f570]) ).
thf(f570,plain,
! [X0: option_game > $o,X1: option_game] :
( ! [X2: game] : ( $true = vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2)) )
=> ( ( $true = vAPP(option_game,$o,X0,none_game) )
=> ( $true = vAPP(option_game,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f569]) ).
thf(f569,plain,
! [X0: option_game > $o,X1: option_game] :
( ! [X2: game] : vAPP(option_game,$o,X0,vAPP(game,option_game,some_game,X2))
=> ( vAPP(option_game,$o,X0,none_game)
=> vAPP(option_game,$o,X0,X1) ) ),
inference(rectify,[],[f180]) ).
thf(f180,axiom,
! [X26: option_game > $o,X68: option_game] :
( ! [X73: game] : vAPP(option_game,$o,X26,vAPP(game,option_game,some_game,X73))
=> ( vAPP(option_game,$o,X26,none_game)
=> vAPP(option_game,$o,X26,X68) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Loopo_Oinduct) ).
thf(f3415,plain,
spl291_93,
inference(avatar_split_clause,[],[f1847,f3413]) ).
thf(f3413,plain,
( spl291_93
<=> ! [X0: variable,X1: trm] : ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),vAPP(trm,option_trm,some_trm,X1)) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_93])]) ).
thf(f1847,plain,
! [X0: variable,X1: trm] : ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),vAPP(trm,option_trm,some_trm,X1)) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1)) ),
inference(cnf_transformation,[],[f914]) ).
thf(f914,plain,
! [X0: variable,X1: trm] : ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),vAPP(trm,option_trm,some_trm,X1)) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1)) ),
inference(rectify,[],[f346]) ).
thf(f346,axiom,
! [X23: variable,X2: trm] : ( vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X23),vAPP(trm,option_trm,some_trm,X2)) = vAPP(game,option_game,some_game,vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X23),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_Assigno_Osimps_I1_J) ).
thf(f3411,plain,
~ spl291_92,
inference(avatar_split_clause,[],[f1744,f3408]) ).
thf(f1744,plain,
none_fml != vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),eta)),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
none_fml != vAPP(fml,option_fml,vAPP(set_variable,sTfun(fml,option_fml),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(fml,option_fml)),uSubst516392804stappf,sigma),ua),vAPP(trm,fml,vAPP(trm,sTfun(trm,fml),geq,theta),eta)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Geq_Oprems_I1_J) ).
thf(f3404,plain,
spl291_91,
inference(avatar_split_clause,[],[f2753,f3402]) ).
thf(f3402,plain,
( spl291_91
<=> ! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) != vAPP(trm,trm,differential,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_91])]) ).
thf(f2753,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) != vAPP(trm,trm,differential,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f2752]) ).
thf(f2752,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,trm,differential,X0) != vAPP(trm,trm,differential,X1) )
| ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f2751]) ).
thf(f2751,plain,
! [X0: trm,X1: trm] :
( ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),vAPP(trm,trm,differential,X0)),vAPP(trm,trm,differential,X1)) )
| ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1857]) ).
thf(f3396,plain,
spl291_90,
inference(avatar_split_clause,[],[f1900,f3394]) ).
thf(f3394,plain,
( spl291_90
<=> ! [X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_90])]) ).
thf(f1900,plain,
! [X0: option_trm,X1: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK120,X1),X0)) = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1422]) ).
thf(f3392,plain,
spl291_89,
inference(avatar_split_clause,[],[f1889,f3390]) ).
thf(f3390,plain,
( spl291_89
<=> ! [X0: option_game,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_89])]) ).
thf(f1889,plain,
! [X0: option_game,X1: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_game,fml,vAPP(option_fml,sTfun(option_game,fml),sK118,X1),X0)) = X1 )
| ( $true != vAPP(option_game,$o,vAPP(option_fml,sTfun(option_game,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1416]) ).
thf(f3388,plain,
spl291_88,
inference(avatar_split_clause,[],[f1813,f3386]) ).
thf(f3386,plain,
( spl291_88
<=> ! [X0: set_char] : ( vAPP(sTfun(char,$o),set_char,collect_char,vAPP(set_char,sTfun(char,$o),vAPP(sTfun(char,sTfun(set_char,$o)),sTfun(set_char,sTfun(char,$o)),cCOMB,member_char),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_88])]) ).
thf(f1813,plain,
! [X0: set_char] : ( vAPP(sTfun(char,$o),set_char,collect_char,vAPP(set_char,sTfun(char,$o),vAPP(sTfun(char,sTfun(set_char,$o)),sTfun(set_char,sTfun(char,$o)),cCOMB,member_char),X0)) = X0 ),
inference(cnf_transformation,[],[f462]) ).
thf(f462,plain,
! [X0: set_char] : ( vAPP(sTfun(char,$o),set_char,collect_char,vAPP(set_char,sTfun(char,$o),vAPP(sTfun(char,sTfun(set_char,$o)),sTfun(set_char,sTfun(char,$o)),cCOMB,member_char),X0)) = X0 ),
inference(fool_elimination,[],[f461]) ).
thf(f461,plain,
! [X0: set_char] :
( vAPP(sTfun(char,$o),set_char,collect_char,
^ [X1: char] : vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X1),X0)) = X0 ),
inference(rectify,[],[f50]) ).
thf(f50,axiom,
! [X20: set_char] :
( vAPP(sTfun(char,$o),set_char,collect_char,
^ [X25: char] : vAPP(set_char,$o,vAPP(char,sTfun(set_char,$o),member_char,X25),X20)) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(f3384,plain,
spl291_87,
inference(avatar_split_clause,[],[f1812,f3382]) ).
thf(f3382,plain,
( spl291_87
<=> ! [X0: set_variable] : ( vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP(set_variable,sTfun(variable,$o),vAPP(sTfun(variable,sTfun(set_variable,$o)),sTfun(set_variable,sTfun(variable,$o)),cCOMB,member_variable),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_87])]) ).
thf(f1812,plain,
! [X0: set_variable] : ( vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP(set_variable,sTfun(variable,$o),vAPP(sTfun(variable,sTfun(set_variable,$o)),sTfun(set_variable,sTfun(variable,$o)),cCOMB,member_variable),X0)) = X0 ),
inference(cnf_transformation,[],[f460]) ).
thf(f460,plain,
! [X0: set_variable] : ( vAPP(sTfun(variable,$o),set_variable,collect_variable,vAPP(set_variable,sTfun(variable,$o),vAPP(sTfun(variable,sTfun(set_variable,$o)),sTfun(set_variable,sTfun(variable,$o)),cCOMB,member_variable),X0)) = X0 ),
inference(fool_elimination,[],[f459]) ).
thf(f459,plain,
! [X0: set_variable] :
( vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X1: variable] : vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X1),X0)) = X0 ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X20: set_variable] :
( vAPP(sTfun(variable,$o),set_variable,collect_variable,
^ [X25: variable] : vAPP(set_variable,$o,vAPP(variable,sTfun(set_variable,$o),member_variable,X25),X20)) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).
thf(f3377,plain,
spl291_86,
inference(avatar_split_clause,[],[f1974,f3375]) ).
thf(f3375,plain,
( spl291_86
<=> ! [X0: set_variable,X1: set_variable] :
( ( X0 = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_86])]) ).
thf(f1974,plain,
! [X0: set_variable,X1: set_variable] :
( ( X0 = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(cnf_transformation,[],[f1057]) ).
thf(f1057,plain,
! [X0: set_variable,X1: set_variable] :
( ( X0 = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(flattening,[],[f1056]) ).
thf(f1056,plain,
! [X0: set_variable,X1: set_variable] :
( ( X0 = X1 )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0) )
| ( $true != vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) ) ),
inference(ennf_transformation,[],[f598]) ).
thf(f598,plain,
! [X0: set_variable,X1: set_variable] :
( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1) )
=> ( ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f597]) ).
thf(f597,plain,
! [X0: set_variable,X1: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X1)
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X29: set_variable,X30: set_variable] :
( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X29),X30)
=> ( vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X30),X29)
=> ( X29 = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dual__order_Oantisym) ).
thf(f3366,plain,
spl291_85,
inference(avatar_split_clause,[],[f2749,f3364]) ).
thf(f3364,plain,
( spl291_85
<=> ! [X0: trm,X1: trm] :
( ( X0 = X1 )
| ( vAPP(trm,option_trm,some_trm,X1) != vAPP(trm,option_trm,some_trm,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_85])]) ).
thf(f2749,plain,
! [X0: trm,X1: trm] :
( ( X0 = X1 )
| ( vAPP(trm,option_trm,some_trm,X1) != vAPP(trm,option_trm,some_trm,X0) ) ),
inference(equality_proxy_clausification,[],[f2748]) ).
thf(f2748,plain,
! [X0: trm,X1: trm] :
( ( X0 = X1 )
| ( $false = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ) ),
inference(equality_proxy_clausification,[],[f2744]) ).
thf(f2744,plain,
! [X0: trm,X1: trm] :
( ( $true = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) )
| ( $false = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ) ),
inference(binary_proxy_clausification,[],[f1858]) ).
thf(f1858,plain,
! [X0: trm,X1: trm] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ),
inference(cnf_transformation,[],[f484]) ).
thf(f484,plain,
! [X0: trm,X1: trm] : ( vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ),
inference(fool_elimination,[],[f483]) ).
thf(f483,plain,
! [X0: trm,X1: trm] :
( ( vAPP(trm,option_trm,some_trm,X1) = vAPP(trm,option_trm,some_trm,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X57: trm,X58: trm] :
( ( vAPP(trm,option_trm,some_trm,X57) = vAPP(trm,option_trm,some_trm,X58) )
= ( X57 = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_option_Oinject) ).
thf(f3358,plain,
spl291_84,
inference(avatar_split_clause,[],[f2369,f3356]) ).
thf(f3356,plain,
( spl291_84
<=> ! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_84])]) ).
thf(f2369,plain,
! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0)) = X0 ) ),
inference(equality_resolution,[],[f1898]) ).
thf(f1898,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0)) = X0 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1418]) ).
thf(f3354,plain,
spl291_83,
inference(avatar_split_clause,[],[f2361,f3352]) ).
thf(f3352,plain,
( spl291_83
<=> ! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_83])]) ).
thf(f2361,plain,
! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0)) = X0 ) ),
inference(equality_resolution,[],[f1887]) ).
thf(f1887,plain,
! [X0: option_fml,X1: option_game] :
( ( none_game = X1 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0)) = X0 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1412]) ).
thf(f3350,plain,
spl291_82,
inference(avatar_split_clause,[],[f2352,f3347]) ).
thf(f3347,plain,
( spl291_82
<=> ( vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu2),omega2),ua) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_82])]) ).
thf(f2352,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu2),omega2),ua) = $true,
inference(cnf_transformation,[],[f866]) ).
thf(f866,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu2),omega2),ua) = $true,
inference(fool_elimination,[],[f865]) ).
thf(f865,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu2),omega2),ua),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu2),omega2),ua),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Geq_Oprems_I2_J) ).
thf(f3345,plain,
spl291_81,
inference(avatar_split_clause,[],[f2351,f3342]) ).
thf(f3342,plain,
( spl291_81
<=> ( vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu),omega),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_81])]) ).
thf(f2351,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu),omega),u) = $true,
inference(cnf_transformation,[],[f864]) ).
thf(f864,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu),omega),u) = $true,
inference(fool_elimination,[],[f863]) ).
thf(f863,plain,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu),omega),u),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,nu),omega),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_vaouter) ).
thf(f3340,plain,
spl291_80,
inference(avatar_split_clause,[],[f1988,f3338]) ).
thf(f3338,plain,
( spl291_80
<=> ! [X0: variable > real,X1: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_80])]) ).
thf(f1988,plain,
! [X0: variable > real,X1: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X0),X1) ),
inference(cnf_transformation,[],[f626]) ).
thf(f626,plain,
! [X0: variable > real,X1: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X0),X1) ),
inference(fool_elimination,[],[f625]) ).
thf(f625,plain,
! [X0: variable > real,X1: set_variable] : vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X0),X0),X1),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X19: variable > real,X4: set_variable] : vAPP(set_variable,$o,vAPP(sTfun(variable,real),sTfun(set_variable,$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set_variable,$o)),denota1419872369iation,X19),X19),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Uvariation__refl) ).
thf(f3329,plain,
spl291_79,
inference(avatar_split_clause,[],[f2747,f3327]) ).
thf(f3327,plain,
( spl291_79
<=> ! [X0: trm,X1: trm] :
( ( X0 != X1 )
| ( vAPP(trm,option_trm,some_trm,X1) = vAPP(trm,option_trm,some_trm,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_79])]) ).
thf(f2747,plain,
! [X0: trm,X1: trm] :
( ( X0 != X1 )
| ( vAPP(trm,option_trm,some_trm,X1) = vAPP(trm,option_trm,some_trm,X0) ) ),
inference(equality_proxy_clausification,[],[f2746]) ).
thf(f2746,plain,
! [X0: trm,X1: trm] :
( ( X0 != X1 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ) ),
inference(equality_proxy_clausification,[],[f2745]) ).
thf(f2745,plain,
! [X0: trm,X1: trm] :
( ( $false = vAPP(trm,$o,vAPP(trm,sTfun(trm,$o),vEQ(trm),X0),X1) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),vAPP(trm,option_trm,some_trm,X1)),vAPP(trm,option_trm,some_trm,X0)) ) ),
inference(binary_proxy_clausification,[],[f1858]) ).
thf(f3293,plain,
spl291_78,
inference(avatar_split_clause,[],[f2371,f3291]) ).
thf(f3291,plain,
( spl291_78
<=> ! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_78])]) ).
thf(f2371,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)),X0)) = X0 ) ),
inference(equality_resolution,[],[f1896]) ).
thf(f1896,plain,
! [X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,vAPP(option_trm,sTfun(option_trm,trm),sK119,X1),X0)) = X0 )
| ( vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1418]) ).
thf(f3289,plain,
spl291_77,
inference(avatar_split_clause,[],[f2363,f3287]) ).
thf(f3287,plain,
( spl291_77
<=> ! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_77])]) ).
thf(f2363,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)),X0)) = X0 ) ),
inference(equality_resolution,[],[f1885]) ).
thf(f1885,plain,
! [X0: option_fml,X1: option_game] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,vAPP(option_game,sTfun(option_fml,fml),sK117,X1),X0)) = X0 )
| ( vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) != X1 ) ),
inference(cnf_transformation,[],[f1412]) ).
thf(f3285,plain,
spl291_76,
inference(avatar_split_clause,[],[f2083,f3283]) ).
thf(f3283,plain,
( spl291_76
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_76])]) ).
thf(f2083,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1554]) ).
thf(f3281,plain,
spl291_75,
inference(avatar_split_clause,[],[f2082,f3279]) ).
thf(f3279,plain,
( spl291_75
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_75])]) ).
thf(f2082,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP17,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1554]) ).
thf(f3277,plain,
spl291_74,
inference(avatar_split_clause,[],[f2072,f3275]) ).
thf(f3275,plain,
( spl291_74
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_74])]) ).
thf(f2072,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1545]) ).
thf(f3273,plain,
spl291_73,
inference(avatar_split_clause,[],[f2071,f3271]) ).
thf(f3271,plain,
( spl291_73
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_73])]) ).
thf(f2071,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1545]) ).
thf(f3269,plain,
spl291_72,
inference(avatar_split_clause,[],[f2064,f3267]) ).
thf(f3267,plain,
( spl291_72
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_72])]) ).
thf(f2064,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1536]) ).
thf(f3262,plain,
spl291_71,
inference(avatar_split_clause,[],[f2063,f3260]) ).
thf(f3260,plain,
( spl291_71
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_71])]) ).
thf(f2063,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP13,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1536]) ).
thf(f3258,plain,
spl291_70,
inference(avatar_split_clause,[],[f2056,f3256]) ).
thf(f3256,plain,
( spl291_70
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_70])]) ).
thf(f2056,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X0 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1527]) ).
thf(f3254,plain,
spl291_69,
inference(avatar_split_clause,[],[f2055,f3252]) ).
thf(f3252,plain,
( spl291_69
<=> ! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_69])]) ).
thf(f2055,plain,
! [X2: option_trm,X0: option_trm,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_trm,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1527]) ).
thf(f3250,plain,
spl291_68,
inference(avatar_split_clause,[],[f2045,f3248]) ).
thf(f3248,plain,
( spl291_68
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_fml = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_68])]) ).
thf(f2045,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_fml = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1518]) ).
thf(f3246,plain,
spl291_67,
inference(avatar_split_clause,[],[f2044,f3244]) ).
thf(f3244,plain,
( spl291_67
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_67])]) ).
thf(f2044,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1518]) ).
thf(f3242,plain,
spl291_66,
inference(avatar_split_clause,[],[f2037,f3240]) ).
thf(f3240,plain,
( spl291_66
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_fml = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_66])]) ).
thf(f2037,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_fml = X0 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1509]) ).
thf(f3238,plain,
spl291_65,
inference(avatar_split_clause,[],[f2036,f3236]) ).
thf(f3236,plain,
( spl291_65
<=> ! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_65])]) ).
thf(f2036,plain,
! [X2: option_trm,X0: option_fml,X1: option_trm] :
( ( none_trm = X1 )
| ( $true != vAPP(option_fml,$o,vAPP(option_trm,sTfun(option_fml,$o),vAPP(option_trm,sTfun(option_trm,sTfun(option_fml,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1509]) ).
thf(f3234,plain,
( spl291_64
| ~ spl291_7
| ~ spl291_55 ),
inference(avatar_split_clause,[],[f3190,f3181,f2961,f3232]) ).
thf(f3232,plain,
( spl291_64
<=> ! [X0: trm] : ( none_trm != vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_64])]) ).
thf(f2961,plain,
( spl291_7
<=> ! [X0: trm] : ( none_trm != vAPP(trm,option_trm,some_trm,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_7])]) ).
thf(f3181,plain,
( spl291_55
<=> ! [X0: trm] : ( vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_55])]) ).
thf(f3190,plain,
( ! [X0: trm] : ( none_trm != vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) )
| ~ spl291_7
| ~ spl291_55 ),
inference(superposition,[],[f2962,f3182]) ).
thf(f3182,plain,
( ! [X0: trm] : ( vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X0)) )
| ~ spl291_55 ),
inference(avatar_component_clause,[],[f3181]) ).
thf(f2962,plain,
( ! [X0: trm] : ( none_trm != vAPP(trm,option_trm,some_trm,X0) )
| ~ spl291_7 ),
inference(avatar_component_clause,[],[f2961]) ).
thf(f3230,plain,
spl291_63,
inference(avatar_split_clause,[],[f2258,f3228]) ).
thf(f3228,plain,
( spl291_63
<=> ! [X2: trm,X0: trm,X1: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_63])]) ).
thf(f2258,plain,
! [X2: trm,X3: trm,X0: trm,X1: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ),
inference(cnf_transformation,[],[f965]) ).
thf(f965,plain,
! [X0: trm,X1: trm,X2: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X10: trm,X11: trm,X6: trm,X7: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_trm_Odistinct_I37_J) ).
thf(f3226,plain,
spl291_62,
inference(avatar_split_clause,[],[f2257,f3224]) ).
thf(f3224,plain,
( spl291_62
<=> ! [X2: trm,X0: char,X1: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_62])]) ).
thf(f2257,plain,
! [X2: trm,X3: trm,X0: char,X1: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(cnf_transformation,[],[f964]) ).
thf(f964,plain,
! [X0: char,X1: trm,X2: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(rectify,[],[f307]) ).
thf(f307,axiom,
! [X99: char,X100: trm,X6: trm,X7: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_trm_Odistinct_I33_J) ).
thf(f3222,plain,
spl291_61,
inference(avatar_split_clause,[],[f2256,f3220]) ).
thf(f3220,plain,
( spl291_61
<=> ! [X2: trm,X0: char,X1: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_61])]) ).
thf(f2256,plain,
! [X2: trm,X3: trm,X0: char,X1: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(cnf_transformation,[],[f963]) ).
thf(f963,plain,
! [X0: char,X1: trm,X2: trm,X3: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X2),X3) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(rectify,[],[f308]) ).
thf(f308,axiom,
! [X99: char,X100: trm,X10: trm,X11: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_trm_Odistinct_I31_J) ).
thf(f3210,plain,
spl291_60,
inference(avatar_split_clause,[],[f1951,f3208]) ).
thf(f3208,plain,
( spl291_60
<=> ! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK142,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_60])]) ).
thf(f1951,plain,
! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK142,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f3206,plain,
spl291_59,
inference(avatar_split_clause,[],[f1950,f3204]) ).
thf(f3204,plain,
( spl291_59
<=> ! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK141,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_59])]) ).
thf(f1950,plain,
! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK141,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f3202,plain,
spl291_58,
inference(avatar_split_clause,[],[f1948,f3200]) ).
thf(f3200,plain,
( spl291_58
<=> ! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK140,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_58])]) ).
thf(f1948,plain,
! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK140,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1462]) ).
thf(f3198,plain,
( spl291_57
| ~ spl291_8
| ~ spl291_54 ),
inference(avatar_split_clause,[],[f3185,f3177,f2965,f3196]) ).
thf(f3196,plain,
( spl291_57
<=> ! [X0: fml] : ( none_game != vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_57])]) ).
thf(f2965,plain,
( spl291_8
<=> ! [X0: game] : ( none_game != vAPP(game,option_game,some_game,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_8])]) ).
thf(f3177,plain,
( spl291_54
<=> ! [X0: fml] : ( vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) = vAPP(game,option_game,some_game,vAPP(fml,game,test,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_54])]) ).
thf(f3185,plain,
( ! [X0: fml] : ( none_game != vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) )
| ~ spl291_8
| ~ spl291_54 ),
inference(superposition,[],[f2966,f3178]) ).
thf(f3178,plain,
( ! [X0: fml] : ( vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) = vAPP(game,option_game,some_game,vAPP(fml,game,test,X0)) )
| ~ spl291_54 ),
inference(avatar_component_clause,[],[f3177]) ).
thf(f2966,plain,
( ! [X0: game] : ( none_game != vAPP(game,option_game,some_game,X0) )
| ~ spl291_8 ),
inference(avatar_component_clause,[],[f2965]) ).
thf(f3194,plain,
spl291_56,
inference(avatar_split_clause,[],[f1947,f3192]) ).
thf(f3192,plain,
( spl291_56
<=> ! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK139,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_56])]) ).
thf(f1947,plain,
! [X0: trm > $o] :
( ( $true = vAPP(trm,$o,X0,vAPP(sTfun(trm,$o),trm,sK139,X0)) )
| ( $true != vAPP(sTfun(trm,$o),$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1462]) ).
thf(f3183,plain,
spl291_55,
inference(avatar_split_clause,[],[f1794,f3181]) ).
thf(f1794,plain,
! [X0: trm] : ( vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X0)) ),
inference(cnf_transformation,[],[f883]) ).
thf(f883,plain,
! [X0: trm] : ( vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X0)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X0)) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
! [X2: trm] : ( vAPP(option_trm,option_trm,uSubst716837505ntialo,vAPP(trm,option_trm,some_trm,X2)) = vAPP(trm,option_trm,some_trm,vAPP(trm,trm,differential,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Differentialo_Osimps_I1_J) ).
thf(f3179,plain,
spl291_54,
inference(avatar_split_clause,[],[f1793,f3177]) ).
thf(f1793,plain,
! [X0: fml] : ( vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) = vAPP(game,option_game,some_game,vAPP(fml,game,test,X0)) ),
inference(cnf_transformation,[],[f882]) ).
thf(f882,plain,
! [X0: fml] : ( vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X0)) = vAPP(game,option_game,some_game,vAPP(fml,game,test,X0)) ),
inference(rectify,[],[f337]) ).
thf(f337,axiom,
! [X5: fml] : ( vAPP(option_fml,option_game,uSubst1367128042_Testo,vAPP(fml,option_fml,some_fml,X5)) = vAPP(game,option_game,some_game,vAPP(fml,game,test,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Testo_Osimps_I1_J) ).
thf(f3164,plain,
spl291_53,
inference(avatar_split_clause,[],[f2007,f3162]) ).
thf(f3162,plain,
( spl291_53
<=> ! [X2: trm,X0: trm,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_53])]) ).
thf(f2007,plain,
! [X2: trm,X0: trm,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1) ),
inference(cnf_transformation,[],[f946]) ).
thf(f946,plain,
! [X0: trm,X1: trm,X2: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X6: trm,X7: trm,X59: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(trm,trm,differential,X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_trm_Odistinct_I41_J) ).
thf(f3160,plain,
spl291_52,
inference(avatar_split_clause,[],[f2006,f3158]) ).
thf(f3158,plain,
( spl291_52
<=> ! [X2: trm,X0: trm,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_52])]) ).
thf(f2006,plain,
! [X2: trm,X0: trm,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ),
inference(cnf_transformation,[],[f945]) ).
thf(f945,plain,
! [X0: trm,X1: trm,X2: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X0),X1) ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X10: trm,X11: trm,X59: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) != vAPP(trm,trm,differential,X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_trm_Odistinct_I39_J) ).
thf(f3156,plain,
spl291_51,
inference(avatar_split_clause,[],[f2005,f3154]) ).
thf(f3154,plain,
( spl291_51
<=> ! [X2: trm,X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_51])]) ).
thf(f2005,plain,
! [X2: trm,X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(cnf_transformation,[],[f944]) ).
thf(f944,plain,
! [X0: char,X1: trm,X2: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(rectify,[],[f304]) ).
thf(f304,axiom,
! [X103: char,X6: trm,X7: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_trm_Odistinct_I27_J) ).
thf(f3152,plain,
spl291_50,
inference(avatar_split_clause,[],[f2004,f3150]) ).
thf(f3150,plain,
( spl291_50
<=> ! [X2: trm,X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_50])]) ).
thf(f2004,plain,
! [X2: trm,X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(cnf_transformation,[],[f943]) ).
thf(f943,plain,
! [X0: char,X1: trm,X2: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(rectify,[],[f305]) ).
thf(f305,axiom,
! [X103: char,X10: trm,X11: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_trm_Odistinct_I25_J) ).
thf(f3148,plain,
spl291_49,
inference(avatar_split_clause,[],[f2003,f3146]) ).
thf(f3146,plain,
( spl291_49
<=> ! [X2: trm,X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_49])]) ).
thf(f2003,plain,
! [X2: trm,X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(cnf_transformation,[],[f942]) ).
thf(f942,plain,
! [X0: variable,X1: trm,X2: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(rectify,[],[f288]) ).
thf(f288,axiom,
! [X93: variable,X6: trm,X7: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(variable,trm,var,X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_trm_Odistinct_I9_J) ).
thf(f3144,plain,
spl291_48,
inference(avatar_split_clause,[],[f2002,f3142]) ).
thf(f3142,plain,
( spl291_48
<=> ! [X2: trm,X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_48])]) ).
thf(f2002,plain,
! [X2: trm,X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(cnf_transformation,[],[f941]) ).
thf(f941,plain,
! [X0: variable,X1: trm,X2: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(rectify,[],[f287]) ).
thf(f287,axiom,
! [X93: variable,X10: trm,X11: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) != vAPP(variable,trm,var,X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_trm_Odistinct_I7_J) ).
thf(f3140,plain,
spl291_47,
inference(avatar_split_clause,[],[f2001,f3138]) ).
thf(f3138,plain,
( spl291_47
<=> ! [X2: trm,X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_47])]) ).
thf(f2001,plain,
! [X2: trm,X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(cnf_transformation,[],[f940]) ).
thf(f940,plain,
! [X0: real,X1: trm,X2: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X1),X2) ),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
! [X57: real,X10: trm,X11: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),plus,X10),X11) != vAPP(real,trm,number,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_trm_Odistinct_I17_J) ).
thf(f3136,plain,
spl291_46,
inference(avatar_split_clause,[],[f2000,f3134]) ).
thf(f3134,plain,
( spl291_46
<=> ! [X2: trm,X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_46])]) ).
thf(f2000,plain,
! [X2: trm,X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(cnf_transformation,[],[f939]) ).
thf(f939,plain,
! [X0: real,X1: trm,X2: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X1),X2) ),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
! [X57: real,X6: trm,X7: trm] : ( vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X6),X7) != vAPP(real,trm,number,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_trm_Odistinct_I19_J) ).
thf(f3131,plain,
spl291_45,
inference(avatar_split_clause,[],[f1999,f3129]) ).
thf(f3129,plain,
( spl291_45
<=> ! [X2: trm,X0: char,X1: char] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_45])]) ).
thf(f1999,plain,
! [X2: trm,X0: char,X1: char] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(cnf_transformation,[],[f938]) ).
thf(f938,plain,
! [X0: char,X1: char,X2: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
! [X103: char,X99: char,X100: trm] : ( vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_trm_Odistinct_I23_J) ).
thf(f3127,plain,
spl291_44,
inference(avatar_split_clause,[],[f1998,f3125]) ).
thf(f3125,plain,
( spl291_44
<=> ! [X2: trm,X0: char,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_44])]) ).
thf(f1998,plain,
! [X2: trm,X0: char,X1: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(cnf_transformation,[],[f937]) ).
thf(f937,plain,
! [X0: char,X1: trm,X2: trm] : ( vAPP(trm,trm,differential,X2) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X0),X1) ),
inference(rectify,[],[f306]) ).
thf(f306,axiom,
! [X99: char,X100: trm,X59: trm] : ( vAPP(trm,trm,differential,X59) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_trm_Odistinct_I35_J) ).
thf(f3123,plain,
spl291_43,
inference(avatar_split_clause,[],[f1997,f3121]) ).
thf(f3121,plain,
( spl291_43
<=> ! [X2: trm,X0: variable,X1: char] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_43])]) ).
thf(f1997,plain,
! [X2: trm,X0: variable,X1: char] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(cnf_transformation,[],[f936]) ).
thf(f936,plain,
! [X0: variable,X1: char,X2: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(rectify,[],[f299]) ).
thf(f299,axiom,
! [X93: variable,X99: char,X100: trm] : ( vAPP(variable,trm,var,X93) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_trm_Odistinct_I5_J) ).
thf(f3119,plain,
spl291_42,
inference(avatar_split_clause,[],[f1996,f3117]) ).
thf(f3117,plain,
( spl291_42
<=> ! [X2: trm,X0: fml,X1: char] : ( vAPP(fml,game,test,X0) != vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_42])]) ).
thf(f1996,plain,
! [X2: trm,X0: fml,X1: char] : ( vAPP(fml,game,test,X0) != vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X1),X2) ),
inference(cnf_transformation,[],[f935]) ).
thf(f935,plain,
! [X0: fml,X1: char,X2: trm] : ( vAPP(fml,game,test,X0) != vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X1),X2) ),
inference(rectify,[],[f352]) ).
thf(f352,axiom,
! [X103: fml,X123: char,X124: trm] : ( vAPP(fml,game,test,X103) != vAPP(trm,game,vAPP(char,sTfun(trm,game),ode,X123),X124) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_game_Odistinct_I35_J) ).
thf(f3115,plain,
spl291_41,
inference(avatar_split_clause,[],[f1995,f3113]) ).
thf(f3113,plain,
( spl291_41
<=> ! [X2: fml,X0: variable,X1: trm] : ( vAPP(fml,game,test,X2) != vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_41])]) ).
thf(f1995,plain,
! [X2: fml,X0: variable,X1: trm] : ( vAPP(fml,game,test,X2) != vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1) ),
inference(cnf_transformation,[],[f934]) ).
thf(f934,plain,
! [X0: variable,X1: trm,X2: fml] : ( vAPP(fml,game,test,X2) != vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X0),X1) ),
inference(rectify,[],[f345]) ).
thf(f345,axiom,
! [X14: variable,X15: trm,X103: fml] : ( vAPP(fml,game,test,X103) != vAPP(trm,game,vAPP(variable,sTfun(trm,game),assign,X14),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_game_Odistinct_I15_J) ).
thf(f3111,plain,
spl291_40,
inference(avatar_split_clause,[],[f1994,f3109]) ).
thf(f3109,plain,
( spl291_40
<=> ! [X2: trm,X0: real,X1: char] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_40])]) ).
thf(f1994,plain,
! [X2: trm,X0: real,X1: char] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(cnf_transformation,[],[f933]) ).
thf(f933,plain,
! [X0: real,X1: char,X2: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X1),X2) ),
inference(rectify,[],[f301]) ).
thf(f301,axiom,
! [X57: real,X99: char,X100: trm] : ( vAPP(real,trm,number,X57) != vAPP(trm,trm,vAPP(char,sTfun(trm,trm),func,X99),X100) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_trm_Odistinct_I15_J) ).
thf(f3107,plain,
spl291_39,
inference(avatar_split_clause,[],[f1792,f3105]) ).
thf(f3105,plain,
( spl291_39
<=> ! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_39])]) ).
thf(f1792,plain,
! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(cnf_transformation,[],[f881]) ).
thf(f881,plain,
! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X71: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,vAPP(trm,option_trm,some_trm,X71)),none_trm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Timeso_Osimps_I3_J) ).
thf(f3103,plain,
spl291_38,
inference(avatar_split_clause,[],[f1791,f3101]) ).
thf(f3101,plain,
( spl291_38
<=> ! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_38])]) ).
thf(f1791,plain,
! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(cnf_transformation,[],[f880]) ).
thf(f880,plain,
! [X0: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X71: trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,vAPP(trm,option_trm,some_trm,X71)),none_trm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Pluso_Osimps_I3_J) ).
thf(f3099,plain,
spl291_37,
inference(avatar_split_clause,[],[f1790,f3097]) ).
thf(f3097,plain,
( spl291_37
<=> ! [X0: trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_37])]) ).
thf(f1790,plain,
! [X0: trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(cnf_transformation,[],[f879]) ).
thf(f879,plain,
! [X0: trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X0)),none_trm) ),
inference(rectify,[],[f151]) ).
thf(f151,axiom,
! [X71: trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,vAPP(trm,option_trm,some_trm,X71)),none_trm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Geqo_Osimps_I3_J) ).
thf(f3079,plain,
spl291_36,
inference(avatar_split_clause,[],[f1826,f3077]) ).
thf(f1826,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK50,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1360]) ).
thf(f1360,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK50,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f981,f1359]) ).
thf(f1359,plain,
! [X0: option_trm] :
( ? [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) = X0 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK50,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f981,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ? [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) = X0 ) ),
inference(ennf_transformation,[],[f896]) ).
thf(f896,plain,
! [X0: option_trm] :
( ! [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) != X0 )
=> ( none_trm = X0 ) ),
inference(rectify,[],[f138]) ).
thf(f138,axiom,
! [X23: option_trm] :
( ! [X54: trm] : ( vAPP(trm,option_trm,some_trm,X54) != X23 )
=> ( none_trm = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Differentialo_Ocases) ).
thf(f3075,plain,
spl291_35,
inference(avatar_split_clause,[],[f1824,f3073]) ).
thf(f1824,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK39,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f1349,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK39,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f978,f1348]) ).
thf(f1348,plain,
! [X0: option_fml] :
( ? [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) = X0 )
=> ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK39,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f978,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ? [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) = X0 ) ),
inference(ennf_transformation,[],[f894]) ).
thf(f894,plain,
! [X0: option_fml] :
( ! [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) != X0 )
=> ( none_fml = X0 ) ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X23: option_fml] :
( ! [X74: fml] : ( vAPP(fml,option_fml,some_fml,X74) != X23 )
=> ( none_fml = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Testo_Ocases) ).
thf(f3071,plain,
spl291_34,
inference(avatar_split_clause,[],[f2825,f3069]) ).
thf(f3069,plain,
( spl291_34
<=> ! [X0: option_fml] :
( ( none_fml = X0 )
| ( none_game != vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_34])]) ).
thf(f2825,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( none_game != vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) ) ),
inference(equality_proxy_clausification,[],[f2824]) ).
thf(f2824,plain,
! [X0: option_fml] :
( ( none_fml = X0 )
| ( $false = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ) ),
inference(equality_proxy_clausification,[],[f2820]) ).
thf(f2820,plain,
! [X0: option_fml] :
( ( $true = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),none_fml),X0) )
| ( $false = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ) ),
inference(binary_proxy_clausification,[],[f1807]) ).
thf(f1807,plain,
! [X0: option_fml] : ( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),none_fml),X0) = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ),
inference(cnf_transformation,[],[f450]) ).
thf(f450,plain,
! [X0: option_fml] : ( vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),none_fml),X0) = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ),
inference(fool_elimination,[],[f449]) ).
thf(f449,plain,
! [X0: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) )
= ( none_fml = X0 ) ),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
! [X5: option_fml] :
( ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X5) )
= ( none_fml = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Testo__undef) ).
thf(f3067,plain,
spl291_33,
inference(avatar_split_clause,[],[f1823,f3065]) ).
thf(f1823,plain,
! [X0: option_game] :
( ( none_game = X0 )
| ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK38,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1347]) ).
thf(f1347,plain,
! [X0: option_game] :
( ( none_game = X0 )
| ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK38,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f977,f1346]) ).
thf(f1346,plain,
! [X0: option_game] :
( ? [X1: game] : ( vAPP(game,option_game,some_game,X1) = X0 )
=> ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK38,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f977,plain,
! [X0: option_game] :
( ( none_game = X0 )
| ? [X1: game] : ( vAPP(game,option_game,some_game,X1) = X0 ) ),
inference(ennf_transformation,[],[f893]) ).
thf(f893,plain,
! [X0: option_game] :
( ! [X1: game] : ( vAPP(game,option_game,some_game,X1) != X0 )
=> ( none_game = X0 ) ),
inference(rectify,[],[f181]) ).
thf(f181,axiom,
! [X23: option_game] :
( ! [X73: game] : ( vAPP(game,option_game,some_game,X73) != X23 )
=> ( none_game = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Loopo_Ocases) ).
thf(f3063,plain,
spl291_32,
inference(avatar_split_clause,[],[f1822,f3061]) ).
thf(f1822,plain,
! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK37,X0)) = X0 )
| ( none_trm = X0 ) ),
inference(cnf_transformation,[],[f1345]) ).
thf(f1345,plain,
! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK37,X0)) = X0 )
| ( none_trm = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f976,f1344]) ).
thf(f1344,plain,
! [X0: option_trm] :
( ? [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) = X0 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,sK37,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f976,plain,
! [X0: option_trm] :
( ? [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) = X0 )
| ( none_trm = X0 ) ),
inference(ennf_transformation,[],[f892]) ).
thf(f892,plain,
! [X0: option_trm] :
( ( none_trm != X0 )
=> ~ ! [X1: trm] : ( vAPP(trm,option_trm,some_trm,X1) != X0 ) ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X36: option_trm] :
( ( none_trm != X36 )
=> ~ ! [X67: trm] : ( vAPP(trm,option_trm,some_trm,X67) != X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_option_Oexhaust) ).
thf(f3059,plain,
spl291_31,
inference(avatar_split_clause,[],[f1820,f3057]) ).
thf(f3057,plain,
( spl291_31
<=> ! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,the_trm,X0)) = X0 )
| ( none_trm = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_31])]) ).
thf(f1820,plain,
! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,the_trm,X0)) = X0 )
| ( none_trm = X0 ) ),
inference(cnf_transformation,[],[f974]) ).
thf(f974,plain,
! [X0: option_trm] :
( ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,the_trm,X0)) = X0 )
| ( none_trm = X0 ) ),
inference(ennf_transformation,[],[f890]) ).
thf(f890,plain,
! [X0: option_trm] :
( ( none_trm != X0 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,the_trm,X0)) = X0 ) ),
inference(rectify,[],[f175]) ).
thf(f175,axiom,
! [X66: option_trm] :
( ( none_trm != X66 )
=> ( vAPP(trm,option_trm,some_trm,vAPP(option_trm,trm,the_trm,X66)) = X66 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_option_Ocollapse) ).
thf(f3055,plain,
spl291_30,
inference(avatar_split_clause,[],[f1819,f3053]) ).
thf(f1819,plain,
! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK36,X0)) = X0 )
| ( none_fml = X0 ) ),
inference(cnf_transformation,[],[f1343]) ).
thf(f1343,plain,
! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK36,X0)) = X0 )
| ( none_fml = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f973,f1342]) ).
thf(f1342,plain,
! [X0: option_fml] :
( ? [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) = X0 )
=> ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,sK36,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f973,plain,
! [X0: option_fml] :
( ? [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) = X0 )
| ( none_fml = X0 ) ),
inference(ennf_transformation,[],[f889]) ).
thf(f889,plain,
! [X0: option_fml] :
( ( none_fml != X0 )
=> ~ ! [X1: fml] : ( vAPP(fml,option_fml,some_fml,X1) != X0 ) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X36: option_fml] :
( ( none_fml != X36 )
=> ~ ! [X67: fml] : ( vAPP(fml,option_fml,some_fml,X67) != X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_option_Oexhaust) ).
thf(f3051,plain,
spl291_29,
inference(avatar_split_clause,[],[f1817,f3049]) ).
thf(f3049,plain,
( spl291_29
<=> ! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,the_fml,X0)) = X0 )
| ( none_fml = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_29])]) ).
thf(f1817,plain,
! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,the_fml,X0)) = X0 )
| ( none_fml = X0 ) ),
inference(cnf_transformation,[],[f971]) ).
thf(f971,plain,
! [X0: option_fml] :
( ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,the_fml,X0)) = X0 )
| ( none_fml = X0 ) ),
inference(ennf_transformation,[],[f887]) ).
thf(f887,plain,
! [X0: option_fml] :
( ( none_fml != X0 )
=> ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,the_fml,X0)) = X0 ) ),
inference(rectify,[],[f176]) ).
thf(f176,axiom,
! [X66: option_fml] :
( ( none_fml != X66 )
=> ( vAPP(fml,option_fml,some_fml,vAPP(option_fml,fml,the_fml,X66)) = X66 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_option_Ocollapse) ).
thf(f3047,plain,
spl291_28,
inference(avatar_split_clause,[],[f1816,f3045]) ).
thf(f1816,plain,
! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK35,X0)) = X0 )
| ( none_game = X0 ) ),
inference(cnf_transformation,[],[f1341]) ).
thf(f1341,plain,
! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK35,X0)) = X0 )
| ( none_game = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f970,f1340]) ).
thf(f1340,plain,
! [X0: option_game] :
( ? [X1: game] : ( vAPP(game,option_game,some_game,X1) = X0 )
=> ( vAPP(game,option_game,some_game,vAPP(option_game,game,sK35,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f970,plain,
! [X0: option_game] :
( ? [X1: game] : ( vAPP(game,option_game,some_game,X1) = X0 )
| ( none_game = X0 ) ),
inference(ennf_transformation,[],[f886]) ).
thf(f886,plain,
! [X0: option_game] :
( ( none_game != X0 )
=> ~ ! [X1: game] : ( vAPP(game,option_game,some_game,X1) != X0 ) ),
inference(rectify,[],[f130]) ).
thf(f130,axiom,
! [X36: option_game] :
( ( none_game != X36 )
=> ~ ! [X67: game] : ( vAPP(game,option_game,some_game,X67) != X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_option_Oexhaust) ).
thf(f3043,plain,
spl291_27,
inference(avatar_split_clause,[],[f1814,f3041]) ).
thf(f3041,plain,
( spl291_27
<=> ! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,the_game,X0)) = X0 )
| ( none_game = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_27])]) ).
thf(f1814,plain,
! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,the_game,X0)) = X0 )
| ( none_game = X0 ) ),
inference(cnf_transformation,[],[f968]) ).
thf(f968,plain,
! [X0: option_game] :
( ( vAPP(game,option_game,some_game,vAPP(option_game,game,the_game,X0)) = X0 )
| ( none_game = X0 ) ),
inference(ennf_transformation,[],[f884]) ).
thf(f884,plain,
! [X0: option_game] :
( ( none_game != X0 )
=> ( vAPP(game,option_game,some_game,vAPP(option_game,game,the_game,X0)) = X0 ) ),
inference(rectify,[],[f190]) ).
thf(f190,axiom,
! [X66: option_game] :
( ( none_game != X66 )
=> ( vAPP(game,option_game,some_game,vAPP(option_game,game,the_game,X66)) = X66 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_option_Oexhaust__sel) ).
thf(f3039,plain,
spl291_26,
inference(avatar_split_clause,[],[f2823,f3037]) ).
thf(f3037,plain,
( spl291_26
<=> ! [X0: option_fml] :
( ( none_fml != X0 )
| ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_26])]) ).
thf(f2823,plain,
! [X0: option_fml] :
( ( none_fml != X0 )
| ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,X0) ) ),
inference(equality_proxy_clausification,[],[f2822]) ).
thf(f2822,plain,
! [X0: option_fml] :
( ( none_fml != X0 )
| ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ) ),
inference(equality_proxy_clausification,[],[f2821]) ).
thf(f2821,plain,
! [X0: option_fml] :
( ( $false = vAPP(option_fml,$o,vAPP(option_fml,sTfun(option_fml,$o),vEQ(option_fml),none_fml),X0) )
| ( $true = vAPP(option_game,$o,vAPP(option_game,sTfun(option_game,$o),vEQ(option_game),none_game),vAPP(option_fml,option_game,uSubst1367128042_Testo,X0)) ) ),
inference(binary_proxy_clausification,[],[f1807]) ).
thf(f3035,plain,
spl291_25,
inference(avatar_split_clause,[],[f1836,f3033]) ).
thf(f3033,plain,
( spl291_25
<=> ! [X0: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_25])]) ).
thf(f1836,plain,
! [X0: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X0) ),
inference(cnf_transformation,[],[f464]) ).
thf(f464,plain,
! [X0: set_variable] : ( $true = vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X0) ),
inference(fool_elimination,[],[f463]) ).
thf(f463,plain,
! [X0: set_variable] : vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X0),X0),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X20: set_variable] : vAPP(set_variable,$o,vAPP(set_variable,sTfun(set_variable,$o),ord_le282106107riable,X20),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_subset__refl) ).
thf(f3031,plain,
spl291_24,
inference(avatar_split_clause,[],[f1789,f3029]) ).
thf(f3029,plain,
( spl291_24
<=> ! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,none_trm),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_24])]) ).
thf(f1789,plain,
! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,none_trm),X0) ),
inference(cnf_transformation,[],[f878]) ).
thf(f878,plain,
! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,none_trm),X0) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
! [X3: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst918876924Timeso,none_trm),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Timeso_Osimps_I2_J) ).
thf(f3027,plain,
spl291_23,
inference(avatar_split_clause,[],[f1788,f3025]) ).
thf(f3025,plain,
( spl291_23
<=> ! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,none_trm),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_23])]) ).
thf(f1788,plain,
! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,none_trm),X0) ),
inference(cnf_transformation,[],[f877]) ).
thf(f877,plain,
! [X0: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,none_trm),X0) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X3: option_trm] : ( none_trm = vAPP(option_trm,option_trm,vAPP(option_trm,sTfun(option_trm,option_trm),uSubst141955042_Pluso,none_trm),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Pluso_Osimps_I2_J) ).
thf(f3023,plain,
spl291_22,
inference(avatar_split_clause,[],[f1787,f3021]) ).
thf(f3021,plain,
( spl291_22
<=> ! [X0: option_trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,none_trm),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_22])]) ).
thf(f1787,plain,
! [X0: option_trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,none_trm),X0) ),
inference(cnf_transformation,[],[f876]) ).
thf(f876,plain,
! [X0: option_trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,none_trm),X0) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X3: option_trm] : ( none_fml = vAPP(option_trm,option_fml,vAPP(option_trm,sTfun(option_trm,option_fml),uSubst152838031e_Geqo,none_trm),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Geqo_Osimps_I2_J) ).
thf(f3019,plain,
spl291_21,
inference(avatar_split_clause,[],[f1786,f3017]) ).
thf(f3017,plain,
( spl291_21
<=> ! [X0: char] : ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_21])]) ).
thf(f1786,plain,
! [X0: char] : ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),none_trm) ),
inference(cnf_transformation,[],[f875]) ).
thf(f875,plain,
! [X0: char] : ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X0),none_trm) ),
inference(rectify,[],[f348]) ).
thf(f348,axiom,
! [X23: char] : ( none_game = vAPP(option_trm,option_game,vAPP(char,sTfun(option_trm,option_game),uSubst1827052306e_ODEo,X23),none_trm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_ODEo_Osimps_I2_J) ).
thf(f3015,plain,
spl291_20,
inference(avatar_split_clause,[],[f1785,f3013]) ).
thf(f3013,plain,
( spl291_20
<=> ! [X0: variable] : ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_20])]) ).
thf(f1785,plain,
! [X0: variable] : ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),none_trm) ),
inference(cnf_transformation,[],[f874]) ).
thf(f874,plain,
! [X0: variable] : ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X0),none_trm) ),
inference(rectify,[],[f341]) ).
thf(f341,axiom,
! [X23: variable] : ( none_game = vAPP(option_trm,option_game,vAPP(variable,sTfun(option_trm,option_game),uSubst834381837ssigno,X23),none_trm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_Assigno_Osimps_I2_J) ).
thf(f3011,plain,
spl291_19,
inference(avatar_split_clause,[],[f2819,f3009]) ).
thf(f3009,plain,
( spl291_19
<=> ! [X0: option_trm] :
( ( none_trm = X0 )
| ( none_trm != vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_19])]) ).
thf(f2819,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( none_trm != vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) ) ),
inference(equality_proxy_clausification,[],[f2818]) ).
thf(f2818,plain,
! [X0: option_trm] :
( ( none_trm = X0 )
| ( $false = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ) ),
inference(equality_proxy_clausification,[],[f2814]) ).
thf(f2814,plain,
! [X0: option_trm] :
( ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),X0) )
| ( $false = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ) ),
inference(binary_proxy_clausification,[],[f1808]) ).
thf(f1808,plain,
! [X0: option_trm] : ( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),X0) = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ),
inference(cnf_transformation,[],[f452]) ).
thf(f452,plain,
! [X0: option_trm] : ( vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),X0) = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ),
inference(fool_elimination,[],[f451]) ).
thf(f451,plain,
! [X0: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) )
= ( none_trm = X0 ) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X2: option_trm] :
( ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X2) )
= ( none_trm = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Differentialo__undef) ).
thf(f3007,plain,
spl291_18,
inference(avatar_split_clause,[],[f1844,f3005]) ).
thf(f3005,plain,
( spl291_18
<=> ! [X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,differential,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_18])]) ).
thf(f1844,plain,
! [X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,differential,X1) ),
inference(cnf_transformation,[],[f911]) ).
thf(f911,plain,
! [X0: char,X1: trm] : ( vAPP(char,trm,const,X0) != vAPP(trm,trm,differential,X1) ),
inference(rectify,[],[f303]) ).
thf(f303,axiom,
! [X103: char,X59: trm] : ( vAPP(trm,trm,differential,X59) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_trm_Odistinct_I29_J) ).
thf(f3003,plain,
spl291_17,
inference(avatar_split_clause,[],[f1843,f3001]) ).
thf(f3001,plain,
( spl291_17
<=> ! [X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,differential,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_17])]) ).
thf(f1843,plain,
! [X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,differential,X1) ),
inference(cnf_transformation,[],[f910]) ).
thf(f910,plain,
! [X0: variable,X1: trm] : ( vAPP(variable,trm,var,X0) != vAPP(trm,trm,differential,X1) ),
inference(rectify,[],[f289]) ).
thf(f289,axiom,
! [X93: variable,X59: trm] : ( vAPP(trm,trm,differential,X59) != vAPP(variable,trm,var,X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_trm_Odistinct_I11_J) ).
thf(f2999,plain,
spl291_16,
inference(avatar_split_clause,[],[f2817,f2997]) ).
thf(f2997,plain,
( spl291_16
<=> ! [X0: option_trm] :
( ( none_trm != X0 )
| ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_16])]) ).
thf(f2817,plain,
! [X0: option_trm] :
( ( none_trm != X0 )
| ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,X0) ) ),
inference(equality_proxy_clausification,[],[f2816]) ).
thf(f2816,plain,
! [X0: option_trm] :
( ( none_trm != X0 )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ) ),
inference(equality_proxy_clausification,[],[f2815]) ).
thf(f2815,plain,
! [X0: option_trm] :
( ( $false = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),X0) )
| ( $true = vAPP(option_trm,$o,vAPP(option_trm,sTfun(option_trm,$o),vEQ(option_trm),none_trm),vAPP(option_trm,option_trm,uSubst716837505ntialo,X0)) ) ),
inference(binary_proxy_clausification,[],[f1808]) ).
thf(f2995,plain,
spl291_15,
inference(avatar_split_clause,[],[f1842,f2993]) ).
thf(f2993,plain,
( spl291_15
<=> ! [X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,differential,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_15])]) ).
thf(f1842,plain,
! [X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,differential,X1) ),
inference(cnf_transformation,[],[f909]) ).
thf(f909,plain,
! [X0: real,X1: trm] : ( vAPP(real,trm,number,X0) != vAPP(trm,trm,differential,X1) ),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
! [X57: real,X59: trm] : ( vAPP(trm,trm,differential,X59) != vAPP(real,trm,number,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_trm_Odistinct_I21_J) ).
thf(f2991,plain,
spl291_14,
inference(avatar_split_clause,[],[f1841,f2989]) ).
thf(f2989,plain,
( spl291_14
<=> ! [X0: variable,X1: char] : ( vAPP(variable,trm,var,X0) != vAPP(char,trm,const,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_14])]) ).
thf(f1841,plain,
! [X0: variable,X1: char] : ( vAPP(variable,trm,var,X0) != vAPP(char,trm,const,X1) ),
inference(cnf_transformation,[],[f908]) ).
thf(f908,plain,
! [X0: variable,X1: char] : ( vAPP(variable,trm,var,X0) != vAPP(char,trm,const,X1) ),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
! [X93: variable,X103: char] : ( vAPP(variable,trm,var,X93) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_trm_Odistinct_I3_J) ).
thf(f2987,plain,
spl291_13,
inference(avatar_split_clause,[],[f1840,f2985]) ).
thf(f2985,plain,
( spl291_13
<=> ! [X0: real,X1: char] : ( vAPP(real,trm,number,X0) != vAPP(char,trm,const,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_13])]) ).
thf(f1840,plain,
! [X0: real,X1: char] : ( vAPP(real,trm,number,X0) != vAPP(char,trm,const,X1) ),
inference(cnf_transformation,[],[f907]) ).
thf(f907,plain,
! [X0: real,X1: char] : ( vAPP(real,trm,number,X0) != vAPP(char,trm,const,X1) ),
inference(rectify,[],[f300]) ).
thf(f300,axiom,
! [X57: real,X103: char] : ( vAPP(real,trm,number,X57) != vAPP(char,trm,const,X103) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_trm_Odistinct_I13_J) ).
thf(f2983,plain,
spl291_12,
inference(avatar_split_clause,[],[f1839,f2981]) ).
thf(f2981,plain,
( spl291_12
<=> ! [X0: variable,X1: real] : ( vAPP(real,trm,number,X1) != vAPP(variable,trm,var,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_12])]) ).
thf(f1839,plain,
! [X0: variable,X1: real] : ( vAPP(real,trm,number,X1) != vAPP(variable,trm,var,X0) ),
inference(cnf_transformation,[],[f906]) ).
thf(f906,plain,
! [X0: variable,X1: real] : ( vAPP(real,trm,number,X1) != vAPP(variable,trm,var,X0) ),
inference(rectify,[],[f290]) ).
thf(f290,axiom,
! [X93: variable,X57: real] : ( vAPP(real,trm,number,X57) != vAPP(variable,trm,var,X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_trm_Odistinct_I1_J) ).
thf(f2979,plain,
spl291_11,
inference(avatar_split_clause,[],[f1784,f2977]) ).
thf(f1784,plain,
! [X0: trm] : ( vAPP(option_trm,trm,the_trm,vAPP(trm,option_trm,some_trm,X0)) = X0 ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: trm] : ( vAPP(option_trm,trm,the_trm,vAPP(trm,option_trm,some_trm,X0)) = X0 ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X57: trm] : ( vAPP(option_trm,trm,the_trm,vAPP(trm,option_trm,some_trm,X57)) = X57 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_option_Osel) ).
thf(f2975,plain,
spl291_10,
inference(avatar_split_clause,[],[f1783,f2973]) ).
thf(f1783,plain,
! [X0: fml] : ( vAPP(option_fml,fml,the_fml,vAPP(fml,option_fml,some_fml,X0)) = X0 ),
inference(cnf_transformation,[],[f872]) ).
thf(f872,plain,
! [X0: fml] : ( vAPP(option_fml,fml,the_fml,vAPP(fml,option_fml,some_fml,X0)) = X0 ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X57: fml] : ( vAPP(option_fml,fml,the_fml,vAPP(fml,option_fml,some_fml,X57)) = X57 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_option_Osel) ).
thf(f2971,plain,
spl291_9,
inference(avatar_split_clause,[],[f1782,f2969]) ).
thf(f1782,plain,
! [X0: game] : ( vAPP(option_game,game,the_game,vAPP(game,option_game,some_game,X0)) = X0 ),
inference(cnf_transformation,[],[f871]) ).
thf(f871,plain,
! [X0: game] : ( vAPP(option_game,game,the_game,vAPP(game,option_game,some_game,X0)) = X0 ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X57: game] : ( vAPP(option_game,game,the_game,vAPP(game,option_game,some_game,X57)) = X57 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_option_Osel) ).
thf(f2967,plain,
spl291_8,
inference(avatar_split_clause,[],[f1781,f2965]) ).
thf(f1781,plain,
! [X0: game] : ( none_game != vAPP(game,option_game,some_game,X0) ),
inference(cnf_transformation,[],[f870]) ).
thf(f870,plain,
! [X0: game] : ( none_game != vAPP(game,option_game,some_game,X0) ),
inference(rectify,[],[f136]) ).
thf(f136,axiom,
! [X57: game] : ( vAPP(game,option_game,some_game,X57) != none_game ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_option_Odistinct_I1_J) ).
thf(f2963,plain,
spl291_7,
inference(avatar_split_clause,[],[f1780,f2961]) ).
thf(f1780,plain,
! [X0: trm] : ( none_trm != vAPP(trm,option_trm,some_trm,X0) ),
inference(cnf_transformation,[],[f869]) ).
thf(f869,plain,
! [X0: trm] : ( none_trm != vAPP(trm,option_trm,some_trm,X0) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X57: trm] : ( none_trm != vAPP(trm,option_trm,some_trm,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_option_Odistinct_I1_J) ).
thf(f2959,plain,
spl291_6,
inference(avatar_split_clause,[],[f1779,f2957]) ).
thf(f2957,plain,
( spl291_6
<=> ! [X0: fml] : ( none_fml != vAPP(fml,option_fml,some_fml,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_6])]) ).
thf(f1779,plain,
! [X0: fml] : ( none_fml != vAPP(fml,option_fml,some_fml,X0) ),
inference(cnf_transformation,[],[f868]) ).
thf(f868,plain,
! [X0: fml] : ( none_fml != vAPP(fml,option_fml,some_fml,X0) ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X57: fml] : ( none_fml != vAPP(fml,option_fml,some_fml,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_option_Odistinct_I1_J) ).
thf(f2955,plain,
spl291_5,
inference(avatar_split_clause,[],[f1743,f2952]) ).
thf(f2952,plain,
( spl291_5
<=> ( none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,none_trm) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_5])]) ).
thf(f1743,plain,
none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,none_trm),
inference(cnf_transformation,[],[f10]) ).
thf(f10,axiom,
none_trm = vAPP(option_trm,option_trm,uSubst716837505ntialo,none_trm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Differentialo_Osimps_I2_J) ).
thf(f2950,plain,
spl291_4,
inference(avatar_split_clause,[],[f1742,f2947]) ).
thf(f2947,plain,
( spl291_4
<=> ( none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,none_fml) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_4])]) ).
thf(f1742,plain,
none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,none_fml),
inference(cnf_transformation,[],[f294]) ).
thf(f294,axiom,
none_game = vAPP(option_fml,option_game,uSubst1367128042_Testo,none_fml),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Testo_Osimps_I2_J) ).
thf(f2917,plain,
spl291_3,
inference(avatar_split_clause,[],[f356,f2915]) ).
thf(f2915,plain,
( spl291_3
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_3])]) ).
thf(f356,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2913,plain,
spl291_2,
inference(avatar_split_clause,[],[f1739,f2910]) ).
thf(f1739,plain,
none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta),
inference(cnf_transformation,[],[f867]) ).
thf(f867,plain,
none_trm = vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta),
inference(flattening,[],[f354]) ).
thf(f354,negated_conjecture,
~ ( ( none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta) ) ),
inference(negated_conjecture,[],[f353]) ).
thf(f353,conjecture,
none_trm != vAPP(trm,option_trm,vAPP(set_variable,sTfun(trm,option_trm),vAPP(produc1418842292n_game,sTfun(set_variable,sTfun(trm,option_trm)),uSubst516392818stappt,sigma),ua),theta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f2908,plain,
~ spl291_1,
inference(avatar_split_clause,[],[f355,f2905]) ).
thf(f2905,plain,
( spl291_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl291_1])]) ).
thf(f355,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP200^1 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 18:09:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (13563)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (13579)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.40 % (13575)WARNING: value z3 for option sas not known
% 0.14/0.40 % (13573)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (13574)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (13576)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (13575)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (13577)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.40 % (13580)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.46 % (13580)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48 % Exception at run slice level
% 0.20/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49 % Exception at run slice level
% 0.20/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49 % Exception at run slice level
% 0.20/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.50 % (13599)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.51 % (13603)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.51 % (13605)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.54 % (13599)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.54 % Exception at run slice level
% 0.20/0.54 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.55 % (13603)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.55 % (13619)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.53/0.61 % (13577)First to succeed.
% 1.93/0.65 % (13577)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13563"
% 1.93/0.65 % (13577)Refutation found. Thanks to Tanya!
% 1.93/0.65 % SZS status Theorem for theBenchmark
% 1.93/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.93/0.67 % (13577)------------------------------
% 1.93/0.67 % (13577)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.93/0.67 % (13577)Termination reason: Refutation
% 1.93/0.67
% 1.93/0.67 % (13577)Memory used [KB]: 4997
% 1.93/0.67 % (13577)Time elapsed: 0.256 s
% 1.93/0.67 % (13577)Instructions burned: 738 (million)
% 1.93/0.67 % (13563)Success in time 0.309 s
%------------------------------------------------------------------------------