TSTP Solution File: ITP177^1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP177^1 : 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 : n009.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 22:54:59 EDT 2024

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  620
% Syntax   : Number of formulae    : 1121 ( 336 unt; 381 typ;   0 def)
%            Number of atoms       : 4960 ( 886 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives : 1021 ( 404   ~; 263   |;  66   &;   0   @)
%                                         ( 118 <=>; 170  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :   53 (  52 usr)
%            Number of type conns  :  649 ( 648   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  400 ( 397 usr; 135 con; 0-6 aty)
%            Number of variables   : 1048 (   6   ^ 939   !;  88   ?;1048   :)
%                                         (  15  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    set_St761939237tant_a: $tType ).

thf(type_def_6,type,
    standard_Constant_a: $tType ).

thf(type_def_7,type,
    product_prod_b_b: $tType ).

thf(type_def_8,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_9,type,
    set_Pr1324126435od_b_b: $tType ).

thf(type_def_10,type,
    set_la1083530965_a_nat: $tType ).

thf(type_def_11,type,
    labele935650037_a_nat: $tType ).

thf(type_def_12,type,
    set_Pr1987088711_a_nat: $tType ).

thf(type_def_13,type,
    produc1213276845od_b_b: $tType ).

thf(type_def_14,type,
    b: $tType ).

thf(type_def_15,type,
    set_Pr1906739389_b_b_b: $tType ).

thf(type_def_16,type,
    set_Product_prod_b_b: $tType ).

thf(type_def_17,type,
    set_Pr357419743_b_b_b: $tType ).

thf(type_def_18,type,
    set_b: $tType ).

thf(type_def_19,type,
    set_Pr1649131859tant_a: $tType ).

thf(type_def_20,type,
    set_Pr2109276827od_b_b: $tType ).

thf(type_def_21,type,
    set_Pr924198087_a_nat: $tType ).

thf(type_def_22,type,
    set_Pr2007082183od_b_b: $tType ).

thf(type_def_23,type,
    labele1644675410od_b_b: $tType ).

thf(type_def_24,type,
    labele1835558936od_b_b: $tType ).

thf(type_def_25,type,
    labele1159362096nt_a_b: $tType ).

thf(type_def_26,type,
    allego510293162tant_a: $tType ).

thf(type_def_27,type,
    set_Pr1190604087od_b_b: $tType ).

thf(type_def_28,type,
    set_Pr1021918435od_b_b: $tType ).

thf(type_def_29,type,
    set_Pr2106913242_nat_b: $tType ).

thf(type_def_30,type,
    labele1322729112_a_nat: $tType ).

thf(type_def_31,type,
    set_Pr812188767_nat_b: $tType ).

thf(type_def_32,type,
    set_Pr197580003_a_nat: $tType ).

thf(type_def_33,type,
    produc90515391tant_a: $tType ).

thf(type_def_34,type,
    produc970027067od_b_b: $tType ).

thf(type_def_35,type,
    produc1084374401od_b_b: $tType ).

thf(type_def_36,type,
    produc1168037607od_b_b: $tType ).

thf(type_def_37,type,
    produc644633773od_b_b: $tType ).

thf(type_def_38,type,
    produc1871334759_a_nat: $tType ).

thf(type_def_39,type,
    produc1398946881nt_a_b: $tType ).

thf(type_def_40,type,
    produc1990339951od_b_b: $tType ).

thf(type_def_41,type,
    produc276146823_b_b_b: $tType ).

thf(type_def_42,type,
    produc1169496899od_b_b: $tType ).

thf(type_def_43,type,
    produc398057191_a_nat: $tType ).

thf(type_def_44,type,
    produc1485083751od_b_b: $tType ).

thf(type_def_45,type,
    produc845793663_nat_b: $tType ).

thf(type_def_46,type,
    produc1052326083od_b_b: $tType ).

thf(type_def_47,type,
    produc2112523263_b_b_b: $tType ).

thf(type_def_48,type,
    produc1605346267od_b_b: $tType ).

thf(type_def_49,type,
    produc255402447od_b_b: $tType ).

thf(type_def_50,type,
    set_Pr2134561957od_b_b: $tType ).

thf(type_def_51,type,
    set_Pr1954438265od_b_b: $tType ).

thf(type_def_52,type,
    set_Pr667377223od_b_b: $tType ).

thf(type_def_53,type,
    set_Pr1071216121od_b_b: $tType ).

thf(type_def_54,type,
    set_Pr2060523537od_b_b: $tType ).

thf(type_def_55,type,
    set_Pr1646010159_a_nat: $tType ).

thf(type_def_56,type,
    set_Pr621705391od_b_b: $tType ).

thf(type_def_57,type,
    set_Pr154086431tant_a: $tType ).

thf(func_def_0,type,
    set_Pr197580003_a_nat: $tType ).

thf(func_def_1,type,
    set_Pr924198087_a_nat: $tType ).

thf(func_def_2,type,
    produc398057191_a_nat: $tType ).

thf(func_def_3,type,
    set_Pr1954438265od_b_b: $tType ).

thf(func_def_4,type,
    produc1169496899od_b_b: $tType ).

thf(func_def_5,type,
    set_Pr1190604087od_b_b: $tType ).

thf(func_def_6,type,
    produc1084374401od_b_b: $tType ).

thf(func_def_7,type,
    labele1322729112_a_nat: $tType ).

thf(func_def_8,type,
    set_Pr667377223od_b_b: $tType ).

thf(func_def_9,type,
    produc1485083751od_b_b: $tType ).

thf(func_def_10,type,
    set_Pr2109276827od_b_b: $tType ).

thf(func_def_11,type,
    set_Pr1646010159_a_nat: $tType ).

thf(func_def_12,type,
    set_Pr812188767_nat_b: $tType ).

thf(func_def_13,type,
    produc970027067od_b_b: $tType ).

thf(func_def_14,type,
    produc845793663_nat_b: $tType ).

thf(func_def_15,type,
    set_Pr1987088711_a_nat: $tType ).

thf(func_def_16,type,
    produc1871334759_a_nat: $tType ).

thf(func_def_17,type,
    produc1398946881nt_a_b: $tType ).

thf(func_def_18,type,
    labele1644675410od_b_b: $tType ).

thf(func_def_19,type,
    set_Pr1071216121od_b_b: $tType ).

thf(func_def_20,type,
    set_Pr2134561957od_b_b: $tType ).

thf(func_def_21,type,
    set_Pr1021918435od_b_b: $tType ).

thf(func_def_22,type,
    produc1052326083od_b_b: $tType ).

thf(func_def_23,type,
    produc1990339951od_b_b: $tType ).

thf(func_def_24,type,
    produc644633773od_b_b: $tType ).

thf(func_def_25,type,
    set_Pr2060523537od_b_b: $tType ).

thf(func_def_26,type,
    set_Pr1906739389_b_b_b: $tType ).

thf(func_def_27,type,
    produc1605346267od_b_b: $tType ).

thf(func_def_28,type,
    produc276146823_b_b_b: $tType ).

thf(func_def_29,type,
    set_Pr154086431tant_a: $tType ).

thf(func_def_30,type,
    set_Pr1324126435od_b_b: $tType ).

thf(func_def_31,type,
    produc90515391tant_a: $tType ).

thf(func_def_32,type,
    labele1835558936od_b_b: $tType ).

thf(func_def_33,type,
    set_Pr2007082183od_b_b: $tType ).

thf(func_def_34,type,
    produc1213276845od_b_b: $tType ).

thf(func_def_35,type,
    set_la1083530965_a_nat: $tType ).

thf(func_def_36,type,
    produc1168037607od_b_b: $tType ).

thf(func_def_37,type,
    labele935650037_a_nat: $tType ).

thf(func_def_38,type,
    set_Pr1649131859tant_a: $tType ).

thf(func_def_39,type,
    allego510293162tant_a: $tType ).

thf(func_def_40,type,
    labele1159362096nt_a_b: $tType ).

thf(func_def_41,type,
    set_Pr621705391od_b_b: $tType ).

thf(func_def_42,type,
    set_Pr357419743_b_b_b: $tType ).

thf(func_def_43,type,
    produc255402447od_b_b: $tType ).

thf(func_def_44,type,
    produc2112523263_b_b_b: $tType ).

thf(func_def_45,type,
    set_St761939237tant_a: $tType ).

thf(func_def_46,type,
    set_Pr2106913242_nat_b: $tType ).

thf(func_def_47,type,
    set_Product_prod_b_b: $tType ).

thf(func_def_48,type,
    standard_Constant_a: $tType ).

thf(func_def_49,type,
    product_prod_b_b: $tType ).

thf(func_def_50,type,
    set_b: $tType ).

thf(func_def_51,type,
    b: $tType ).

thf(func_def_52,type,
    bNF_Gr1272216980od_b_b: set_St761939237tant_a > ( standard_Constant_a > product_prod_b_b ) > set_Pr1324126435od_b_b ).

thf(func_def_53,type,
    bNF_Gr996500706_a_nat: set_la1083530965_a_nat > ( labele935650037_a_nat > labele935650037_a_nat ) > set_Pr1987088711_a_nat ).

thf(func_def_54,type,
    bNF_Gr492676974_b_b_b: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > set_Pr1906739389_b_b_b ).

thf(func_def_55,type,
    bNF_Gr521784954_b_b_b: set_Product_prod_b_b > ( product_prod_b_b > b ) > set_Pr357419743_b_b_b ).

thf(func_def_56,type,
    bNF_Gr230160332tant_a: set_b > ( b > standard_Constant_a ) > set_Pr1649131859tant_a ).

thf(func_def_57,type,
    bNF_Gr_b_b: set_b > ( b > b ) > set_Product_prod_b_b ).

thf(func_def_58,type,
    equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).

thf(func_def_59,type,
    equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).

thf(func_def_60,type,
    equiv_291114781_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).

thf(func_def_61,type,
    equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).

thf(func_def_62,type,
    equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).

thf(func_def_63,type,
    hilbert_Eps_b: ( b > $o ) > b ).

thf(func_def_64,type,
    if_b: $o > b > b > b ).

thf(func_def_65,type,
    standard_S_Idt_a: standard_Constant_a ).

thf(func_def_66,type,
    getRel59882567od_b_b: standard_Constant_a > labele1644675410od_b_b > set_Pr2109276827od_b_b ).

thf(func_def_67,type,
    getRel118493133od_b_b: standard_Constant_a > labele1835558936od_b_b > set_Pr2007082183od_b_b ).

thf(func_def_68,type,
    getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).

thf(func_def_69,type,
    semant55076487nt_a_b: labele1159362096nt_a_b > allego510293162tant_a > set_Product_prod_b_b ).

thf(func_def_70,type,
    edge_p1817988046tant_a: set_Pr1906739389_b_b_b > set_Pr1190604087od_b_b > set_Pr1324126435od_b_b > $o ).

thf(func_def_71,type,
    edge_p1969196346tant_a: set_Pr357419743_b_b_b > set_Pr1021918435od_b_b > set_Pr1324126435od_b_b > $o ).

thf(func_def_72,type,
    edge_p1384198690tant_a: set_Product_prod_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).

thf(func_def_73,type,
    graph_714568023_nat_b: labele935650037_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o ).

thf(func_def_74,type,
    graph_726202286_nat_b: labele1322729112_a_nat > labele1159362096nt_a_b > set_Pr812188767_nat_b > $o ).

thf(func_def_75,type,
    graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).

thf(func_def_76,type,
    graph_1309249505nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).

thf(func_def_77,type,
    labele27098724_a_nat: set_Pr197580003_a_nat > set_Pr1987088711_a_nat > labele1322729112_a_nat ).

thf(func_def_78,type,
    labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).

thf(func_def_79,type,
    labele2032816061od_b_b: labele1644675410od_b_b > set_Pr1190604087od_b_b ).

thf(func_def_80,type,
    labele372159959od_b_b: labele1835558936od_b_b > set_Pr1021918435od_b_b ).

thf(func_def_81,type,
    labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).

thf(func_def_82,type,
    labele595103470od_b_b: labele1644675410od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_83,type,
    labele442485990od_b_b: labele1835558936od_b_b > set_Product_prod_b_b ).

thf(func_def_84,type,
    labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).

thf(func_def_85,type,
    map_gr1495881666tant_a: set_Pr1906739389_b_b_b > labele1644675410od_b_b > labele1159362096nt_a_b ).

thf(func_def_86,type,
    map_gr1314489926tant_a: set_Pr357419743_b_b_b > labele1835558936od_b_b > labele1159362096nt_a_b ).

thf(func_def_87,type,
    map_gr926947118tant_a: set_Product_prod_b_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).

thf(func_def_88,type,
    restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).

thf(func_def_89,type,
    bot_bo1160111033tant_a: set_St761939237tant_a ).

thf(func_def_90,type,
    bot_bo2122869057_a_nat: set_la1083530965_a_nat ).

thf(func_def_91,type,
    bot_bo1653310327_a_nat: set_Pr197580003_a_nat ).

thf(func_def_92,type,
    bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).

thf(func_def_93,type,
    bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).

thf(func_def_94,type,
    bot_bo1973379891_a_nat: set_Pr924198087_a_nat ).

thf(func_def_95,type,
    bot_bo1113554635_nat_b: set_Pr812188767_nat_b ).

thf(func_def_96,type,
    bot_bo1343651123od_b_b: set_Product_prod_b_b ).

thf(func_def_97,type,
    bot_bot_set_b: set_b ).

thf(func_def_98,type,
    ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).

thf(func_def_99,type,
    ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).

thf(func_def_100,type,
    ord_le1484132922_nat_b: set_Pr2106913242_nat_b > set_Pr2106913242_nat_b > $o ).

thf(func_def_101,type,
    ord_le107617383_a_nat: set_Pr924198087_a_nat > set_Pr924198087_a_nat > $o ).

thf(func_def_102,type,
    ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).

thf(func_def_103,type,
    ord_less_eq_set_b: set_b > set_b > $o ).

thf(func_def_104,type,
    produc342647tant_a: standard_Constant_a > standard_Constant_a > produc90515391tant_a ).

thf(func_def_105,type,
    produc1788032435od_b_b: standard_Constant_a > produc970027067od_b_b > produc1084374401od_b_b ).

thf(func_def_106,type,
    produc618266719od_b_b: standard_Constant_a > produc1168037607od_b_b > produc644633773od_b_b ).

thf(func_def_107,type,
    produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).

thf(func_def_108,type,
    produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).

thf(func_def_109,type,
    produc1569511545nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > produc1398946881nt_a_b ).

thf(func_def_110,type,
    produc449289715od_b_b: produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b ).

thf(func_def_111,type,
    produc1597690145od_b_b: produc1213276845od_b_b > product_prod_b_b > produc1990339951od_b_b ).

thf(func_def_112,type,
    produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).

thf(func_def_113,type,
    produc401731773od_b_b: produc1871334759_a_nat > produc1213276845od_b_b > produc1169496899od_b_b ).

thf(func_def_114,type,
    produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat ).

thf(func_def_115,type,
    produc590959831od_b_b: produc1871334759_a_nat > product_prod_b_b > produc1485083751od_b_b ).

thf(func_def_116,type,
    produc2059954415_nat_b: produc1871334759_a_nat > b > produc845793663_nat_b ).

thf(func_def_117,type,
    produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b ).

thf(func_def_118,type,
    produc546497367od_b_b: product_prod_b_b > product_prod_b_b > produc1168037607od_b_b ).

thf(func_def_119,type,
    produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).

thf(func_def_120,type,
    produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).

thf(func_def_121,type,
    produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).

thf(func_def_122,type,
    product_Pair_b_b: b > b > product_prod_b_b ).

thf(func_def_123,type,
    id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_124,type,
    id_on_250271696od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b ).

thf(func_def_125,type,
    id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat ).

thf(func_def_126,type,
    id_on_2019020932od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b ).

thf(func_def_127,type,
    id_on_b: set_b > set_Product_prod_b_b ).

thf(func_def_128,type,
    image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).

thf(func_def_129,type,
    image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).

thf(func_def_130,type,
    image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_131,type,
    image_1397930469od_b_b: set_Pr2134561957od_b_b > set_Pr1324126435od_b_b > set_Product_prod_b_b ).

thf(func_def_132,type,
    image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).

thf(func_def_133,type,
    image_480774529od_b_b: set_Pr1954438265od_b_b > set_Pr1987088711_a_nat > set_Pr1324126435od_b_b ).

thf(func_def_134,type,
    image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_135,type,
    image_1214223635od_b_b: set_Pr667377223od_b_b > set_Pr1987088711_a_nat > set_Product_prod_b_b ).

thf(func_def_136,type,
    image_924992811_nat_b: set_Pr812188767_nat_b > set_Pr1987088711_a_nat > set_b ).

thf(func_def_137,type,
    image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b ).

thf(func_def_138,type,
    image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_139,type,
    image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).

thf(func_def_140,type,
    image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).

thf(func_def_141,type,
    image_1749766139_a_nat: set_Pr1646010159_a_nat > set_b > set_Pr1987088711_a_nat ).

thf(func_def_142,type,
    image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).

thf(func_def_143,type,
    image_b_b: set_Product_prod_b_b > set_b > set_b ).

thf(func_def_144,type,
    refl_o1031343860_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat > $o ).

thf(func_def_145,type,
    refl_o1921098222od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).

thf(func_def_146,type,
    refl_o1213627494_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).

thf(func_def_147,type,
    refl_o2134473190od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).

thf(func_def_148,type,
    refl_on_b: set_b > set_Product_prod_b_b > $o ).

thf(func_def_149,type,
    relcom883816262od_b_b: set_Pr154086431tant_a > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_150,type,
    relcom1823941168od_b_b: set_Pr1324126435od_b_b > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_151,type,
    relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_152,type,
    relcom112561144od_b_b: set_Pr1649131859tant_a > set_Pr1324126435od_b_b > set_Pr621705391od_b_b ).

thf(func_def_153,type,
    relcomp_b_b_b: set_Product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_154,type,
    agree_221379389_a_b_b: labele1159362096nt_a_b > set_Product_prod_b_b > set_Product_prod_b_b > $o ).

thf(func_def_155,type,
    conseq956760372_nat_b: set_Pr1987088711_a_nat > labele1159362096nt_a_b > $o ).

thf(func_def_156,type,
    extens1554515172_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o ).

thf(func_def_157,type,
    extens1779443913_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).

thf(func_def_158,type,
    mainta1604381365_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > $o ).

thf(func_def_159,type,
    mainta374363448_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > $o ).

thf(func_def_160,type,
    collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).

thf(func_def_161,type,
    collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).

thf(func_def_162,type,
    collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).

thf(func_def_163,type,
    collect_b: ( b > $o ) > set_b ).

thf(func_def_164,type,
    image_1683732397od_b_b: ( b > product_prod_b_b ) > set_b > set_Product_prod_b_b ).

thf(func_def_165,type,
    insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).

thf(func_def_166,type,
    insert1167839429_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).

thf(func_def_167,type,
    insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_168,type,
    insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_169,type,
    insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat ).

thf(func_def_170,type,
    insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_171,type,
    insert_b: b > set_b > set_b ).

thf(func_def_172,type,
    standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).

thf(func_def_173,type,
    standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_174,type,
    standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_175,type,
    standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_176,type,
    member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).

thf(func_def_177,type,
    member1214736488tant_a: produc90515391tant_a > set_Pr154086431tant_a > $o ).

thf(func_def_178,type,
    member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o ).

thf(func_def_179,type,
    member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o ).

thf(func_def_180,type,
    member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).

thf(func_def_181,type,
    member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).

thf(func_def_182,type,
    member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o ).

thf(func_def_183,type,
    member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o ).

thf(func_def_184,type,
    member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).

thf(func_def_185,type,
    member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o ).

thf(func_def_186,type,
    member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).

thf(func_def_187,type,
    member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o ).

thf(func_def_188,type,
    member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o ).

thf(func_def_189,type,
    member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).

thf(func_def_190,type,
    member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o ).

thf(func_def_191,type,
    member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).

thf(func_def_192,type,
    member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).

thf(func_def_193,type,
    member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).

thf(func_def_194,type,
    member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).

thf(func_def_195,type,
    member_b: b > set_b > $o ).

thf(func_def_196,type,
    g: labele1159362096nt_a_b ).

thf(func_def_197,type,
    l: set_St761939237tant_a ).

thf(func_def_198,type,
    p: b > b > $o ).

thf(func_def_199,type,
    f: b > b ).

thf(func_def_200,type,
    l2: standard_Constant_a ).

thf(func_def_201,type,
    x: b ).

thf(func_def_202,type,
    y: b ).

thf(func_def_206,type,
    vIMP: $o > $o > $o ).

thf(func_def_207,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_208,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_209,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_210,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_211,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_212,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_213,type,
    vNOT: $o > $o ).

thf(func_def_214,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_215,type,
    vAND: $o > $o > $o ).

thf(func_def_216,type,
    vOR: $o > $o > $o ).

thf(func_def_217,type,
    sK0: set_Pr1987088711_a_nat > produc1871334759_a_nat ).

thf(func_def_218,type,
    sK1: set_Pr1324126435od_b_b > produc1213276845od_b_b ).

thf(func_def_219,type,
    sK2: set_b > b ).

thf(func_def_220,type,
    sK3: set_Product_prod_b_b > product_prod_b_b ).

thf(func_def_221,type,
    sK4: produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_222,type,
    sK5: produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_223,type,
    sK6: product_prod_b_b > b ).

thf(func_def_224,type,
    sK7: product_prod_b_b > b ).

thf(func_def_225,type,
    sK8: produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_226,type,
    sK9: produc1213276845od_b_b > b ).

thf(func_def_227,type,
    sK10: produc1213276845od_b_b > b ).

thf(func_def_228,type,
    sK11: produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_229,type,
    sK12: produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_230,type,
    sK13: product_prod_b_b > b ).

thf(func_def_231,type,
    sK14: product_prod_b_b > b ).

thf(func_def_232,type,
    sK15: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b ).

thf(func_def_233,type,
    sK16: set_b > set_b > b ).

thf(func_def_234,type,
    sK17: set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b ).

thf(func_def_235,type,
    sK18: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > standard_Constant_a ).

thf(func_def_236,type,
    sK19: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > product_prod_b_b ).

thf(func_def_237,type,
    sK20: set_Product_prod_b_b > set_Product_prod_b_b > b ).

thf(func_def_238,type,
    sK21: set_Product_prod_b_b > set_Product_prod_b_b > b ).

thf(func_def_239,type,
    sK22: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).

thf(func_def_240,type,
    sK23: ( produc1213276845od_b_b > $o ) > product_prod_b_b ).

thf(func_def_241,type,
    sK24: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).

thf(func_def_242,type,
    sK25: ( produc1213276845od_b_b > $o ) > product_prod_b_b ).

thf(func_def_243,type,
    sK26: ( product_prod_b_b > $o ) > b ).

thf(func_def_244,type,
    sK27: ( product_prod_b_b > $o ) > b ).

thf(func_def_245,type,
    sK28: ( product_prod_b_b > $o ) > b ).

thf(func_def_246,type,
    sK29: ( product_prod_b_b > $o ) > b ).

thf(func_def_247,type,
    sK30: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).

thf(func_def_248,type,
    sK31: ( produc1213276845od_b_b > $o ) > b ).

thf(func_def_249,type,
    sK32: ( produc1213276845od_b_b > $o ) > b ).

thf(func_def_250,type,
    sK33: set_Pr1987088711_a_nat > produc1871334759_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_251,type,
    sK34: set_Pr1987088711_a_nat > produc1871334759_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_252,type,
    sK35: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_253,type,
    sK36: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_254,type,
    sK37: set_b > b > set_b ).

thf(func_def_255,type,
    sK38: set_b > b > set_b ).

thf(func_def_256,type,
    sK39: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_257,type,
    sK40: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_258,type,
    sK41: set_Pr1324126435od_b_b > produc970027067od_b_b > produc1213276845od_b_b ).

thf(func_def_259,type,
    sK42: set_Product_prod_b_b > produc1168037607od_b_b > product_prod_b_b ).

thf(func_def_260,type,
    sK43: set_b > product_prod_b_b > b ).

thf(func_def_261,type,
    sK44: ( b > b ) > ( b > b ) > labele1159362096nt_a_b > b ).

thf(func_def_262,type,
    sK45: labele935650037_a_nat > labele1159362096nt_a_b > labele935650037_a_nat > set_Pr2106913242_nat_b ).

thf(func_def_263,type,
    sK46: labele1159362096nt_a_b > labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b ).

thf(func_def_264,type,
    sK47: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > labele1644675410od_b_b > standard_Constant_a ).

thf(func_def_265,type,
    sK48: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > labele1644675410od_b_b > produc1213276845od_b_b ).

thf(func_def_266,type,
    sK49: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > labele1644675410od_b_b > produc1213276845od_b_b ).

thf(func_def_267,type,
    sK50: set_Pr1324126435od_b_b > ( product_prod_b_b > b ) > labele1835558936od_b_b > standard_Constant_a ).

thf(func_def_268,type,
    sK51: set_Pr1324126435od_b_b > ( product_prod_b_b > b ) > labele1835558936od_b_b > product_prod_b_b ).

thf(func_def_269,type,
    sK52: set_Pr1324126435od_b_b > ( product_prod_b_b > b ) > labele1835558936od_b_b > product_prod_b_b ).

thf(func_def_270,type,
    sK53: set_Pr1324126435od_b_b > ( b > b ) > labele1159362096nt_a_b > standard_Constant_a ).

thf(func_def_271,type,
    sK54: set_Pr1324126435od_b_b > ( b > b ) > labele1159362096nt_a_b > b ).

thf(func_def_272,type,
    sK55: set_Pr1324126435od_b_b > ( b > b ) > labele1159362096nt_a_b > b ).

thf(func_def_273,type,
    sK56: set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_274,type,
    sK57: set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_275,type,
    sK58: set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_276,type,
    sK59: set_Pr1324126435od_b_b > set_Pr154086431tant_a > produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_277,type,
    sK60: set_Pr1324126435od_b_b > set_Pr154086431tant_a > produc1213276845od_b_b > standard_Constant_a ).

thf(func_def_278,type,
    sK61: set_Pr1324126435od_b_b > set_Pr154086431tant_a > produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_279,type,
    sK62: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b > produc1213276845od_b_b ).

thf(func_def_280,type,
    sK63: set_b > set_Pr2060523537od_b_b > produc1213276845od_b_b > b ).

thf(func_def_281,type,
    sK64: set_Product_prod_b_b > set_Pr1071216121od_b_b > produc1213276845od_b_b > product_prod_b_b ).

thf(func_def_282,type,
    sK65: set_Pr1324126435od_b_b > set_Pr1906739389_b_b_b > b > produc1213276845od_b_b ).

thf(func_def_283,type,
    sK66: set_b > set_Product_prod_b_b > b > b ).

thf(func_def_284,type,
    sK67: set_Product_prod_b_b > set_Pr357419743_b_b_b > b > product_prod_b_b ).

thf(func_def_285,type,
    sK68: set_St761939237tant_a > set_Pr1324126435od_b_b > product_prod_b_b > standard_Constant_a ).

thf(func_def_286,type,
    sK69: set_Pr1324126435od_b_b > set_Pr2134561957od_b_b > product_prod_b_b > produc1213276845od_b_b ).

thf(func_def_287,type,
    sK70: set_b > set_Pr621705391od_b_b > product_prod_b_b > b ).

thf(func_def_288,type,
    sK71: set_Product_prod_b_b > set_Pr2007082183od_b_b > product_prod_b_b > product_prod_b_b ).

thf(func_def_289,type,
    sK72: set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b > b ).

thf(func_def_290,type,
    sK73: set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b > b ).

thf(func_def_291,type,
    sK74: set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b > b ).

thf(func_def_292,type,
    sK75: set_Product_prod_b_b > labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b ).

thf(func_def_293,type,
    sK76: set_Pr2106913242_nat_b > labele1159362096nt_a_b > labele935650037_a_nat > set_Pr2106913242_nat_b ).

thf(func_def_294,type,
    sK77: set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > product_prod_b_b > standard_Constant_a > product_prod_b_b ).

thf(func_def_295,type,
    sK78: set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > product_prod_b_b > standard_Constant_a > product_prod_b_b ).

thf(func_def_296,type,
    sK79: set_Pr1324126435od_b_b > set_Pr154086431tant_a > product_prod_b_b > standard_Constant_a > standard_Constant_a ).

thf(func_def_297,type,
    sK80: set_Pr1324126435od_b_b > set_Pr154086431tant_a > product_prod_b_b > standard_Constant_a > standard_Constant_a ).

thf(func_def_298,type,
    sK81: set_Product_prod_b_b > set_Product_prod_b_b > b > b > b ).

thf(func_def_299,type,
    sK82: set_Product_prod_b_b > set_Product_prod_b_b > b > b > b ).

thf(func_def_300,type,
    sK83: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > standard_Constant_a ).

thf(func_def_301,type,
    sK84: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > product_prod_b_b ).

thf(func_def_302,type,
    sK85: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b > product_prod_b_b ).

thf(func_def_303,type,
    sK86: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr1324126435od_b_b > set_Pr154086431tant_a > standard_Constant_a ).

thf(func_def_304,type,
    sK87: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr1324126435od_b_b > set_Pr154086431tant_a > standard_Constant_a ).

thf(func_def_305,type,
    sK88: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr1324126435od_b_b > set_Pr154086431tant_a > product_prod_b_b ).

thf(func_def_306,type,
    sK89: ( b > b > $o ) > set_Product_prod_b_b > set_Product_prod_b_b > b ).

thf(func_def_307,type,
    sK90: ( b > b > $o ) > set_Product_prod_b_b > set_Product_prod_b_b > b ).

thf(func_def_308,type,
    sK91: ( b > b > $o ) > set_Product_prod_b_b > set_Product_prod_b_b > b ).

thf(func_def_310,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_311,type,
    sK93: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).

thf(func_def_312,type,
    sK94: set_b > b > set_b > b > set_b ).

thf(func_def_313,type,
    sK95: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).

thf(func_def_314,type,
    sK96: set_Pr1987088711_a_nat > produc1871334759_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat > set_Pr1987088711_a_nat ).

thf(func_def_315,type,
    sK97: b > set_Product_prod_b_b > b > set_Product_prod_b_b > b ).

thf(func_def_316,type,
    sK98: product_prod_b_b > set_Pr1324126435od_b_b > standard_Constant_a > set_Pr154086431tant_a > product_prod_b_b ).

thf(func_def_317,type,
    sK99: product_prod_b_b > set_Pr2007082183od_b_b > standard_Constant_a > set_Pr1324126435od_b_b > product_prod_b_b ).

thf(func_def_318,type,
    sK100: set_Pr1324126435od_b_b > set_St761939237tant_a > product_prod_b_b > standard_Constant_a ).

thf(func_def_319,type,
    sK101: set_Product_prod_b_b > set_b > b > b ).

thf(func_def_320,type,
    sK102: set_Product_prod_b_b > product_prod_b_b ).

thf(func_def_321,type,
    sK103: set_b > b ).

thf(func_def_322,type,
    sK104: set_Pr1324126435od_b_b > produc1213276845od_b_b ).

thf(func_def_323,type,
    sK105: set_Pr1987088711_a_nat > produc1871334759_a_nat ).

thf(func_def_324,type,
    sK106: set_Product_prod_b_b > product_prod_b_b ).

thf(func_def_325,type,
    sK107: set_b > b ).

thf(func_def_326,type,
    sK108: set_Pr1324126435od_b_b > produc1213276845od_b_b ).

thf(func_def_327,type,
    sK109: set_Pr1987088711_a_nat > produc1871334759_a_nat ).

thf(func_def_328,type,
    sK110: ( b > $o ) > b ).

thf(func_def_329,type,
    sK111: ( b > $o ) > b ).

thf(func_def_330,type,
    sK112: ( produc1871334759_a_nat > $o ) > produc1871334759_a_nat ).

thf(func_def_331,type,
    sK113: ( produc1871334759_a_nat > $o ) > produc1871334759_a_nat ).

thf(f3370,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2498,f2503,f2507,f2542,f2547,f2552,f2557,f2562,f2566,f2570,f2574,f2578,f2582,f2586,f2590,f2594,f2601,f2605,f2609,f2613,f2617,f2621,f2625,f2629,f2633,f2638,f2643,f2648,f2660,f2664,f2668,f2674,f2678,f2682,f2686,f2690,f2694,f2699,f2703,f2707,f2711,f2717,f2723,f2727,f2731,f2735,f2739,f2743,f2747,f2752,f2756,f2761,f2776,f2780,f2784,f2788,f2792,f2801,f2805,f2817,f2821,f2825,f2829,f2870,f2875,f2880,f2885,f2889,f2899,f2903,f2914,f2924,f2934,f2938,f2942,f2946,f2950,f2966,f2976,f2980,f2984,f2988,f2992,f2996,f3000,f3004,f3008,f3012,f3016,f3020,f3024,f3028,f3032,f3036,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3105,f3109,f3171,f3231,f3305,f3332,f3345,f3349,f3369]) ).

thf(f3369,plain,
    ( ~ spl92_8
    | ~ spl92_52
    | ~ spl92_118 ),
    inference(avatar_contradiction_clause,[],[f3368]) ).

thf(f3368,plain,
    ( $false
    | ~ spl92_8
    | ~ spl92_52
    | ~ spl92_118 ),
    inference(trivial_inequality_removal,[],[f3367]) ).

thf(f3367,plain,
    ( ( $true = $false )
    | ~ spl92_8
    | ~ spl92_52
    | ~ spl92_118 ),
    inference(forward_demodulation,[],[f3365,f2561]) ).

thf(f2561,plain,
    ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $false )
    | ~ spl92_8 ),
    inference(avatar_component_clause,[],[f2559]) ).

thf(f2559,plain,
    ( spl92_8
  <=> ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_8])]) ).

thf(f3365,plain,
    ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
    | ~ spl92_52
    | ~ spl92_118 ),
    inference(trivial_inequality_removal,[],[f3362]) ).

thf(f3362,plain,
    ( ( $true != $true )
    | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
    | ~ spl92_52
    | ~ spl92_118 ),
    inference(superposition,[],[f3348,f2760]) ).

thf(f2760,plain,
    ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
    | ~ spl92_52 ),
    inference(avatar_component_clause,[],[f2758]) ).

thf(f2758,plain,
    ( spl92_52
  <=> ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_52])]) ).

thf(f3348,plain,
    ( ! [X0: b] :
        ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true )
        | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) )
    | ~ spl92_118 ),
    inference(avatar_component_clause,[],[f3347]) ).

thf(f3347,plain,
    ( spl92_118
  <=> ! [X0: b] :
        ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
        | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_118])]) ).

thf(f3349,plain,
    spl92_118,
    inference(avatar_split_clause,[],[f1575,f3347]) ).

thf(f1575,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
      | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ),
    inference(cnf_transformation,[],[f1081]) ).

thf(f1081,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
      | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ),
    inference(ennf_transformation,[],[f447]) ).

thf(f447,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
     => ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) ),
    inference(fool_elimination,[],[f446]) ).

thf(f446,plain,
    ! [X0: b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g))
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g))
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).

thf(f3345,plain,
    spl92_117,
    inference(avatar_split_clause,[],[f1572,f3343]) ).

thf(f3343,plain,
    ( spl92_117
  <=> ! [X0: b] :
        ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
        | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_117])]) ).

thf(f1572,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
      | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ),
    inference(cnf_transformation,[],[f1078]) ).

thf(f1078,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
      | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true ) ),
    inference(ennf_transformation,[],[f441]) ).

thf(f441,plain,
    ! [X0: b] :
      ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true )
     => ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) ),
    inference(fool_elimination,[],[f440]) ).

thf(f440,plain,
    ! [X0: b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g))
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g))
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,X1)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_gu2) ).

thf(f3332,plain,
    spl92_116,
    inference(avatar_split_clause,[],[f1598,f3330]) ).

thf(f3330,plain,
    ( spl92_116
  <=> ! [X0: labele1159362096nt_a_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o),vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o)),graph_222606102_a_b_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_116])]) ).

thf(f1598,plain,
    ! [X0: labele1159362096nt_a_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o),vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o)),graph_222606102_a_b_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))) ),
    inference(cnf_transformation,[],[f483]) ).

thf(f483,plain,
    ! [X0: labele1159362096nt_a_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o),vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o)),graph_222606102_a_b_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))) ),
    inference(fool_elimination,[],[f482]) ).

thf(f482,plain,
    ! [X0: labele1159362096nt_a_b] : vAPP(set_Product_prod_b_b,$o,vAPP(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o),vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o)),graph_222606102_a_b_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)),vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))),
    inference(rectify,[],[f27]) ).

thf(f27,axiom,
    ! [X14: labele1159362096nt_a_b] : vAPP(set_Product_prod_b_b,$o,vAPP(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o),vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,sTfun(set_Product_prod_b_b,$o)),graph_222606102_a_b_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X14)),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X14)),vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X14))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_graph__homomorphism__Id) ).

thf(f3305,plain,
    ( spl92_115
    | ~ spl92_85
    | ~ spl92_86 ),
    inference(avatar_split_clause,[],[f3151,f3002,f2998,f3303]) ).

thf(f3303,plain,
    ( spl92_115
  <=> ! [X0: set_Product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_115])]) ).

thf(f2998,plain,
    ( spl92_85
  <=> ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_85])]) ).

thf(f3002,plain,
    ( spl92_86
  <=> ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_86])]) ).

thf(f3151,plain,
    ( ! [X0: set_Product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X0) )
    | ~ spl92_85
    | ~ spl92_86 ),
    inference(trivial_inequality_removal,[],[f3150]) ).

thf(f3150,plain,
    ( ! [X0: set_Product_prod_b_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X0) ) )
    | ~ spl92_85
    | ~ spl92_86 ),
    inference(duplicate_literal_removal,[],[f3146]) ).

thf(f3146,plain,
    ( ! [X0: set_Product_prod_b_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X0) )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X0) ) )
    | ~ spl92_85
    | ~ spl92_86 ),
    inference(superposition,[],[f3003,f2999]) ).

thf(f2999,plain,
    ( ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X0) )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) ) )
    | ~ spl92_85 ),
    inference(avatar_component_clause,[],[f2998]) ).

thf(f3003,plain,
    ( ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X1) )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) ) )
    | ~ spl92_86 ),
    inference(avatar_component_clause,[],[f3002]) ).

thf(f3231,plain,
    ( spl92_114
    | ~ spl92_83
    | ~ spl92_84 ),
    inference(avatar_split_clause,[],[f3137,f2994,f2990,f3229]) ).

thf(f3229,plain,
    ( spl92_114
  <=> ! [X0: set_b] : ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_114])]) ).

thf(f2990,plain,
    ( spl92_83
  <=> ! [X0: set_b,X1: set_b] :
        ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
        | ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_83])]) ).

thf(f2994,plain,
    ( spl92_84
  <=> ! [X0: set_b,X1: set_b] :
        ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_84])]) ).

thf(f3137,plain,
    ( ! [X0: set_b] : ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X0) )
    | ~ spl92_83
    | ~ spl92_84 ),
    inference(trivial_inequality_removal,[],[f3136]) ).

thf(f3136,plain,
    ( ! [X0: set_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X0) ) )
    | ~ spl92_83
    | ~ spl92_84 ),
    inference(duplicate_literal_removal,[],[f3132]) ).

thf(f3132,plain,
    ( ! [X0: set_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X0) )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X0) ) )
    | ~ spl92_83
    | ~ spl92_84 ),
    inference(superposition,[],[f2995,f2991]) ).

thf(f2991,plain,
    ( ! [X0: set_b,X1: set_b] :
        ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X0) )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) ) )
    | ~ spl92_83 ),
    inference(avatar_component_clause,[],[f2990]) ).

thf(f2995,plain,
    ( ! [X0: set_b,X1: set_b] :
        ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X1) )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) ) )
    | ~ spl92_84 ),
    inference(avatar_component_clause,[],[f2994]) ).

thf(f3171,plain,
    ( spl92_113
    | ~ spl92_81
    | ~ spl92_82 ),
    inference(avatar_split_clause,[],[f3123,f2986,f2982,f3169]) ).

thf(f3169,plain,
    ( spl92_113
  <=> ! [X0: set_Pr1324126435od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_113])]) ).

thf(f2982,plain,
    ( spl92_81
  <=> ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_81])]) ).

thf(f2986,plain,
    ( spl92_82
  <=> ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_82])]) ).

thf(f3123,plain,
    ( ! [X0: set_Pr1324126435od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X0) )
    | ~ spl92_81
    | ~ spl92_82 ),
    inference(trivial_inequality_removal,[],[f3122]) ).

thf(f3122,plain,
    ( ! [X0: set_Pr1324126435od_b_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X0) ) )
    | ~ spl92_81
    | ~ spl92_82 ),
    inference(duplicate_literal_removal,[],[f3118]) ).

thf(f3118,plain,
    ( ! [X0: set_Pr1324126435od_b_b] :
        ( ( $true != $true )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X0) )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X0) ) )
    | ~ spl92_81
    | ~ spl92_82 ),
    inference(superposition,[],[f2987,f2983]) ).

thf(f2983,plain,
    ( ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X0) )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) ) )
    | ~ spl92_81 ),
    inference(avatar_component_clause,[],[f2982]) ).

thf(f2987,plain,
    ( ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X1) )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) ) )
    | ~ spl92_82 ),
    inference(avatar_component_clause,[],[f2986]) ).

thf(f3109,plain,
    spl92_112,
    inference(avatar_split_clause,[],[f1727,f3107]) ).

thf(f3107,plain,
    ( spl92_112
  <=> ! [X2: product_prod_b_b,X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_112])]) ).

thf(f1727,plain,
    ! [X2: product_prod_b_b,X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1145]) ).

thf(f1145,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b,X2: product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) )
      | ( ( X0 != X2 )
        & ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f1038]) ).

thf(f1038,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b,X2: product_prod_b_b] :
      ( ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) ) ),
    inference(flattening,[],[f639]) ).

thf(f639,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b,X2: product_prod_b_b] :
      ( ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) ) ),
    inference(fool_elimination,[],[f638]) ).

thf(f638,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b,X2: product_prod_b_b] :
      ( ( ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1)
       => ( X0 = X2 ) )
     => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X2),X1)) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X14: product_prod_b_b,X9: set_Product_prod_b_b,X24: product_prod_b_b] :
      ( ( ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),X9)
       => ( X14 = X24 ) )
     => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X24),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insertCI) ).

thf(f3105,plain,
    spl92_111,
    inference(avatar_split_clause,[],[f1725,f3103]) ).

thf(f3103,plain,
    ( spl92_111
  <=> ! [X2: b,X0: b,X1: set_b] :
        ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_111])]) ).

thf(f1725,plain,
    ! [X2: b,X0: b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1144]) ).

thf(f1144,plain,
    ! [X0: b,X1: set_b,X2: b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) )
      | ( ( X0 != X2 )
        & ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f1037]) ).

thf(f1037,plain,
    ! [X0: b,X1: set_b,X2: b] :
      ( ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) ) ),
    inference(flattening,[],[f637]) ).

thf(f637,plain,
    ! [X0: b,X1: set_b,X2: b] :
      ( ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) ) ),
    inference(fool_elimination,[],[f636]) ).

thf(f636,plain,
    ! [X0: b,X1: set_b,X2: b] :
      ( ( ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1)
       => ( X0 = X2 ) )
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X2),X1)) ),
    inference(rectify,[],[f265]) ).

thf(f265,axiom,
    ! [X14: b,X9: set_b,X24: b] :
      ( ( ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),X9)
       => ( X14 = X24 ) )
     => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X24),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insertCI) ).

thf(f3100,plain,
    spl92_110,
    inference(avatar_split_clause,[],[f1723,f3098]) ).

thf(f3098,plain,
    ( spl92_110
  <=> ! [X2: produc1213276845od_b_b,X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_110])]) ).

thf(f1723,plain,
    ! [X2: produc1213276845od_b_b,X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1143]) ).

thf(f1143,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b,X2: produc1213276845od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) )
      | ( ( X0 != X2 )
        & ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f1036]) ).

thf(f1036,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b,X2: produc1213276845od_b_b] :
      ( ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) ) ),
    inference(flattening,[],[f635]) ).

thf(f635,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b,X2: produc1213276845od_b_b] :
      ( ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) ) ),
    inference(fool_elimination,[],[f634]) ).

thf(f634,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b,X2: produc1213276845od_b_b] :
      ( ( ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1)
       => ( X0 = X2 ) )
     => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X2),X1)) ),
    inference(rectify,[],[f267]) ).

thf(f267,axiom,
    ! [X14: produc1213276845od_b_b,X9: set_Pr1324126435od_b_b,X24: produc1213276845od_b_b] :
      ( ( ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),X9)
       => ( X14 = X24 ) )
     => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X24),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insertCI) ).

thf(f3096,plain,
    spl92_109,
    inference(avatar_split_clause,[],[f1721,f3094]) ).

thf(f3094,plain,
    ( spl92_109
  <=> ! [X2: produc1871334759_a_nat,X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_109])]) ).

thf(f1721,plain,
    ! [X2: produc1871334759_a_nat,X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1142]) ).

thf(f1142,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat,X2: produc1871334759_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) )
      | ( ( X0 != X2 )
        & ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f1035]) ).

thf(f1035,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat,X2: produc1871334759_a_nat] :
      ( ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) ) ),
    inference(flattening,[],[f633]) ).

thf(f633,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat,X2: produc1871334759_a_nat] :
      ( ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
       => ( X0 = X2 ) )
     => ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) ) ),
    inference(fool_elimination,[],[f632]) ).

thf(f632,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat,X2: produc1871334759_a_nat] :
      ( ( ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1)
       => ( X0 = X2 ) )
     => vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X2),X1)) ),
    inference(rectify,[],[f264]) ).

thf(f264,axiom,
    ! [X14: produc1871334759_a_nat,X9: set_Pr1987088711_a_nat,X24: produc1871334759_a_nat] :
      ( ( ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),X9)
       => ( X14 = X24 ) )
     => vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X24),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insertCI) ).

thf(f3092,plain,
    spl92_108,
    inference(avatar_split_clause,[],[f1669,f3090]) ).

thf(f3090,plain,
    ( spl92_108
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_108])]) ).

thf(f1669,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f1443,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) )
        & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1126,f1442]) ).

thf(f1442,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) )
        & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1126,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f1020]) ).

thf(f1020,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
     => ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) ) ),
    inference(flattening,[],[f563]) ).

thf(f563,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
     => ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) ) ),
    inference(fool_elimination,[],[f562]) ).

thf(f562,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1)
     => ? [X2: set_Product_prod_b_b] :
          ( ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2)
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) ) ),
    inference(rectify,[],[f314]) ).

thf(f314,axiom,
    ! [X14: product_prod_b_b,X8: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),X8)
     => ? [X82: set_Product_prod_b_b] :
          ( ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),X82)
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X14),X82) = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_mk__disjoint__insert) ).

thf(f3088,plain,
    spl92_107,
    inference(avatar_split_clause,[],[f1668,f3086]) ).

thf(f3086,plain,
    ( spl92_107
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) = X1 )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_107])]) ).

thf(f1668,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK40,X1),X0)) = X1 )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1443]) ).

thf(f3084,plain,
    spl92_106,
    inference(avatar_split_clause,[],[f1667,f3082]) ).

thf(f3082,plain,
    ( spl92_106
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_106])]) ).

thf(f1667,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1441]) ).

thf(f1441,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) )
        & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1125,f1440]) ).

thf(f1440,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) )
        & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1125,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ? [X2: set_Product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) )
          & ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f561]) ).

thf(f561,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
     => ~ ! [X2: set_Product_prod_b_b] :
            ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 )
           => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) ) ) ),
    inference(fool_elimination,[],[f560]) ).

thf(f560,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1)
     => ~ ! [X2: set_Product_prod_b_b] :
            ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X2) = X1 )
           => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X2) ) ),
    inference(rectify,[],[f332]) ).

thf(f332,axiom,
    ! [X1: product_prod_b_b,X8: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X8)
     => ~ ! [X82: set_Product_prod_b_b] :
            ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X1),X82) = X8 )
           => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X82) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Set_Oset__insert) ).

thf(f3080,plain,
    spl92_105,
    inference(avatar_split_clause,[],[f1666,f3078]) ).

thf(f3078,plain,
    ( spl92_105
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) = X1 )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_105])]) ).

thf(f1666,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),vAPP(product_prod_b_b,set_Product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,set_Product_prod_b_b),sK39,X1),X0)) = X1 )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1441]) ).

thf(f3076,plain,
    spl92_104,
    inference(avatar_split_clause,[],[f1663,f3074]) ).

thf(f3074,plain,
    ( spl92_104
  <=> ! [X0: b,X1: set_b] :
        ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_104])]) ).

thf(f1663,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1439]) ).

thf(f1439,plain,
    ! [X0: b,X1: set_b] :
      ( ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) )
        & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1122,f1438]) ).

thf(f1438,plain,
    ! [X0: b,X1: set_b] :
      ( ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) )
        & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1122,plain,
    ! [X0: b,X1: set_b] :
      ( ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f1019]) ).

thf(f1019,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
     => ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) ) ),
    inference(flattening,[],[f555]) ).

thf(f555,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
     => ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) ) ),
    inference(fool_elimination,[],[f554]) ).

thf(f554,plain,
    ! [X0: b,X1: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1)
     => ? [X2: set_b] :
          ( ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2)
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) ) ),
    inference(rectify,[],[f313]) ).

thf(f313,axiom,
    ! [X14: b,X8: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),X8)
     => ? [X82: set_b] :
          ( ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),X82)
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X14),X82) = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_mk__disjoint__insert) ).

thf(f3072,plain,
    spl92_103,
    inference(avatar_split_clause,[],[f1662,f3070]) ).

thf(f3070,plain,
    ( spl92_103
  <=> ! [X0: b,X1: set_b] :
        ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) = X1 )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_103])]) ).

thf(f1662,plain,
    ! [X0: b,X1: set_b] :
      ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK38,X1),X0)) = X1 )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1439]) ).

thf(f3068,plain,
    spl92_102,
    inference(avatar_split_clause,[],[f1661,f3066]) ).

thf(f3066,plain,
    ( spl92_102
  <=> ! [X0: b,X1: set_b] :
        ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_102])]) ).

thf(f1661,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1437]) ).

thf(f1437,plain,
    ! [X0: b,X1: set_b] :
      ( ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) )
        & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f1121,f1436]) ).

thf(f1436,plain,
    ! [X0: b,X1: set_b] :
      ( ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) )
        & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1121,plain,
    ! [X0: b,X1: set_b] :
      ( ? [X2: set_b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) )
          & ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f553]) ).

thf(f553,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
     => ~ ! [X2: set_b] :
            ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 )
           => ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) ) ) ),
    inference(fool_elimination,[],[f552]) ).

thf(f552,plain,
    ! [X0: b,X1: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1)
     => ~ ! [X2: set_b] :
            ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X2) = X1 )
           => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X2) ) ),
    inference(rectify,[],[f331]) ).

thf(f331,axiom,
    ! [X1: b,X8: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X8)
     => ~ ! [X82: set_b] :
            ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X1),X82) = X8 )
           => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X82) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Set_Oset__insert) ).

thf(f3064,plain,
    spl92_101,
    inference(avatar_split_clause,[],[f1660,f3062]) ).

thf(f3062,plain,
    ( spl92_101
  <=> ! [X0: b,X1: set_b] :
        ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) = X1 )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_101])]) ).

thf(f1660,plain,
    ! [X0: b,X1: set_b] :
      ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(b,set_b,vAPP(set_b,sTfun(b,set_b),sK37,X1),X0)) = X1 )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1437]) ).

thf(f3060,plain,
    spl92_100,
    inference(avatar_split_clause,[],[f2402,f3058]) ).

thf(f3058,plain,
    ( spl92_100
  <=> ! [X0: set_Pr1987088711_a_nat] :
        ( ( bot_bo1836341171_a_nat = X0 )
        | ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_100])]) ).

thf(f2402,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( bot_bo1836341171_a_nat = X0 )
      | ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    inference(equality_proxy_clausification,[],[f2399]) ).

thf(f2399,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),vEQ(set_Pr1987088711_a_nat),bot_bo1836341171_a_nat),X0) )
      | ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    inference(binary_proxy_clausification,[],[f1558]) ).

thf(f1558,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),vEQ(set_Pr1987088711_a_nat),bot_bo1836341171_a_nat),X0) = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(cnf_transformation,[],[f415]) ).

thf(f415,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),vEQ(set_Pr1987088711_a_nat),bot_bo1836341171_a_nat),X0) = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(fool_elimination,[],[f414]) ).

thf(f414,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat)
      = ( bot_bo1836341171_a_nat = X0 ) ),
    inference(rectify,[],[f271]) ).

thf(f271,axiom,
    ! [X8: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X8),bot_bo1836341171_a_nat)
      = ( bot_bo1836341171_a_nat = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subset__empty) ).

thf(f3056,plain,
    spl92_99,
    inference(avatar_split_clause,[],[f1657,f3054]) ).

thf(f3054,plain,
    ( spl92_99
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_99])]) ).

thf(f1657,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1435]) ).

thf(f1435,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) )
        & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f1118,f1434]) ).

thf(f1434,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) )
        & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1118,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f1018]) ).

thf(f1018,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
     => ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) ) ),
    inference(flattening,[],[f547]) ).

thf(f547,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
     => ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) ) ),
    inference(fool_elimination,[],[f546]) ).

thf(f546,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1)
     => ? [X2: set_Pr1324126435od_b_b] :
          ( ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2)
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) ) ),
    inference(rectify,[],[f315]) ).

thf(f315,axiom,
    ! [X14: produc1213276845od_b_b,X8: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),X8)
     => ? [X82: set_Pr1324126435od_b_b] :
          ( ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),X82)
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X14),X82) = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_mk__disjoint__insert) ).

thf(f3052,plain,
    spl92_98,
    inference(avatar_split_clause,[],[f1656,f3050]) ).

thf(f3050,plain,
    ( spl92_98
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) = X1 )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_98])]) ).

thf(f1656,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK36,X1),X0)) = X1 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1435]) ).

thf(f3048,plain,
    spl92_97,
    inference(avatar_split_clause,[],[f1655,f3046]) ).

thf(f3046,plain,
    ( spl92_97
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_97])]) ).

thf(f1655,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1433]) ).

thf(f1433,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) )
        & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f1117,f1432]) ).

thf(f1432,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) )
        & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1117,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ? [X2: set_Pr1324126435od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) )
          & ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f545]) ).

thf(f545,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
     => ~ ! [X2: set_Pr1324126435od_b_b] :
            ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 )
           => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) ) ) ),
    inference(fool_elimination,[],[f544]) ).

thf(f544,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1)
     => ~ ! [X2: set_Pr1324126435od_b_b] :
            ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X2) = X1 )
           => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X2) ) ),
    inference(rectify,[],[f333]) ).

thf(f333,axiom,
    ! [X1: produc1213276845od_b_b,X8: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X8)
     => ~ ! [X82: set_Pr1324126435od_b_b] :
            ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X1),X82) = X8 )
           => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X82) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_Set_Oset__insert) ).

thf(f3044,plain,
    spl92_96,
    inference(avatar_split_clause,[],[f1654,f3042]) ).

thf(f3042,plain,
    ( spl92_96
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) = X1 )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_96])]) ).

thf(f1654,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),vAPP(produc1213276845od_b_b,set_Pr1324126435od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,set_Pr1324126435od_b_b),sK35,X1),X0)) = X1 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1433]) ).

thf(f3040,plain,
    spl92_95,
    inference(avatar_split_clause,[],[f1652,f3038]) ).

thf(f3038,plain,
    ( spl92_95
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_95])]) ).

thf(f1652,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1431]) ).

thf(f1431,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) )
        & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f1115,f1430]) ).

thf(f1430,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) )
        & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1115,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f1017]) ).

thf(f1017,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
     => ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) ) ),
    inference(flattening,[],[f541]) ).

thf(f541,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
     => ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) ) ),
    inference(fool_elimination,[],[f540]) ).

thf(f540,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1)
     => ? [X2: set_Pr1987088711_a_nat] :
          ( ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2)
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) ) ),
    inference(rectify,[],[f312]) ).

thf(f312,axiom,
    ! [X14: produc1871334759_a_nat,X8: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),X8)
     => ? [X82: set_Pr1987088711_a_nat] :
          ( ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),X82)
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X14),X82) = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_mk__disjoint__insert) ).

thf(f3036,plain,
    spl92_94,
    inference(avatar_split_clause,[],[f1651,f3034]) ).

thf(f3034,plain,
    ( spl92_94
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) = X1 )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_94])]) ).

thf(f1651,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK34,X1),X0)) = X1 )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1431]) ).

thf(f3032,plain,
    spl92_93,
    inference(avatar_split_clause,[],[f1650,f3030]) ).

thf(f3030,plain,
    ( spl92_93
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_93])]) ).

thf(f1650,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1429]) ).

thf(f1429,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) )
        & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) = X1 ) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f1114,f1428]) ).

thf(f1428,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) )
     => ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) )
        & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1114,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ? [X2: set_Pr1987088711_a_nat] :
          ( ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) )
          & ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 ) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f539]) ).

thf(f539,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
     => ~ ! [X2: set_Pr1987088711_a_nat] :
            ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 )
           => ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) ) ) ),
    inference(fool_elimination,[],[f538]) ).

thf(f538,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1)
     => ~ ! [X2: set_Pr1987088711_a_nat] :
            ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X2) = X1 )
           => vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X2) ) ),
    inference(rectify,[],[f330]) ).

thf(f330,axiom,
    ! [X1: produc1871334759_a_nat,X8: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X8)
     => ~ ! [X82: set_Pr1987088711_a_nat] :
            ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X1),X82) = X8 )
           => vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X82) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Set_Oset__insert) ).

thf(f3028,plain,
    spl92_92,
    inference(avatar_split_clause,[],[f1649,f3026]) ).

thf(f3026,plain,
    ( spl92_92
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) = X1 )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_92])]) ).

thf(f1649,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(produc1871334759_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(produc1871334759_a_nat,set_Pr1987088711_a_nat),sK33,X1),X0)) = X1 )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1429]) ).

thf(f3024,plain,
    spl92_91,
    inference(avatar_split_clause,[],[f1646,f3022]) ).

thf(f3022,plain,
    ( spl92_91
  <=> ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
        ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
        | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK28,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK29,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_91])]) ).

thf(f1646,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK28,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK29,X0))) ) ),
    inference(cnf_transformation,[],[f1425]) ).

thf(f1425,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK28,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK29,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f1111,f1424]) ).

thf(f1424,plain,
    ! [X0: product_prod_b_b > $o] :
      ( ? [X2: b,X3: b] : ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) )
     => ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK28,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK29,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1111,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ? [X2: b,X3: b] : ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) ) ),
    inference(ennf_transformation,[],[f533]) ).

thf(f533,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ! [X2: b,X3: b] : ( $true = vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) )
     => ( $true = vAPP(product_prod_b_b,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f532]) ).

thf(f532,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ! [X2: b,X3: b] : vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3))
     => vAPP(product_prod_b_b,$o,X0,X1) ),
    inference(rectify,[],[f103]) ).

thf(f103,axiom,
    ! [X25: product_prod_b_b > $o,X50: product_prod_b_b] :
      ( ! [X51: b,X52: b] : vAPP(product_prod_b_b,$o,X25,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X51),X52))
     => vAPP(product_prod_b_b,$o,X25,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_prod__cases) ).

thf(f3020,plain,
    spl92_90,
    inference(avatar_split_clause,[],[f1645,f3018]) ).

thf(f3018,plain,
    ( spl92_90
  <=> ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
        ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
        | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK26,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK27,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_90])]) ).

thf(f1645,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK26,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK27,X0))) ) ),
    inference(cnf_transformation,[],[f1423]) ).

thf(f1423,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK26,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK27,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f1110,f1422]) ).

thf(f1422,plain,
    ! [X0: product_prod_b_b > $o] :
      ( ? [X2: b,X3: b] : ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) )
     => ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(sTfun(product_prod_b_b,$o),b,sK26,X0)),vAPP(sTfun(product_prod_b_b,$o),b,sK27,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1110,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ( $true = vAPP(product_prod_b_b,$o,X0,X1) )
      | ? [X2: b,X3: b] : ( $true != vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) ) ),
    inference(ennf_transformation,[],[f531]) ).

thf(f531,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ! [X2: b,X3: b] : ( $true = vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) )
     => ( $true = vAPP(product_prod_b_b,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f530]) ).

thf(f530,plain,
    ! [X0: product_prod_b_b > $o,X1: product_prod_b_b] :
      ( ! [X2: b,X3: b] : vAPP(product_prod_b_b,$o,X0,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3))
     => vAPP(product_prod_b_b,$o,X0,X1) ),
    inference(rectify,[],[f109]) ).

thf(f109,axiom,
    ! [X25: product_prod_b_b > $o,X53: product_prod_b_b] :
      ( ! [X51: b,X52: b] : vAPP(product_prod_b_b,$o,X25,vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X51),X52))
     => vAPP(product_prod_b_b,$o,X25,X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Oprod_Oinducts) ).

thf(f3016,plain,
    spl92_89,
    inference(avatar_split_clause,[],[f2401,f3014]) ).

thf(f3014,plain,
    ( spl92_89
  <=> ! [X0: set_Pr1987088711_a_nat] :
        ( ( bot_bo1836341171_a_nat != X0 )
        | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_89])]) ).

thf(f2401,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( bot_bo1836341171_a_nat != X0 )
      | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    inference(equality_proxy_clausification,[],[f2400]) ).

thf(f2400,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),vEQ(set_Pr1987088711_a_nat),bot_bo1836341171_a_nat),X0) )
      | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    inference(binary_proxy_clausification,[],[f1558]) ).

thf(f3012,plain,
    spl92_88,
    inference(avatar_split_clause,[],[f1644,f3010]) ).

thf(f3010,plain,
    ( spl92_88
  <=> ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
        ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
        | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK24,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK25,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_88])]) ).

thf(f1644,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK24,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK25,X0))) ) ),
    inference(cnf_transformation,[],[f1421]) ).

thf(f1421,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK24,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK25,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f1109,f1420]) ).

thf(f1420,plain,
    ! [X0: produc1213276845od_b_b > $o] :
      ( ? [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) )
     => ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK24,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK25,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1109,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ? [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) ) ),
    inference(ennf_transformation,[],[f529]) ).

thf(f529,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ! [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true = vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) )
     => ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f528]) ).

thf(f528,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ! [X2: standard_Constant_a,X3: product_prod_b_b] : vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3))
     => vAPP(produc1213276845od_b_b,$o,X0,X1) ),
    inference(rectify,[],[f104]) ).

thf(f104,axiom,
    ! [X25: produc1213276845od_b_b > $o,X50: produc1213276845od_b_b] :
      ( ! [X51: standard_Constant_a,X52: product_prod_b_b] : vAPP(produc1213276845od_b_b,$o,X25,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X51),X52))
     => vAPP(produc1213276845od_b_b,$o,X25,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_prod__cases) ).

thf(f3008,plain,
    spl92_87,
    inference(avatar_split_clause,[],[f1643,f3006]) ).

thf(f3006,plain,
    ( spl92_87
  <=> ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
        ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
        | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK22,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK23,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_87])]) ).

thf(f1643,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK22,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK23,X0))) ) ),
    inference(cnf_transformation,[],[f1419]) ).

thf(f1419,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK22,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK23,X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f1108,f1418]) ).

thf(f1418,plain,
    ! [X0: produc1213276845od_b_b > $o] :
      ( ? [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) )
     => ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(sTfun(produc1213276845od_b_b,$o),standard_Constant_a,sK22,X0)),vAPP(sTfun(produc1213276845od_b_b,$o),product_prod_b_b,sK23,X0))) ) ),
    introduced(choice_axiom,[]) ).

thf(f1108,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) )
      | ? [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true != vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) ) ),
    inference(ennf_transformation,[],[f527]) ).

thf(f527,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ! [X2: standard_Constant_a,X3: product_prod_b_b] : ( $true = vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3)) )
     => ( $true = vAPP(produc1213276845od_b_b,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f526]) ).

thf(f526,plain,
    ! [X0: produc1213276845od_b_b > $o,X1: produc1213276845od_b_b] :
      ( ! [X2: standard_Constant_a,X3: product_prod_b_b] : vAPP(produc1213276845od_b_b,$o,X0,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X2),X3))
     => vAPP(produc1213276845od_b_b,$o,X0,X1) ),
    inference(rectify,[],[f110]) ).

thf(f110,axiom,
    ! [X25: produc1213276845od_b_b > $o,X53: produc1213276845od_b_b] :
      ( ! [X51: standard_Constant_a,X52: product_prod_b_b] : vAPP(produc1213276845od_b_b,$o,X25,vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X51),X52))
     => vAPP(produc1213276845od_b_b,$o,X25,X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oinducts) ).

thf(f3004,plain,
    spl92_86,
    inference(avatar_split_clause,[],[f1638,f3002]) ).

thf(f1638,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X1) ) ),
    inference(cnf_transformation,[],[f1413]) ).

thf(f1413,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
      | ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X1) )
        & ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1105,f1412]) ).

thf(f1412,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ? [X2: product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X1) )
          & ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X0) ) )
     => ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X1) )
        & ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1105,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
      | ? [X2: product_prod_b_b] :
          ( ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X1) )
          & ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X0) ) ) ),
    inference(ennf_transformation,[],[f521]) ).

thf(f521,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ! [X2: product_prod_b_b] :
          ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X0) )
         => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X1) ) )
     => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) ) ),
    inference(fool_elimination,[],[f520]) ).

thf(f520,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ! [X2: product_prod_b_b] :
          ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X0)
         => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X2),X1) )
     => vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) ),
    inference(rectify,[],[f256]) ).

thf(f256,axiom,
    ! [X8: set_Product_prod_b_b,X9: set_Product_prod_b_b] :
      ( ! [X18: product_prod_b_b] :
          ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X18),X8)
         => vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X18),X9) )
     => vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X8),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subsetI) ).

thf(f3000,plain,
    spl92_85,
    inference(avatar_split_clause,[],[f1637,f2998]) ).

thf(f1637,plain,
    ! [X0: set_Product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,$o),ord_le1036320359od_b_b,X0),X1) )
      | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,vAPP(set_Product_prod_b_b,sTfun(set_Product_prod_b_b,product_prod_b_b),sK17,X1),X0)),X0) ) ),
    inference(cnf_transformation,[],[f1413]) ).

thf(f2996,plain,
    spl92_84,
    inference(avatar_split_clause,[],[f1636,f2994]) ).

thf(f1636,plain,
    ! [X0: set_b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X1) ) ),
    inference(cnf_transformation,[],[f1411]) ).

thf(f1411,plain,
    ! [X0: set_b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
      | ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X1) )
        & ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1104,f1410]) ).

thf(f1410,plain,
    ! [X0: set_b,X1: set_b] :
      ( ? [X2: b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X1) )
          & ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X0) ) )
     => ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X1) )
        & ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1104,plain,
    ! [X0: set_b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
      | ? [X2: b] :
          ( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X1) )
          & ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X0) ) ) ),
    inference(ennf_transformation,[],[f519]) ).

thf(f519,plain,
    ! [X0: set_b,X1: set_b] :
      ( ! [X2: b] :
          ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X0) )
         => ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X1) ) )
     => ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) ) ),
    inference(fool_elimination,[],[f518]) ).

thf(f518,plain,
    ! [X0: set_b,X1: set_b] :
      ( ! [X2: b] :
          ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X0)
         => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),X1) )
     => vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) ),
    inference(rectify,[],[f255]) ).

thf(f255,axiom,
    ! [X8: set_b,X9: set_b] :
      ( ! [X18: b] :
          ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X18),X8)
         => vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X18),X9) )
     => vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X8),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_subsetI) ).

thf(f2992,plain,
    spl92_83,
    inference(avatar_split_clause,[],[f1635,f2990]) ).

thf(f1635,plain,
    ! [X0: set_b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),X1) )
      | ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,vAPP(set_b,sTfun(set_b,b),sK16,X1),X0)),X0) ) ),
    inference(cnf_transformation,[],[f1411]) ).

thf(f2988,plain,
    spl92_82,
    inference(avatar_split_clause,[],[f1634,f2986]) ).

thf(f1634,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X1) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f1409,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
      | ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X1) )
        & ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1103,f1408]) ).

thf(f1408,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ? [X2: produc1213276845od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X1) )
          & ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X0) ) )
     => ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X1) )
        & ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1103,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
      | ? [X2: produc1213276845od_b_b] :
          ( ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X1) )
          & ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X0) ) ) ),
    inference(ennf_transformation,[],[f517]) ).

thf(f517,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ! [X2: produc1213276845od_b_b] :
          ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X0) )
         => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X1) ) )
     => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) ) ),
    inference(fool_elimination,[],[f516]) ).

thf(f516,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ! [X2: produc1213276845od_b_b] :
          ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X0)
         => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X2),X1) )
     => vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) ),
    inference(rectify,[],[f257]) ).

thf(f257,axiom,
    ! [X8: set_Pr1324126435od_b_b,X9: set_Pr1324126435od_b_b] :
      ( ! [X18: produc1213276845od_b_b] :
          ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X18),X8)
         => vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X18),X9) )
     => vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X8),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_subsetI) ).

thf(f2984,plain,
    spl92_81,
    inference(avatar_split_clause,[],[f1633,f2982]) ).

thf(f1633,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,X0),X1) )
      | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,produc1213276845od_b_b),sK15,X1),X0)),X0) ) ),
    inference(cnf_transformation,[],[f1409]) ).

thf(f2980,plain,
    spl92_80,
    inference(avatar_split_clause,[],[f1580,f2978]) ).

thf(f2978,plain,
    ( spl92_80
  <=> ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK8,X0)),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(produc1213276845od_b_b,b,sK9,X0)),vAPP(produc1213276845od_b_b,b,sK10,X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_80])]) ).

thf(f1580,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK8,X0)),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(produc1213276845od_b_b,b,sK9,X0)),vAPP(produc1213276845od_b_b,b,sK10,X0))) = X0 ),
    inference(cnf_transformation,[],[f1403]) ).

thf(f1403,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK8,X0)),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(produc1213276845od_b_b,b,sK9,X0)),vAPP(produc1213276845od_b_b,b,sK10,X0))) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f1086,f1402]) ).

thf(f1402,plain,
    ! [X0: produc1213276845od_b_b] :
      ( ? [X1: standard_Constant_a,X2: b,X3: b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) = X0 )
     => ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK8,X0)),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(produc1213276845od_b_b,b,sK9,X0)),vAPP(produc1213276845od_b_b,b,sK10,X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1086,plain,
    ! [X0: produc1213276845od_b_b] :
    ? [X1: standard_Constant_a,X2: b,X3: b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) = X0 ),
    inference(ennf_transformation,[],[f984]) ).

thf(f984,plain,
    ! [X0: produc1213276845od_b_b] :
      ~ ! [X1: standard_Constant_a,X2: b,X3: b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X2),X3)) != X0 ),
    inference(rectify,[],[f111]) ).

thf(f111,axiom,
    ! [X4: produc1213276845od_b_b] :
      ~ ! [X51: standard_Constant_a,X52: b,X54: b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X51),vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X52),X54)) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod__cases3) ).

thf(f2976,plain,
    spl92_79,
    inference(avatar_split_clause,[],[f2398,f2974]) ).

thf(f2974,plain,
    ( spl92_79
  <=> ! [X0: set_b] :
        ( ( bot_bot_set_b = X0 )
        | ( $false = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_79])]) ).

thf(f2398,plain,
    ! [X0: set_b] :
      ( ( bot_bot_set_b = X0 )
      | ( $false = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ),
    inference(equality_proxy_clausification,[],[f2395]) ).

thf(f2395,plain,
    ! [X0: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),vEQ(set_b),bot_bot_set_b),X0) )
      | ( $false = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ),
    inference(binary_proxy_clausification,[],[f1559]) ).

thf(f1559,plain,
    ! [X0: set_b] : ( vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),vEQ(set_b),bot_bot_set_b),X0) = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ),
    inference(cnf_transformation,[],[f417]) ).

thf(f417,plain,
    ! [X0: set_b] : ( vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),vEQ(set_b),bot_bot_set_b),X0) = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ),
    inference(fool_elimination,[],[f416]) ).

thf(f416,plain,
    ! [X0: set_b] :
      ( vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b)
      = ( bot_bot_set_b = X0 ) ),
    inference(rectify,[],[f270]) ).

thf(f270,axiom,
    ! [X8: set_b] :
      ( vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X8),bot_bot_set_b)
      = ( bot_bot_set_b = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__empty) ).

thf(f2966,plain,
    spl92_78,
    inference(avatar_split_clause,[],[f1625,f2964]) ).

thf(f2964,plain,
    ( spl92_78
  <=> ! [X0: labele1159362096nt_a_b,X1: set_Product_prod_b_b] :
        ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0)) )
        | ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_78])]) ).

thf(f1625,plain,
    ! [X0: labele1159362096nt_a_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0)) )
      | ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) != X0 ) ),
    inference(cnf_transformation,[],[f1091]) ).

thf(f1091,plain,
    ! [X0: labele1159362096nt_a_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0)) )
      | ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) != X0 ) ),
    inference(ennf_transformation,[],[f1012]) ).

thf(f1012,plain,
    ! [X0: labele1159362096nt_a_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 )
     => ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X1),X0)) ) ),
    inference(rectify,[],[f22]) ).

thf(f22,axiom,
    ! [X7: labele1159362096nt_a_b,X10: set_Product_prod_b_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X7) = X7 )
     => ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X10),X7) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X10),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_map__graph__preserves__restricted) ).

thf(f2950,plain,
    spl92_77,
    inference(avatar_split_clause,[],[f1613,f2948]) ).

thf(f2948,plain,
    ( spl92_77
  <=> ! [X0: b,X1: set_b] : ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_77])]) ).

thf(f1613,plain,
    ! [X0: b,X1: set_b] : ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ),
    inference(cnf_transformation,[],[f1006]) ).

thf(f1006,plain,
    ! [X0: b,X1: set_b] : ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ),
    inference(rectify,[],[f258]) ).

thf(f258,axiom,
    ! [X1: b,X8: set_b] : ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X1),X8) = vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X1),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X1),X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__absorb2) ).

thf(f2946,plain,
    spl92_76,
    inference(avatar_split_clause,[],[f1612,f2944]) ).

thf(f2944,plain,
    ( spl92_76
  <=> ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_76])]) ).

thf(f1612,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1)) ),
    inference(cnf_transformation,[],[f1005]) ).

thf(f1005,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X1)) ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ! [X8: labele1159362096nt_a_b,X9: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X8),X9) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X8),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X8),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_graph__union__idemp_I2_J) ).

thf(f2942,plain,
    spl92_75,
    inference(avatar_split_clause,[],[f1611,f2940]) ).

thf(f2940,plain,
    ( spl92_75
  <=> ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_75])]) ).

thf(f1611,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0)) ),
    inference(cnf_transformation,[],[f1004]) ).

thf(f1004,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X1),X0)) ),
    inference(rectify,[],[f19]) ).

thf(f19,axiom,
    ! [X8: labele1159362096nt_a_b,X9: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X9),X8) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X8),vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X9),X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_graph__union__idemp_I3_J) ).

thf(f2938,plain,
    spl92_74,
    inference(avatar_split_clause,[],[f1610,f2936]) ).

thf(f2936,plain,
    ( spl92_74
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_74])]) ).

thf(f1610,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f1003,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ),
    inference(rectify,[],[f259]) ).

thf(f259,axiom,
    ! [X1: produc1871334759_a_nat,X8: set_Pr1987088711_a_nat] : ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X1),X8) = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X1),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X1),X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__absorb2) ).

thf(f2934,plain,
    spl92_73,
    inference(avatar_split_clause,[],[f2397,f2932]) ).

thf(f2932,plain,
    ( spl92_73
  <=> ! [X0: set_b] :
        ( ( bot_bot_set_b != X0 )
        | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_73])]) ).

thf(f2397,plain,
    ! [X0: set_b] :
      ( ( bot_bot_set_b != X0 )
      | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ),
    inference(equality_proxy_clausification,[],[f2396]) ).

thf(f2396,plain,
    ! [X0: set_b] :
      ( ( $false = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),vEQ(set_b),bot_bot_set_b),X0) )
      | ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,X0),bot_bot_set_b) ) ),
    inference(binary_proxy_clausification,[],[f1559]) ).

thf(f2924,plain,
    spl92_72,
    inference(avatar_split_clause,[],[f1576,f2922]) ).

thf(f2922,plain,
    ( spl92_72
  <=> ! [X0: labele1159362096nt_a_b] :
        ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_72])]) ).

thf(f1576,plain,
    ! [X0: labele1159362096nt_a_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0))) ) ),
    inference(cnf_transformation,[],[f1082]) ).

thf(f1082,plain,
    ! [X0: labele1159362096nt_a_b] :
      ( ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0))) ) ),
    inference(ennf_transformation,[],[f449]) ).

thf(f449,plain,
    ! [X0: labele1159362096nt_a_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0))) )
     => ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 ) ),
    inference(fool_elimination,[],[f448]) ).

thf(f448,plain,
    ! [X0: labele1159362096nt_a_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)))
     => ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = X0 ) ),
    inference(rectify,[],[f223]) ).

thf(f223,axiom,
    ! [X7: labele1159362096nt_a_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(set_Pr1324126435od_b_b,sTfun(set_Pr1324126435od_b_b,$o),ord_le123089219od_b_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X7)),vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X7)))
     => ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X7) = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_restrict__subsD) ).

thf(f2914,plain,
    spl92_71,
    inference(avatar_split_clause,[],[f1609,f2912]) ).

thf(f2912,plain,
    ( spl92_71
  <=> ! [X0: set_Product_prod_b_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X0),X1)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_71])]) ).

thf(f1609,plain,
    ! [X0: set_Product_prod_b_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X0),X1)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1)) ),
    inference(cnf_transformation,[],[f1002]) ).

thf(f1002,plain,
    ! [X0: set_Product_prod_b_b,X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X0),X1)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1)) ),
    inference(rectify,[],[f156]) ).

thf(f156,axiom,
    ! [X10: set_Product_prod_b_b,X7: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,X10),X7)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X10),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_map__graph__selectors_I1_J) ).

thf(f2903,plain,
    spl92_70,
    inference(avatar_split_clause,[],[f1571,f2901]) ).

thf(f2901,plain,
    ( spl92_70
  <=> ! [X0: produc1871334759_a_nat] :
        ( ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X0),g) )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_70])]) ).

thf(f1571,plain,
    ! [X0: produc1871334759_a_nat] :
      ( ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X0),g) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l)) ) ),
    inference(cnf_transformation,[],[f1077]) ).

thf(f1077,plain,
    ! [X0: produc1871334759_a_nat] :
      ( ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X0),g) )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l)) ) ),
    inference(ennf_transformation,[],[f439]) ).

thf(f439,plain,
    ! [X0: produc1871334759_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l)) )
     => ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X0),g) ) ),
    inference(fool_elimination,[],[f438]) ).

thf(f438,plain,
    ! [X0: produc1871334759_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l))
     => vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X0),g) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ! [X2: produc1871334759_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X2),vAPP(set_St761939237tant_a,set_Pr1987088711_a_nat,standa1568205540ules_a,l))
     => vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,X2),g) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms_I2_J) ).

thf(f2899,plain,
    spl92_69,
    inference(avatar_split_clause,[],[f1564,f2897]) ).

thf(f2897,plain,
    ( spl92_69
  <=> ! [X0: set_b] : ( vAPP(sTfun(b,$o),set_b,collect_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_69])]) ).

thf(f1564,plain,
    ! [X0: set_b] : ( vAPP(sTfun(b,$o),set_b,collect_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),X0)) = X0 ),
    inference(cnf_transformation,[],[f427]) ).

thf(f427,plain,
    ! [X0: set_b] : ( vAPP(sTfun(b,$o),set_b,collect_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),X0)) = X0 ),
    inference(fool_elimination,[],[f426]) ).

thf(f426,plain,
    ! [X0: set_b] :
      ( vAPP(sTfun(b,$o),set_b,collect_b,
          ^ [X1: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0)) = X0 ),
    inference(rectify,[],[f50]) ).

thf(f50,axiom,
    ! [X8: set_b] :
      ( vAPP(sTfun(b,$o),set_b,collect_b,
          ^ [X26: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X26),X8)) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).

thf(f2889,plain,
    spl92_68,
    inference(avatar_split_clause,[],[f1563,f2887]) ).

thf(f2887,plain,
    ( spl92_68
  <=> ! [X0: set_Product_prod_b_b] : ( vAPP(sTfun(product_prod_b_b,$o),set_Product_prod_b_b,collec1481886546od_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,$o),vAPP(sTfun(product_prod_b_b,sTfun(set_Product_prod_b_b,$o)),sTfun(set_Product_prod_b_b,sTfun(product_prod_b_b,$o)),cCOMB,member1285940496od_b_b),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_68])]) ).

thf(f1563,plain,
    ! [X0: set_Product_prod_b_b] : ( vAPP(sTfun(product_prod_b_b,$o),set_Product_prod_b_b,collec1481886546od_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,$o),vAPP(sTfun(product_prod_b_b,sTfun(set_Product_prod_b_b,$o)),sTfun(set_Product_prod_b_b,sTfun(product_prod_b_b,$o)),cCOMB,member1285940496od_b_b),X0)) = X0 ),
    inference(cnf_transformation,[],[f425]) ).

thf(f425,plain,
    ! [X0: set_Product_prod_b_b] : ( vAPP(sTfun(product_prod_b_b,$o),set_Product_prod_b_b,collec1481886546od_b_b,vAPP(set_Product_prod_b_b,sTfun(product_prod_b_b,$o),vAPP(sTfun(product_prod_b_b,sTfun(set_Product_prod_b_b,$o)),sTfun(set_Product_prod_b_b,sTfun(product_prod_b_b,$o)),cCOMB,member1285940496od_b_b),X0)) = X0 ),
    inference(fool_elimination,[],[f424]) ).

thf(f424,plain,
    ! [X0: set_Product_prod_b_b] :
      ( vAPP(sTfun(product_prod_b_b,$o),set_Product_prod_b_b,collec1481886546od_b_b,
          ^ [X1: product_prod_b_b] : vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0)) = X0 ),
    inference(rectify,[],[f51]) ).

thf(f51,axiom,
    ! [X8: set_Product_prod_b_b] :
      ( vAPP(sTfun(product_prod_b_b,$o),set_Product_prod_b_b,collec1481886546od_b_b,
          ^ [X26: product_prod_b_b] : vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X26),X8)) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__mem__eq) ).

thf(f2885,plain,
    spl92_67,
    inference(avatar_split_clause,[],[f1562,f2883]) ).

thf(f2883,plain,
    ( spl92_67
  <=> ! [X0: set_Pr1324126435od_b_b] : ( vAPP(sTfun(produc1213276845od_b_b,$o),set_Pr1324126435od_b_b,collec279084418od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o),vAPP(sTfun(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o)),sTfun(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o)),cCOMB,member1516365892od_b_b),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_67])]) ).

thf(f1562,plain,
    ! [X0: set_Pr1324126435od_b_b] : ( vAPP(sTfun(produc1213276845od_b_b,$o),set_Pr1324126435od_b_b,collec279084418od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o),vAPP(sTfun(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o)),sTfun(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o)),cCOMB,member1516365892od_b_b),X0)) = X0 ),
    inference(cnf_transformation,[],[f423]) ).

thf(f423,plain,
    ! [X0: set_Pr1324126435od_b_b] : ( vAPP(sTfun(produc1213276845od_b_b,$o),set_Pr1324126435od_b_b,collec279084418od_b_b,vAPP(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o),vAPP(sTfun(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o)),sTfun(set_Pr1324126435od_b_b,sTfun(produc1213276845od_b_b,$o)),cCOMB,member1516365892od_b_b),X0)) = X0 ),
    inference(fool_elimination,[],[f422]) ).

thf(f422,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( vAPP(sTfun(produc1213276845od_b_b,$o),set_Pr1324126435od_b_b,collec279084418od_b_b,
          ^ [X1: produc1213276845od_b_b] : vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0)) = X0 ),
    inference(rectify,[],[f52]) ).

thf(f52,axiom,
    ! [X8: set_Pr1324126435od_b_b] :
      ( vAPP(sTfun(produc1213276845od_b_b,$o),set_Pr1324126435od_b_b,collec279084418od_b_b,
          ^ [X26: produc1213276845od_b_b] : vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X26),X8)) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Collect__mem__eq) ).

thf(f2880,plain,
    spl92_66,
    inference(avatar_split_clause,[],[f1935,f2877]) ).

thf(f2877,plain,
    ( spl92_66
  <=> ( vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_66])]) ).

thf(f1935,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true,
    inference(cnf_transformation,[],[f951]) ).

thf(f951,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true,
    inference(fool_elimination,[],[f950]) ).

thf(f950,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Orefl) ).

thf(f2875,plain,
    spl92_65,
    inference(avatar_split_clause,[],[f1934,f2872]) ).

thf(f2872,plain,
    ( spl92_65
  <=> ( vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),equiv_equiv_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_65])]) ).

thf(f1934,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),equiv_equiv_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true,
    inference(cnf_transformation,[],[f949]) ).

thf(f949,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),equiv_equiv_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)) = $true,
    inference(fool_elimination,[],[f948]) ).

thf(f948,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),equiv_equiv_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),
    inference(rectify,[],[f11]) ).

thf(f11,axiom,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),equiv_equiv_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_equiv) ).

thf(f2870,plain,
    spl92_64,
    inference(avatar_split_clause,[],[f1543,f2868]) ).

thf(f2868,plain,
    ( spl92_64
  <=> ! [X0: set_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_64])]) ).

thf(f1543,plain,
    ! [X0: set_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0)) ),
    inference(cnf_transformation,[],[f975]) ).

thf(f975,plain,
    ! [X0: set_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X0)) ),
    inference(rectify,[],[f282]) ).

thf(f282,axiom,
    ! [X32: set_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X32) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,bot_bo1664927607od_b_b),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_graph__empty__e) ).

thf(f2829,plain,
    spl92_63,
    inference(avatar_split_clause,[],[f1665,f2827]) ).

thf(f2827,plain,
    ( spl92_63
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
        ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1) = X1 )
        | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_63])]) ).

thf(f1665,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1) = X1 )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1124]) ).

thf(f1124,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1) = X1 )
      | ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f559]) ).

thf(f559,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1) )
     => ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1) = X1 ) ),
    inference(fool_elimination,[],[f558]) ).

thf(f558,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),X1)
     => ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1) = X1 ) ),
    inference(rectify,[],[f324]) ).

thf(f324,axiom,
    ! [X14: product_prod_b_b,X8: set_Product_prod_b_b] :
      ( vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),X8)
     => ( vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X14),X8) = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_insert__absorb) ).

thf(f2825,plain,
    spl92_62,
    inference(avatar_split_clause,[],[f1659,f2823]) ).

thf(f2823,plain,
    ( spl92_62
  <=> ! [X0: b,X1: set_b] :
        ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = X1 )
        | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_62])]) ).

thf(f1659,plain,
    ! [X0: b,X1: set_b] :
      ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = X1 )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1120]) ).

thf(f1120,plain,
    ! [X0: b,X1: set_b] :
      ( ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = X1 )
      | ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f551]) ).

thf(f551,plain,
    ! [X0: b,X1: set_b] :
      ( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1) )
     => ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = X1 ) ),
    inference(fool_elimination,[],[f550]) ).

thf(f550,plain,
    ! [X0: b,X1: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),X1)
     => ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) = X1 ) ),
    inference(rectify,[],[f323]) ).

thf(f323,axiom,
    ! [X14: b,X8: set_b] :
      ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),X8)
     => ( vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X14),X8) = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_insert__absorb) ).

thf(f2821,plain,
    spl92_61,
    inference(avatar_split_clause,[],[f1653,f2819]) ).

thf(f2819,plain,
    ( spl92_61
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
        ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1) = X1 )
        | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_61])]) ).

thf(f1653,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1) = X1 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(cnf_transformation,[],[f1116]) ).

thf(f1116,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1) = X1 )
      | ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) ) ),
    inference(ennf_transformation,[],[f543]) ).

thf(f543,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1) )
     => ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1) = X1 ) ),
    inference(fool_elimination,[],[f542]) ).

thf(f542,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),X1)
     => ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1) = X1 ) ),
    inference(rectify,[],[f325]) ).

thf(f325,axiom,
    ! [X14: produc1213276845od_b_b,X8: set_Pr1324126435od_b_b] :
      ( vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),X8)
     => ( vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X14),X8) = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__absorb) ).

thf(f2817,plain,
    spl92_60,
    inference(avatar_split_clause,[],[f1648,f2815]) ).

thf(f2815,plain,
    ( spl92_60
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
        ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = X1 )
        | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_60])]) ).

thf(f1648,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = X1 )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f1113]) ).

thf(f1113,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = X1 )
      | ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f537]) ).

thf(f537,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1) )
     => ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = X1 ) ),
    inference(fool_elimination,[],[f536]) ).

thf(f536,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),X1)
     => ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) = X1 ) ),
    inference(rectify,[],[f322]) ).

thf(f322,axiom,
    ! [X14: produc1871334759_a_nat,X8: set_Pr1987088711_a_nat] :
      ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),X8)
     => ( vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X14),X8) = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_insert__absorb) ).

thf(f2805,plain,
    spl92_59,
    inference(avatar_split_clause,[],[f1632,f2803]) ).

thf(f2803,plain,
    ( spl92_59
  <=> ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] :
        ( ( X0 = X1 )
        | ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1) )
        | ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_59])]) ).

thf(f1632,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] :
      ( ( X0 = X1 )
      | ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1) )
      | ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X1) ) ),
    inference(cnf_transformation,[],[f1102]) ).

thf(f1102,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] :
      ( ( X0 = X1 )
      | ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1) )
      | ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X1) ) ),
    inference(flattening,[],[f1101]) ).

thf(f1101,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] :
      ( ( X0 = X1 )
      | ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1) )
      | ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0) != vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X1) ) ),
    inference(ennf_transformation,[],[f1016]) ).

thf(f1016,plain,
    ! [X0: labele1159362096nt_a_b,X1: labele1159362096nt_a_b] :
      ( ( ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X1) )
        & ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0) = vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X1) ) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f38]) ).

thf(f38,axiom,
    ! [X13: labele1159362096nt_a_b,X20: labele1159362096nt_a_b] :
      ( ( ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X13) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X20) )
        & ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X13) = vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X20) ) )
     => ( X13 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_labeled__graph_Oexpand) ).

thf(f2801,plain,
    spl92_58,
    inference(avatar_split_clause,[],[f1542,f2799]) ).

thf(f2799,plain,
    ( spl92_58
  <=> ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_58])]) ).

thf(f1542,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))),X0) ),
    inference(cnf_transformation,[],[f974]) ).

thf(f974,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0))),X0) ),
    inference(rectify,[],[f29]) ).

thf(f29,axiom,
    ! [X15: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(set_Product_prod_b_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),map_gr926947118tant_a,vAPP(set_b,set_Product_prod_b_b,id_on_b,vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X15))),X15) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_map__graph__fn__id_I2_J) ).

thf(f2792,plain,
    spl92_57,
    inference(avatar_split_clause,[],[f1685,f2790]) ).

thf(f2790,plain,
    ( spl92_57
  <=> ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_57])]) ).

thf(f1685,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1)) ),
    inference(cnf_transformation,[],[f589]) ).

thf(f589,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1)) ),
    inference(fool_elimination,[],[f588]) ).

thf(f588,plain,
    ! [X0: product_prod_b_b,X1: set_Product_prod_b_b] : vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X0),X1)),
    inference(rectify,[],[f340]) ).

thf(f340,axiom,
    ! [X14: product_prod_b_b,X9: set_Product_prod_b_b] : vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X14),vAPP(set_Product_prod_b_b,set_Product_prod_b_b,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,set_Product_prod_b_b),insert1952693431od_b_b,X14),X9)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_insertI1) ).

thf(f2788,plain,
    spl92_56,
    inference(avatar_split_clause,[],[f1684,f2786]) ).

thf(f2786,plain,
    ( spl92_56
  <=> ! [X0: b,X1: set_b] : ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_56])]) ).

thf(f1684,plain,
    ! [X0: b,X1: set_b] : ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ),
    inference(cnf_transformation,[],[f587]) ).

thf(f587,plain,
    ! [X0: b,X1: set_b] : ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)) ),
    inference(fool_elimination,[],[f586]) ).

thf(f586,plain,
    ! [X0: b,X1: set_b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1)),
    inference(rectify,[],[f339]) ).

thf(f339,axiom,
    ! [X14: b,X9: set_b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X14),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X14),X9)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_insertI1) ).

thf(f2784,plain,
    spl92_55,
    inference(avatar_split_clause,[],[f1683,f2782]) ).

thf(f2782,plain,
    ( spl92_55
  <=> ! [X0: labele935650037_a_nat,X1: labele1159362096nt_a_b] : ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,vAPP(labele935650037_a_nat,produc1871334759_a_nat,vAPP(labele935650037_a_nat,sTfun(labele935650037_a_nat,produc1871334759_a_nat),produc1676969687_a_nat,X0),X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_55])]) ).

thf(f1683,plain,
    ! [X0: labele935650037_a_nat,X1: labele1159362096nt_a_b] : ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,vAPP(labele935650037_a_nat,produc1871334759_a_nat,vAPP(labele935650037_a_nat,sTfun(labele935650037_a_nat,produc1871334759_a_nat),produc1676969687_a_nat,X0),X0)),X1) ),
    inference(cnf_transformation,[],[f585]) ).

thf(f585,plain,
    ! [X0: labele935650037_a_nat,X1: labele1159362096nt_a_b] : ( $true = vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,vAPP(labele935650037_a_nat,produc1871334759_a_nat,vAPP(labele935650037_a_nat,sTfun(labele935650037_a_nat,produc1871334759_a_nat),produc1676969687_a_nat,X0),X0)),X1) ),
    inference(fool_elimination,[],[f584]) ).

thf(f584,plain,
    ! [X0: labele935650037_a_nat,X1: labele1159362096nt_a_b] : vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,vAPP(labele935650037_a_nat,produc1871334759_a_nat,vAPP(labele935650037_a_nat,sTfun(labele935650037_a_nat,produc1871334759_a_nat),produc1676969687_a_nat,X0),X0)),X1),
    inference(rectify,[],[f83]) ).

thf(f83,axiom,
    ! [X33: labele935650037_a_nat,X7: labele1159362096nt_a_b] : vAPP(labele1159362096nt_a_b,$o,vAPP(produc1871334759_a_nat,sTfun(labele1159362096nt_a_b,$o),mainta1604381365_nat_b,vAPP(labele935650037_a_nat,produc1871334759_a_nat,vAPP(labele935650037_a_nat,sTfun(labele935650037_a_nat,produc1871334759_a_nat),produc1676969687_a_nat,X33),X33)),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_maintained__refl) ).

thf(f2780,plain,
    spl92_54,
    inference(avatar_split_clause,[],[f1682,f2778]) ).

thf(f2778,plain,
    ( spl92_54
  <=> ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_54])]) ).

thf(f1682,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1)) ),
    inference(cnf_transformation,[],[f583]) ).

thf(f583,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1)) ),
    inference(fool_elimination,[],[f582]) ).

thf(f582,plain,
    ! [X0: produc1213276845od_b_b,X1: set_Pr1324126435od_b_b] : vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X0),X1)),
    inference(rectify,[],[f341]) ).

thf(f341,axiom,
    ! [X14: produc1213276845od_b_b,X9: set_Pr1324126435od_b_b] : vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X14),vAPP(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,set_Pr1324126435od_b_b),insert2037698781od_b_b,X14),X9)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insertI1) ).

thf(f2776,plain,
    spl92_53,
    inference(avatar_split_clause,[],[f1681,f2774]) ).

thf(f2774,plain,
    ( spl92_53
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_53])]) ).

thf(f1681,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f581]) ).

thf(f581,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)) ),
    inference(fool_elimination,[],[f580]) ).

thf(f580,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1)),
    inference(rectify,[],[f338]) ).

thf(f338,axiom,
    ! [X14: produc1871334759_a_nat,X9: set_Pr1987088711_a_nat] : vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X14),vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X14),X9)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_insertI1) ).

thf(f2761,plain,
    spl92_52,
    inference(avatar_split_clause,[],[f1933,f2758]) ).

thf(f1933,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true,
    inference(cnf_transformation,[],[f947]) ).

thf(f947,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true,
    inference(fool_elimination,[],[f946]) ).

thf(f946,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,x)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fv_I1_J) ).

thf(f2756,plain,
    ( spl92_51
    | ~ spl92_3
    | ~ spl92_21 ),
    inference(avatar_split_clause,[],[f2656,f2615,f2505,f2754]) ).

thf(f2754,plain,
    ( spl92_51
  <=> ! [X0: product_prod_b_b] : ( $false = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_51])]) ).

thf(f2505,plain,
    ( spl92_3
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_3])]) ).

thf(f2615,plain,
    ( spl92_21
  <=> ! [X0: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_21])]) ).

thf(f2656,plain,
    ( ! [X0: product_prod_b_b] : ( $false = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) )
    | ~ spl92_3
    | ~ spl92_21 ),
    inference(trivial_inequality_removal,[],[f2655]) ).

thf(f2655,plain,
    ( ! [X0: product_prod_b_b] :
        ( ( $true != $true )
        | ( $false = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ) )
    | ~ spl92_3
    | ~ spl92_21 ),
    inference(superposition,[],[f2616,f2506]) ).

thf(f2506,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl92_3 ),
    inference(avatar_component_clause,[],[f2505]) ).

thf(f2616,plain,
    ( ! [X0: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) )
    | ~ spl92_21 ),
    inference(avatar_component_clause,[],[f2615]) ).

thf(f2752,plain,
    spl92_50,
    inference(avatar_split_clause,[],[f1932,f2749]) ).

thf(f2749,plain,
    ( spl92_50
  <=> ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,y)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_50])]) ).

thf(f1932,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,y)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true,
    inference(cnf_transformation,[],[f945]) ).

thf(f945,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,y)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true,
    inference(fool_elimination,[],[f944]) ).

thf(f944,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,y)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(b,b,f,y)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_fv_I2_J) ).

thf(f2747,plain,
    spl92_49,
    inference(avatar_split_clause,[],[f1620,f2745]) ).

thf(f2745,plain,
    ( spl92_49
  <=> ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$true),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_49])]) ).

thf(f1620,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$true),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f501]) ).

thf(f501,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$true),X0),X1) = X0 ),
    inference(fool_elimination,[],[f500]) ).

thf(f500,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$true),X0),X1) = X0 ),
    inference(rectify,[],[f359]) ).

thf(f359,axiom,
    ! [X1: b,X4: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$true),X1),X4) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001tf__b_T) ).

thf(f2743,plain,
    spl92_48,
    inference(avatar_split_clause,[],[f1619,f2741]) ).

thf(f2741,plain,
    ( spl92_48
  <=> ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$false),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_48])]) ).

thf(f1619,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$false),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f499]) ).

thf(f499,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$false),X0),X1) = X1 ),
    inference(fool_elimination,[],[f498]) ).

thf(f498,plain,
    ! [X0: b,X1: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$false),X0),X1) = X1 ),
    inference(rectify,[],[f358]) ).

thf(f358,axiom,
    ! [X1: b,X4: b] : ( vAPP(b,b,vAPP(b,sTfun(b,b),vAPP($o,sTfun(b,sTfun(b,b)),if_b,$false),X1),X4) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001tf__b_T) ).

thf(f2739,plain,
    spl92_47,
    inference(avatar_split_clause,[],[f1590,f2737]) ).

thf(f2737,plain,
    ( spl92_47
  <=> ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK13,X0)),vAPP(product_prod_b_b,b,sK14,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_47])]) ).

thf(f1590,plain,
    ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK13,X0)),vAPP(product_prod_b_b,b,sK14,X0)) = X0 ),
    inference(cnf_transformation,[],[f1407]) ).

thf(f1407,plain,
    ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK13,X0)),vAPP(product_prod_b_b,b,sK14,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f994,f1406]) ).

thf(f1406,plain,
    ! [X0: product_prod_b_b] :
      ( ? [X1: b,X2: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X1),X2) = X0 )
     => ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK13,X0)),vAPP(product_prod_b_b,b,sK14,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f994,plain,
    ! [X0: product_prod_b_b] :
    ? [X1: b,X2: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X1),X2) = X0 ),
    inference(rectify,[],[f101]) ).

thf(f101,axiom,
    ! [X50: product_prod_b_b] :
    ? [X18: b,X36: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X18),X36) = X50 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_surj__pair) ).

thf(f2735,plain,
    spl92_46,
    inference(avatar_split_clause,[],[f1589,f2733]) ).

thf(f2733,plain,
    ( spl92_46
  <=> ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK11,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK12,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_46])]) ).

thf(f1589,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK11,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK12,X0)) = X0 ),
    inference(cnf_transformation,[],[f1405]) ).

thf(f1405,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK11,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK12,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f993,f1404]) ).

thf(f1404,plain,
    ! [X0: produc1213276845od_b_b] :
      ( ? [X1: standard_Constant_a,X2: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),X2) = X0 )
     => ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK11,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK12,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f993,plain,
    ! [X0: produc1213276845od_b_b] :
    ? [X1: standard_Constant_a,X2: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),X2) = X0 ),
    inference(rectify,[],[f102]) ).

thf(f102,axiom,
    ! [X50: produc1213276845od_b_b] :
    ? [X18: standard_Constant_a,X36: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X18),X36) = X50 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_surj__pair) ).

thf(f2731,plain,
    spl92_45,
    inference(avatar_split_clause,[],[f1579,f2729]) ).

thf(f2729,plain,
    ( spl92_45
  <=> ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK6,X0)),vAPP(product_prod_b_b,b,sK7,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_45])]) ).

thf(f1579,plain,
    ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK6,X0)),vAPP(product_prod_b_b,b,sK7,X0)) = X0 ),
    inference(cnf_transformation,[],[f1401]) ).

thf(f1401,plain,
    ! [X0: product_prod_b_b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK6,X0)),vAPP(product_prod_b_b,b,sK7,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f1085,f1400]) ).

thf(f1400,plain,
    ! [X0: product_prod_b_b] :
      ( ? [X1: b,X2: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X1),X2) = X0 )
     => ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,vAPP(product_prod_b_b,b,sK6,X0)),vAPP(product_prod_b_b,b,sK7,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1085,plain,
    ! [X0: product_prod_b_b] :
    ? [X1: b,X2: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X1),X2) = X0 ),
    inference(ennf_transformation,[],[f983]) ).

thf(f983,plain,
    ! [X0: product_prod_b_b] :
      ~ ! [X1: b,X2: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X1),X2) != X0 ),
    inference(rectify,[],[f107]) ).

thf(f107,axiom,
    ! [X4: product_prod_b_b] :
      ~ ! [X51: b,X52: b] : ( vAPP(b,product_prod_b_b,vAPP(b,sTfun(b,product_prod_b_b),product_Pair_b_b,X51),X52) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Oexhaust) ).

thf(f2727,plain,
    spl92_44,
    inference(avatar_split_clause,[],[f1578,f2725]) ).

thf(f2725,plain,
    ( spl92_44
  <=> ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK4,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK5,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_44])]) ).

thf(f1578,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK4,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK5,X0)) = X0 ),
    inference(cnf_transformation,[],[f1399]) ).

thf(f1399,plain,
    ! [X0: produc1213276845od_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK4,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK5,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f1084,f1398]) ).

thf(f1398,plain,
    ! [X0: produc1213276845od_b_b] :
      ( ? [X1: standard_Constant_a,X2: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),X2) = X0 )
     => ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,vAPP(produc1213276845od_b_b,standard_Constant_a,sK4,X0)),vAPP(produc1213276845od_b_b,product_prod_b_b,sK5,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1084,plain,
    ! [X0: produc1213276845od_b_b] :
    ? [X1: standard_Constant_a,X2: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),X2) = X0 ),
    inference(ennf_transformation,[],[f982]) ).

thf(f982,plain,
    ! [X0: produc1213276845od_b_b] :
      ~ ! [X1: standard_Constant_a,X2: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X1),X2) != X0 ),
    inference(rectify,[],[f108]) ).

thf(f108,axiom,
    ! [X4: produc1213276845od_b_b] :
      ~ ! [X51: standard_Constant_a,X52: product_prod_b_b] : ( vAPP(product_prod_b_b,produc1213276845od_b_b,vAPP(standard_Constant_a,sTfun(product_prod_b_b,produc1213276845od_b_b),produc1432590431od_b_b,X51),X52) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Oprod_Oexhaust) ).

thf(f2723,plain,
    spl92_43,
    inference(avatar_split_clause,[],[f1540,f2721]) ).

thf(f2721,plain,
    ( spl92_43
  <=> ! [X0: labele1159362096nt_a_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_43])]) ).

thf(f1540,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0)) = X0 ),
    inference(cnf_transformation,[],[f972]) ).

thf(f972,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X0)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0)) = X0 ),
    inference(rectify,[],[f24]) ).

thf(f24,axiom,
    ! [X13: labele1159362096nt_a_b] : ( vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,X13)),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X13)) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_labeled__graph_Ocollapse) ).

thf(f2717,plain,
    ( spl92_42
    | ~ spl92_3
    | ~ spl92_20 ),
    inference(avatar_split_clause,[],[f2654,f2611,f2505,f2715]) ).

thf(f2715,plain,
    ( spl92_42
  <=> ! [X0: b] : ( $false = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_42])]) ).

thf(f2611,plain,
    ( spl92_20
  <=> ! [X0: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_20])]) ).

thf(f2654,plain,
    ( ! [X0: b] : ( $false = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) )
    | ~ spl92_3
    | ~ spl92_20 ),
    inference(trivial_inequality_removal,[],[f2653]) ).

thf(f2653,plain,
    ( ! [X0: b] :
        ( ( $true != $true )
        | ( $false = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ) )
    | ~ spl92_3
    | ~ spl92_20 ),
    inference(superposition,[],[f2612,f2506]) ).

thf(f2612,plain,
    ( ! [X0: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) )
    | ~ spl92_20 ),
    inference(avatar_component_clause,[],[f2611]) ).

thf(f2711,plain,
    spl92_41,
    inference(avatar_split_clause,[],[f1570,f2709]) ).

thf(f2709,plain,
    ( spl92_41
  <=> ! [X0: set_Product_prod_b_b] :
        ( ( bot_bo1343651123od_b_b = X0 )
        | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,sK3,X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_41])]) ).

thf(f1570,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ( bot_bo1343651123od_b_b = X0 )
      | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,sK3,X0)),X0) ) ),
    inference(cnf_transformation,[],[f1397]) ).

thf(f1397,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ( bot_bo1343651123od_b_b = X0 )
      | ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,sK3,X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1076,f1396]) ).

thf(f1396,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ? [X1: product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0) )
     => ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,vAPP(set_Product_prod_b_b,product_prod_b_b,sK3,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1076,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ( bot_bo1343651123od_b_b = X0 )
      | ? [X1: product_prod_b_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0) ) ),
    inference(ennf_transformation,[],[f981]) ).

thf(f981,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ! [X1: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0) )
     => ( bot_bo1343651123od_b_b = X0 ) ),
    inference(flattening,[],[f437]) ).

thf(f437,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ! [X1: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0) )
     => ( bot_bo1343651123od_b_b = X0 ) ),
    inference(fool_elimination,[],[f436]) ).

thf(f436,plain,
    ! [X0: set_Product_prod_b_b] :
      ( ! [X1: product_prod_b_b] : ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X1),X0)
     => ( bot_bo1343651123od_b_b = X0 ) ),
    inference(rectify,[],[f288]) ).

thf(f288,axiom,
    ! [X8: set_Product_prod_b_b] :
      ( ! [X36: product_prod_b_b] : ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X36),X8)
     => ( bot_bo1343651123od_b_b = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_equals0I) ).

thf(f2707,plain,
    spl92_40,
    inference(avatar_split_clause,[],[f1569,f2705]) ).

thf(f2705,plain,
    ( spl92_40
  <=> ! [X0: set_b] :
        ( ( bot_bot_set_b = X0 )
        | ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,sK2,X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_40])]) ).

thf(f1569,plain,
    ! [X0: set_b] :
      ( ( bot_bot_set_b = X0 )
      | ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,sK2,X0)),X0) ) ),
    inference(cnf_transformation,[],[f1395]) ).

thf(f1395,plain,
    ! [X0: set_b] :
      ( ( bot_bot_set_b = X0 )
      | ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,sK2,X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f1075,f1394]) ).

thf(f1394,plain,
    ! [X0: set_b] :
      ( ? [X1: b] : ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0) )
     => ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(set_b,b,sK2,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1075,plain,
    ! [X0: set_b] :
      ( ( bot_bot_set_b = X0 )
      | ? [X1: b] : ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0) ) ),
    inference(ennf_transformation,[],[f980]) ).

thf(f980,plain,
    ! [X0: set_b] :
      ( ! [X1: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0) )
     => ( bot_bot_set_b = X0 ) ),
    inference(flattening,[],[f435]) ).

thf(f435,plain,
    ! [X0: set_b] :
      ( ! [X1: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0) )
     => ( bot_bot_set_b = X0 ) ),
    inference(fool_elimination,[],[f434]) ).

thf(f434,plain,
    ! [X0: set_b] :
      ( ! [X1: b] : ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),X0)
     => ( bot_bot_set_b = X0 ) ),
    inference(rectify,[],[f290]) ).

thf(f290,axiom,
    ! [X8: set_b] :
      ( ! [X36: b] : ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X36),X8)
     => ( bot_bot_set_b = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_equals0I) ).

thf(f2703,plain,
    spl92_39,
    inference(avatar_split_clause,[],[f1568,f2701]) ).

thf(f2701,plain,
    ( spl92_39
  <=> ! [X0: set_Pr1324126435od_b_b] :
        ( ( bot_bo1664927607od_b_b = X0 )
        | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,sK1,X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_39])]) ).

thf(f1568,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ( bot_bo1664927607od_b_b = X0 )
      | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,sK1,X0)),X0) ) ),
    inference(cnf_transformation,[],[f1393]) ).

thf(f1393,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ( bot_bo1664927607od_b_b = X0 )
      | ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,sK1,X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1074,f1392]) ).

thf(f1392,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ? [X1: produc1213276845od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0) )
     => ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,vAPP(set_Pr1324126435od_b_b,produc1213276845od_b_b,sK1,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1074,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ( bot_bo1664927607od_b_b = X0 )
      | ? [X1: produc1213276845od_b_b] : ( $true = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0) ) ),
    inference(ennf_transformation,[],[f979]) ).

thf(f979,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ! [X1: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0) )
     => ( bot_bo1664927607od_b_b = X0 ) ),
    inference(flattening,[],[f433]) ).

thf(f433,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ! [X1: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0) )
     => ( bot_bo1664927607od_b_b = X0 ) ),
    inference(fool_elimination,[],[f432]) ).

thf(f432,plain,
    ! [X0: set_Pr1324126435od_b_b] :
      ( ! [X1: produc1213276845od_b_b] : ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X1),X0)
     => ( bot_bo1664927607od_b_b = X0 ) ),
    inference(rectify,[],[f289]) ).

thf(f289,axiom,
    ! [X8: set_Pr1324126435od_b_b] :
      ( ! [X36: produc1213276845od_b_b] : ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X36),X8)
     => ( bot_bo1664927607od_b_b = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_equals0I) ).

thf(f2699,plain,
    spl92_38,
    inference(avatar_split_clause,[],[f1567,f2697]) ).

thf(f2697,plain,
    ( spl92_38
  <=> ! [X0: set_Pr1987088711_a_nat] :
        ( ( bot_bo1836341171_a_nat = X0 )
        | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,vAPP(set_Pr1987088711_a_nat,produc1871334759_a_nat,sK0,X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_38])]) ).

thf(f1567,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( bot_bo1836341171_a_nat = X0 )
      | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,vAPP(set_Pr1987088711_a_nat,produc1871334759_a_nat,sK0,X0)),X0) ) ),
    inference(cnf_transformation,[],[f1391]) ).

thf(f1391,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( bot_bo1836341171_a_nat = X0 )
      | ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,vAPP(set_Pr1987088711_a_nat,produc1871334759_a_nat,sK0,X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1073,f1390]) ).

thf(f1390,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ? [X1: produc1871334759_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X0) )
     => ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,vAPP(set_Pr1987088711_a_nat,produc1871334759_a_nat,sK0,X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

thf(f1073,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ( bot_bo1836341171_a_nat = X0 )
      | ? [X1: produc1871334759_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X0) ) ),
    inference(ennf_transformation,[],[f978]) ).

thf(f978,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ! [X1: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X0) )
     => ( bot_bo1836341171_a_nat = X0 ) ),
    inference(flattening,[],[f431]) ).

thf(f431,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ! [X1: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X0) )
     => ( bot_bo1836341171_a_nat = X0 ) ),
    inference(fool_elimination,[],[f430]) ).

thf(f430,plain,
    ! [X0: set_Pr1987088711_a_nat] :
      ( ! [X1: produc1871334759_a_nat] : ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X1),X0)
     => ( bot_bo1836341171_a_nat = X0 ) ),
    inference(rectify,[],[f291]) ).

thf(f291,axiom,
    ! [X8: set_Pr1987088711_a_nat] :
      ( ! [X36: produc1871334759_a_nat] : ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X36),X8)
     => ( bot_bo1836341171_a_nat = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_equals0I) ).

thf(f2694,plain,
    ( spl92_37
    | ~ spl92_3
    | ~ spl92_19 ),
    inference(avatar_split_clause,[],[f2652,f2607,f2505,f2692]) ).

thf(f2692,plain,
    ( spl92_37
  <=> ! [X0: produc1213276845od_b_b] : ( $false = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_37])]) ).

thf(f2607,plain,
    ( spl92_19
  <=> ! [X0: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_19])]) ).

thf(f2652,plain,
    ( ! [X0: produc1213276845od_b_b] : ( $false = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) )
    | ~ spl92_3
    | ~ spl92_19 ),
    inference(trivial_inequality_removal,[],[f2651]) ).

thf(f2651,plain,
    ( ! [X0: produc1213276845od_b_b] :
        ( ( $true != $true )
        | ( $false = vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ) )
    | ~ spl92_3
    | ~ spl92_19 ),
    inference(superposition,[],[f2608,f2506]) ).

thf(f2608,plain,
    ( ! [X0: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) )
    | ~ spl92_19 ),
    inference(avatar_component_clause,[],[f2607]) ).

thf(f2690,plain,
    spl92_36,
    inference(avatar_split_clause,[],[f1605,f2688]) ).

thf(f2688,plain,
    ( spl92_36
  <=> ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_36])]) ).

thf(f1605,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X1 ),
    inference(cnf_transformation,[],[f998]) ).

thf(f998,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X1 ),
    inference(rectify,[],[f15]) ).

thf(f15,axiom,
    ! [X5: set_Pr1324126435od_b_b,X6: set_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X5),X6)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_labeled__graph_Osel_I2_J) ).

thf(f2686,plain,
    spl92_35,
    inference(avatar_split_clause,[],[f1604,f2684]) ).

thf(f2684,plain,
    ( spl92_35
  <=> ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_35])]) ).

thf(f1604,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X0 ),
    inference(cnf_transformation,[],[f997]) ).

thf(f997,plain,
    ! [X0: set_Pr1324126435od_b_b,X1: set_b] : ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X0),X1)) = X0 ),
    inference(rectify,[],[f32]) ).

thf(f32,axiom,
    ! [X5: set_Pr1324126435od_b_b,X6: set_b] : ( vAPP(labele1159362096nt_a_b,set_Pr1324126435od_b_b,labele1741081071nt_a_b,vAPP(set_b,labele1159362096nt_a_b,vAPP(set_Pr1324126435od_b_b,sTfun(set_b,labele1159362096nt_a_b),labele1230159100nt_a_b,X5),X6)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_labeled__graph_Osel_I1_J) ).

thf(f2682,plain,
    spl92_34,
    inference(avatar_split_clause,[],[f1593,f2680]) ).

thf(f2680,plain,
    ( spl92_34
  <=> ! [X0: set_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,X0),vAPP(set_b,set_Product_prod_b_b,id_on_b,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_34])]) ).

thf(f1593,plain,
    ! [X0: set_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,X0),vAPP(set_b,set_Product_prod_b_b,id_on_b,X0)) ),
    inference(cnf_transformation,[],[f473]) ).

thf(f473,plain,
    ! [X0: set_b] : ( $true = vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,X0),vAPP(set_b,set_Product_prod_b_b,id_on_b,X0)) ),
    inference(fool_elimination,[],[f472]) ).

thf(f472,plain,
    ! [X0: set_b] : vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,X0),vAPP(set_b,set_Product_prod_b_b,id_on_b,X0)),
    inference(rectify,[],[f81]) ).

thf(f81,axiom,
    ! [X8: set_b] : vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,X8),vAPP(set_b,set_Product_prod_b_b,id_on_b,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_refl__on__Id__on) ).

thf(f2678,plain,
    spl92_33,
    inference(avatar_split_clause,[],[f1539,f2676]) ).

thf(f2676,plain,
    ( spl92_33
  <=> ! [X0: labele935650037_a_nat > labele935650037_a_nat] : ( bot_bo1836341171_a_nat = vAPP(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat,vAPP(set_la1083530965_a_nat,sTfun(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat),bNF_Gr996500706_a_nat,bot_bo2122869057_a_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_33])]) ).

thf(f1539,plain,
    ! [X0: labele935650037_a_nat > labele935650037_a_nat] : ( bot_bo1836341171_a_nat = vAPP(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat,vAPP(set_la1083530965_a_nat,sTfun(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat),bNF_Gr996500706_a_nat,bot_bo2122869057_a_nat),X0) ),
    inference(cnf_transformation,[],[f971]) ).

thf(f971,plain,
    ! [X0: labele935650037_a_nat > labele935650037_a_nat] : ( bot_bo1836341171_a_nat = vAPP(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat,vAPP(set_la1083530965_a_nat,sTfun(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat),bNF_Gr996500706_a_nat,bot_bo2122869057_a_nat),X0) ),
    inference(rectify,[],[f149]) ).

thf(f149,axiom,
    ! [X10: labele935650037_a_nat > labele935650037_a_nat] : ( bot_bo1836341171_a_nat = vAPP(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat,vAPP(set_la1083530965_a_nat,sTfun(sTfun(labele935650037_a_nat,labele935650037_a_nat),set_Pr1987088711_a_nat),bNF_Gr996500706_a_nat,bot_bo2122869057_a_nat),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Gr__empty) ).

thf(f2674,plain,
    spl92_32,
    inference(avatar_split_clause,[],[f1538,f2672]) ).

thf(f2672,plain,
    ( spl92_32
  <=> ! [X0: b > b] : ( bot_bo1343651123od_b_b = vAPP(sTfun(b,b),set_Product_prod_b_b,vAPP(set_b,sTfun(sTfun(b,b),set_Product_prod_b_b),bNF_Gr_b_b,bot_bot_set_b),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_32])]) ).

thf(f1538,plain,
    ! [X0: b > b] : ( bot_bo1343651123od_b_b = vAPP(sTfun(b,b),set_Product_prod_b_b,vAPP(set_b,sTfun(sTfun(b,b),set_Product_prod_b_b),bNF_Gr_b_b,bot_bot_set_b),X0) ),
    inference(cnf_transformation,[],[f970]) ).

thf(f970,plain,
    ! [X0: b > b] : ( bot_bo1343651123od_b_b = vAPP(sTfun(b,b),set_Product_prod_b_b,vAPP(set_b,sTfun(sTfun(b,b),set_Product_prod_b_b),bNF_Gr_b_b,bot_bot_set_b),X0) ),
    inference(rectify,[],[f150]) ).

thf(f150,axiom,
    ! [X10: b > b] : ( bot_bo1343651123od_b_b = vAPP(sTfun(b,b),set_Product_prod_b_b,vAPP(set_b,sTfun(sTfun(b,b),set_Product_prod_b_b),bNF_Gr_b_b,bot_bot_set_b),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Gr__empty) ).

thf(f2668,plain,
    spl92_31,
    inference(avatar_split_clause,[],[f1537,f2666]) ).

thf(f2666,plain,
    ( spl92_31
  <=> ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_31])]) ).

thf(f1537,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ),
    inference(cnf_transformation,[],[f969]) ).

thf(f969,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X0) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ),
    inference(rectify,[],[f17]) ).

thf(f17,axiom,
    ! [X7: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X7)) = vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_vertices__restrict) ).

thf(f2664,plain,
    spl92_30,
    inference(avatar_split_clause,[],[f1536,f2662]) ).

thf(f2662,plain,
    ( spl92_30
  <=> ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_30])]) ).

thf(f1536,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ),
    inference(cnf_transformation,[],[f968]) ).

thf(f968,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X0)) ),
    inference(rectify,[],[f18]) ).

thf(f18,axiom,
    ! [X1: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X1) = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_restrict__idemp) ).

thf(f2660,plain,
    ( spl92_29
    | ~ spl92_3
    | ~ spl92_18 ),
    inference(avatar_split_clause,[],[f2650,f2603,f2505,f2658]) ).

thf(f2658,plain,
    ( spl92_29
  <=> ! [X0: produc1871334759_a_nat] : ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_29])]) ).

thf(f2603,plain,
    ( spl92_18
  <=> ! [X0: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_18])]) ).

thf(f2650,plain,
    ( ! [X0: produc1871334759_a_nat] : ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) )
    | ~ spl92_3
    | ~ spl92_18 ),
    inference(trivial_inequality_removal,[],[f2649]) ).

thf(f2649,plain,
    ( ! [X0: produc1871334759_a_nat] :
        ( ( $true != $true )
        | ( $false = vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ) )
    | ~ spl92_3
    | ~ spl92_18 ),
    inference(superposition,[],[f2604,f2506]) ).

thf(f2604,plain,
    ( ! [X0: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) )
    | ~ spl92_18 ),
    inference(avatar_component_clause,[],[f2603]) ).

thf(f2648,plain,
    spl92_28,
    inference(avatar_split_clause,[],[f1931,f2645]) ).

thf(f2645,plain,
    ( spl92_28
  <=> ( vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,bot_bot_set_b),bot_bo1343651123od_b_b) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_28])]) ).

thf(f1931,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,bot_bot_set_b),bot_bo1343651123od_b_b) = $true,
    inference(cnf_transformation,[],[f943]) ).

thf(f943,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,bot_bot_set_b),bot_bo1343651123od_b_b) = $true,
    inference(fool_elimination,[],[f942]) ).

thf(f942,plain,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,bot_bot_set_b),bot_bo1343651123od_b_b),
    inference(rectify,[],[f218]) ).

thf(f218,axiom,
    vAPP(set_Product_prod_b_b,$o,vAPP(set_b,sTfun(set_Product_prod_b_b,$o),refl_on_b,bot_bot_set_b),bot_bo1343651123od_b_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_refl__on__empty) ).

thf(f2643,plain,
    spl92_27,
    inference(avatar_split_clause,[],[f1930,f2640]) ).

thf(f2640,plain,
    ( spl92_27
  <=> ( vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_la1083530965_a_nat,sTfun(set_Pr1987088711_a_nat,$o),refl_o1031343860_a_nat,bot_bo2122869057_a_nat),bot_bo1836341171_a_nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_27])]) ).

thf(f1930,plain,
    vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_la1083530965_a_nat,sTfun(set_Pr1987088711_a_nat,$o),refl_o1031343860_a_nat,bot_bo2122869057_a_nat),bot_bo1836341171_a_nat) = $true,
    inference(cnf_transformation,[],[f941]) ).

thf(f941,plain,
    vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_la1083530965_a_nat,sTfun(set_Pr1987088711_a_nat,$o),refl_o1031343860_a_nat,bot_bo2122869057_a_nat),bot_bo1836341171_a_nat) = $true,
    inference(fool_elimination,[],[f940]) ).

thf(f940,plain,
    vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_la1083530965_a_nat,sTfun(set_Pr1987088711_a_nat,$o),refl_o1031343860_a_nat,bot_bo2122869057_a_nat),bot_bo1836341171_a_nat),
    inference(rectify,[],[f217]) ).

thf(f217,axiom,
    vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_la1083530965_a_nat,sTfun(set_Pr1987088711_a_nat,$o),refl_o1031343860_a_nat,bot_bo2122869057_a_nat),bot_bo1836341171_a_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_refl__on__empty) ).

thf(f2638,plain,
    spl92_26,
    inference(avatar_split_clause,[],[f1929,f2635]) ).

thf(f2635,plain,
    ( spl92_26
  <=> ( vAPP(set_Pr924198087_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr924198087_a_nat,$o),refl_o1213627494_a_nat,bot_bo1836341171_a_nat),bot_bo1973379891_a_nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_26])]) ).

thf(f1929,plain,
    vAPP(set_Pr924198087_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr924198087_a_nat,$o),refl_o1213627494_a_nat,bot_bo1836341171_a_nat),bot_bo1973379891_a_nat) = $true,
    inference(cnf_transformation,[],[f939]) ).

thf(f939,plain,
    vAPP(set_Pr924198087_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr924198087_a_nat,$o),refl_o1213627494_a_nat,bot_bo1836341171_a_nat),bot_bo1973379891_a_nat) = $true,
    inference(fool_elimination,[],[f938]) ).

thf(f938,plain,
    vAPP(set_Pr924198087_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr924198087_a_nat,$o),refl_o1213627494_a_nat,bot_bo1836341171_a_nat),bot_bo1973379891_a_nat),
    inference(rectify,[],[f219]) ).

thf(f219,axiom,
    vAPP(set_Pr924198087_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr924198087_a_nat,$o),refl_o1213627494_a_nat,bot_bo1836341171_a_nat),bot_bo1973379891_a_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_refl__on__empty) ).

thf(f2633,plain,
    spl92_25,
    inference(avatar_split_clause,[],[f1603,f2631]) ).

thf(f2631,plain,
    ( spl92_25
  <=> ! [X0: b,X1: set_b] : ( bot_bot_set_b != vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_25])]) ).

thf(f1603,plain,
    ! [X0: b,X1: set_b] : ( bot_bot_set_b != vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) ),
    inference(cnf_transformation,[],[f996]) ).

thf(f996,plain,
    ! [X0: b,X1: set_b] : ( bot_bot_set_b != vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X0),X1) ),
    inference(rectify,[],[f348]) ).

thf(f348,axiom,
    ! [X14: b,X8: set_b] : ( bot_bot_set_b != vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,X14),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_insert__not__empty) ).

thf(f2629,plain,
    spl92_24,
    inference(avatar_split_clause,[],[f1602,f2627]) ).

thf(f2627,plain,
    ( spl92_24
  <=> ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat != vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_24])]) ).

thf(f1602,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat != vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) ),
    inference(cnf_transformation,[],[f995]) ).

thf(f995,plain,
    ! [X0: produc1871334759_a_nat,X1: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat != vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X0),X1) ),
    inference(rectify,[],[f349]) ).

thf(f349,axiom,
    ! [X14: produc1871334759_a_nat,X8: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat != vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),insert1574423351_a_nat,X14),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_insert__not__empty) ).

thf(f2625,plain,
    spl92_23,
    inference(avatar_split_clause,[],[f1592,f2623]) ).

thf(f2623,plain,
    ( spl92_23
  <=> ! [X0: set_b] : ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,bot_bot_set_b),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_23])]) ).

thf(f1592,plain,
    ! [X0: set_b] : ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,bot_bot_set_b),X0) ),
    inference(cnf_transformation,[],[f471]) ).

thf(f471,plain,
    ! [X0: set_b] : ( $true = vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,bot_bot_set_b),X0) ),
    inference(fool_elimination,[],[f470]) ).

thf(f470,plain,
    ! [X0: set_b] : vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,bot_bot_set_b),X0),
    inference(rectify,[],[f268]) ).

thf(f268,axiom,
    ! [X8: set_b] : vAPP(set_b,$o,vAPP(set_b,sTfun(set_b,$o),ord_less_eq_set_b,bot_bot_set_b),X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_empty__subsetI) ).

thf(f2621,plain,
    spl92_22,
    inference(avatar_split_clause,[],[f1591,f2619]) ).

thf(f2619,plain,
    ( spl92_22
  <=> ! [X0: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,bot_bo1836341171_a_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_22])]) ).

thf(f1591,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(cnf_transformation,[],[f469]) ).

thf(f469,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( $true = vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(fool_elimination,[],[f468]) ).

thf(f468,plain,
    ! [X0: set_Pr1987088711_a_nat] : vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,bot_bo1836341171_a_nat),X0),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ! [X8: set_Pr1987088711_a_nat] : vAPP(set_Pr1987088711_a_nat,$o,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,$o),ord_le1718765799_a_nat,bot_bo1836341171_a_nat),X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_empty__subsetI) ).

thf(f2617,plain,
    spl92_21,
    inference(avatar_split_clause,[],[f1587,f2615]) ).

thf(f1587,plain,
    ! [X0: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ),
    inference(cnf_transformation,[],[f991]) ).

thf(f991,plain,
    ! [X0: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ),
    inference(flattening,[],[f465]) ).

thf(f465,plain,
    ! [X0: product_prod_b_b] : ( $true != vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b) ),
    inference(fool_elimination,[],[f464]) ).

thf(f464,plain,
    ! [X0: product_prod_b_b] : ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X0),bot_bo1343651123od_b_b),
    inference(rectify,[],[f251]) ).

thf(f251,axiom,
    ! [X29: product_prod_b_b] : ~ vAPP(set_Product_prod_b_b,$o,vAPP(product_prod_b_b,sTfun(set_Product_prod_b_b,$o),member1285940496od_b_b,X29),bot_bo1343651123od_b_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_empty__iff) ).

thf(f2613,plain,
    spl92_20,
    inference(avatar_split_clause,[],[f1585,f2611]) ).

thf(f1585,plain,
    ! [X0: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ),
    inference(cnf_transformation,[],[f989]) ).

thf(f989,plain,
    ! [X0: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ),
    inference(flattening,[],[f461]) ).

thf(f461,plain,
    ! [X0: b] : ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b) ),
    inference(fool_elimination,[],[f460]) ).

thf(f460,plain,
    ! [X0: b] : ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),bot_bot_set_b),
    inference(rectify,[],[f253]) ).

thf(f253,axiom,
    ! [X29: b] : ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X29),bot_bot_set_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_empty__iff) ).

thf(f2609,plain,
    spl92_19,
    inference(avatar_split_clause,[],[f1583,f2607]) ).

thf(f1583,plain,
    ! [X0: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ),
    inference(cnf_transformation,[],[f987]) ).

thf(f987,plain,
    ! [X0: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ),
    inference(flattening,[],[f457]) ).

thf(f457,plain,
    ! [X0: produc1213276845od_b_b] : ( $true != vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b) ),
    inference(fool_elimination,[],[f456]) ).

thf(f456,plain,
    ! [X0: produc1213276845od_b_b] : ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X0),bot_bo1664927607od_b_b),
    inference(rectify,[],[f252]) ).

thf(f252,axiom,
    ! [X29: produc1213276845od_b_b] : ~ vAPP(set_Pr1324126435od_b_b,$o,vAPP(produc1213276845od_b_b,sTfun(set_Pr1324126435od_b_b,$o),member1516365892od_b_b,X29),bot_bo1664927607od_b_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_empty__iff) ).

thf(f2605,plain,
    spl92_18,
    inference(avatar_split_clause,[],[f1581,f2603]) ).

thf(f1581,plain,
    ! [X0: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(cnf_transformation,[],[f985]) ).

thf(f985,plain,
    ! [X0: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(flattening,[],[f453]) ).

thf(f453,plain,
    ! [X0: produc1871334759_a_nat] : ( $true != vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(fool_elimination,[],[f452]) ).

thf(f452,plain,
    ! [X0: produc1871334759_a_nat] : ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X0),bot_bo1836341171_a_nat),
    inference(rectify,[],[f254]) ).

thf(f254,axiom,
    ! [X29: produc1871334759_a_nat] : ~ vAPP(set_Pr1987088711_a_nat,$o,vAPP(produc1871334759_a_nat,sTfun(set_Pr1987088711_a_nat,$o),member832397200_a_nat,X29),bot_bo1836341171_a_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_empty__iff) ).

thf(f2601,plain,
    spl92_17,
    inference(avatar_split_clause,[],[f1535,f2599]) ).

thf(f2599,plain,
    ( spl92_17
  <=> ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_17])]) ).

thf(f1535,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X0) = X0 ),
    inference(cnf_transformation,[],[f967]) ).

thf(f967,plain,
    ! [X0: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X0),X0) = X0 ),
    inference(rectify,[],[f21]) ).

thf(f21,axiom,
    ! [X8: labele1159362096nt_a_b] : ( vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,vAPP(labele1159362096nt_a_b,sTfun(labele1159362096nt_a_b,labele1159362096nt_a_b),graph_1309249505nt_a_b,X8),X8) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_graph__union__idemp_I1_J) ).

thf(f2594,plain,
    spl92_16,
    inference(avatar_split_clause,[],[f1534,f2592]) ).

thf(f2592,plain,
    ( spl92_16
  <=> ! [X0: set_Pr1646010159_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_b,set_Pr1987088711_a_nat,vAPP(set_Pr1646010159_a_nat,sTfun(set_b,set_Pr1987088711_a_nat),image_1749766139_a_nat,X0),bot_bot_set_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_16])]) ).

thf(f1534,plain,
    ! [X0: set_Pr1646010159_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_b,set_Pr1987088711_a_nat,vAPP(set_Pr1646010159_a_nat,sTfun(set_b,set_Pr1987088711_a_nat),image_1749766139_a_nat,X0),bot_bot_set_b) ),
    inference(cnf_transformation,[],[f966]) ).

thf(f966,plain,
    ! [X0: set_Pr1646010159_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_b,set_Pr1987088711_a_nat,vAPP(set_Pr1646010159_a_nat,sTfun(set_b,set_Pr1987088711_a_nat),image_1749766139_a_nat,X0),bot_bot_set_b) ),
    inference(rectify,[],[f141]) ).

thf(f141,axiom,
    ! [X33: set_Pr1646010159_a_nat] : ( vAPP(set_b,set_Pr1987088711_a_nat,vAPP(set_Pr1646010159_a_nat,sTfun(set_b,set_Pr1987088711_a_nat),image_1749766139_a_nat,X33),bot_bot_set_b) = bot_bo1836341171_a_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Image__empty2) ).

thf(f2590,plain,
    spl92_15,
    inference(avatar_split_clause,[],[f1533,f2588]) ).

thf(f2588,plain,
    ( spl92_15
  <=> ! [X0: set_la1083530965_a_nat] : ( bot_bo2122869057_a_nat = vAPP(set_la1083530965_a_nat,set_la1083530965_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_la1083530965_a_nat,set_la1083530965_a_nat),image_1971191571_a_nat,bot_bo1836341171_a_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_15])]) ).

thf(f1533,plain,
    ! [X0: set_la1083530965_a_nat] : ( bot_bo2122869057_a_nat = vAPP(set_la1083530965_a_nat,set_la1083530965_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_la1083530965_a_nat,set_la1083530965_a_nat),image_1971191571_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(cnf_transformation,[],[f965]) ).

thf(f965,plain,
    ! [X0: set_la1083530965_a_nat] : ( bot_bo2122869057_a_nat = vAPP(set_la1083530965_a_nat,set_la1083530965_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_la1083530965_a_nat,set_la1083530965_a_nat),image_1971191571_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(rectify,[],[f145]) ).

thf(f145,axiom,
    ! [X15: set_la1083530965_a_nat] : ( vAPP(set_la1083530965_a_nat,set_la1083530965_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_la1083530965_a_nat,set_la1083530965_a_nat),image_1971191571_a_nat,bot_bo1836341171_a_nat),X15) = bot_bo2122869057_a_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Image__empty1) ).

thf(f2586,plain,
    spl92_14,
    inference(avatar_split_clause,[],[f1532,f2584]) ).

thf(f2584,plain,
    ( spl92_14
  <=> ! [X0: set_Product_prod_b_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),bot_bot_set_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_14])]) ).

thf(f1532,plain,
    ! [X0: set_Product_prod_b_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),bot_bot_set_b) ),
    inference(cnf_transformation,[],[f964]) ).

thf(f964,plain,
    ! [X0: set_Product_prod_b_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X0),bot_bot_set_b) ),
    inference(rectify,[],[f140]) ).

thf(f140,axiom,
    ! [X33: set_Product_prod_b_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,X33),bot_bot_set_b) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Image__empty2) ).

thf(f2582,plain,
    spl92_13,
    inference(avatar_split_clause,[],[f1531,f2580]) ).

thf(f2580,plain,
    ( spl92_13
  <=> ! [X0: set_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,bot_bo1343651123od_b_b),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_13])]) ).

thf(f1531,plain,
    ! [X0: set_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,bot_bo1343651123od_b_b),X0) ),
    inference(cnf_transformation,[],[f963]) ).

thf(f963,plain,
    ! [X0: set_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,bot_bo1343651123od_b_b),X0) ),
    inference(rectify,[],[f144]) ).

thf(f144,axiom,
    ! [X15: set_b] : ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,bot_bo1343651123od_b_b),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Image__empty1) ).

thf(f2578,plain,
    spl92_12,
    inference(avatar_split_clause,[],[f1530,f2576]) ).

thf(f2576,plain,
    ( spl92_12
  <=> ! [X0: set_Pr812188767_nat_b] : ( bot_bot_set_b = vAPP(set_Pr1987088711_a_nat,set_b,vAPP(set_Pr812188767_nat_b,sTfun(set_Pr1987088711_a_nat,set_b),image_924992811_nat_b,X0),bot_bo1836341171_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_12])]) ).

thf(f1530,plain,
    ! [X0: set_Pr812188767_nat_b] : ( bot_bot_set_b = vAPP(set_Pr1987088711_a_nat,set_b,vAPP(set_Pr812188767_nat_b,sTfun(set_Pr1987088711_a_nat,set_b),image_924992811_nat_b,X0),bot_bo1836341171_a_nat) ),
    inference(cnf_transformation,[],[f962]) ).

thf(f962,plain,
    ! [X0: set_Pr812188767_nat_b] : ( bot_bot_set_b = vAPP(set_Pr1987088711_a_nat,set_b,vAPP(set_Pr812188767_nat_b,sTfun(set_Pr1987088711_a_nat,set_b),image_924992811_nat_b,X0),bot_bo1836341171_a_nat) ),
    inference(rectify,[],[f142]) ).

thf(f142,axiom,
    ! [X33: set_Pr812188767_nat_b] : ( bot_bot_set_b = vAPP(set_Pr1987088711_a_nat,set_b,vAPP(set_Pr812188767_nat_b,sTfun(set_Pr1987088711_a_nat,set_b),image_924992811_nat_b,X33),bot_bo1836341171_a_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Image__empty2) ).

thf(f2574,plain,
    spl92_11,
    inference(avatar_split_clause,[],[f1529,f2572]) ).

thf(f2572,plain,
    ( spl92_11
  <=> ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_11])]) ).

thf(f1529,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(cnf_transformation,[],[f961]) ).

thf(f961,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    ! [X33: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,X33),bot_bo1836341171_a_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_relcomp__empty2) ).

thf(f2570,plain,
    spl92_10,
    inference(avatar_split_clause,[],[f1528,f2568]) ).

thf(f2568,plain,
    ( spl92_10
  <=> ! [X0: set_Pr924198087_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr924198087_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),image_1168831379_a_nat,X0),bot_bo1836341171_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_10])]) ).

thf(f1528,plain,
    ! [X0: set_Pr924198087_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr924198087_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),image_1168831379_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(cnf_transformation,[],[f960]) ).

thf(f960,plain,
    ! [X0: set_Pr924198087_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr924198087_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),image_1168831379_a_nat,X0),bot_bo1836341171_a_nat) ),
    inference(rectify,[],[f143]) ).

thf(f143,axiom,
    ! [X33: set_Pr924198087_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr924198087_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),image_1168831379_a_nat,X33),bot_bo1836341171_a_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Image__empty2) ).

thf(f2566,plain,
    spl92_9,
    inference(avatar_split_clause,[],[f1527,f2564]) ).

thf(f2564,plain,
    ( spl92_9
  <=> ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,bot_bo1836341171_a_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_9])]) ).

thf(f1527,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(cnf_transformation,[],[f959]) ).

thf(f959,plain,
    ! [X0: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,bot_bo1836341171_a_nat),X0) ),
    inference(rectify,[],[f280]) ).

thf(f280,axiom,
    ! [X33: set_Pr1987088711_a_nat] : ( bot_bo1836341171_a_nat = vAPP(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat,vAPP(set_Pr1987088711_a_nat,sTfun(set_Pr1987088711_a_nat,set_Pr1987088711_a_nat),relcom1338300020_a_nat,bot_bo1836341171_a_nat),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_relcomp__empty1) ).

thf(f2562,plain,
    ( spl92_8
    | spl92_2
    | ~ spl92_3 ),
    inference(avatar_split_clause,[],[f2519,f2505,f2500,f2559]) ).

thf(f2500,plain,
    ( spl92_2
  <=> ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_2])]) ).

thf(f2519,plain,
    ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $false )
    | spl92_2
    | ~ spl92_3 ),
    inference(trivial_inequality_removal,[],[f2517]) ).

thf(f2517,plain,
    ( ( $true != $true )
    | ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) = $false )
    | spl92_2
    | ~ spl92_3 ),
    inference(superposition,[],[f2502,f2506]) ).

thf(f2502,plain,
    ( ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true )
    | spl92_2 ),
    inference(avatar_component_clause,[],[f2500]) ).

thf(f2557,plain,
    spl92_7,
    inference(avatar_split_clause,[],[f1514,f2554]) ).

thf(f2554,plain,
    ( spl92_7
  <=> ( vAPP(set_Pr1987088711_a_nat,set_Pr924198087_a_nat,id_on_1651096324_a_nat,bot_bo1836341171_a_nat) = bot_bo1973379891_a_nat ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_7])]) ).

thf(f1514,plain,
    vAPP(set_Pr1987088711_a_nat,set_Pr924198087_a_nat,id_on_1651096324_a_nat,bot_bo1836341171_a_nat) = bot_bo1973379891_a_nat,
    inference(cnf_transformation,[],[f148]) ).

thf(f148,axiom,
    vAPP(set_Pr1987088711_a_nat,set_Pr924198087_a_nat,id_on_1651096324_a_nat,bot_bo1836341171_a_nat) = bot_bo1973379891_a_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Id__on__empty) ).

thf(f2552,plain,
    spl92_6,
    inference(avatar_split_clause,[],[f1513,f2549]) ).

thf(f2549,plain,
    ( spl92_6
  <=> ( g = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,g) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_6])]) ).

thf(f1513,plain,
    g = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,g),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,axiom,
    g = vAPP(labele1159362096nt_a_b,labele1159362096nt_a_b,restri446606278nt_a_b,g),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).

thf(f2547,plain,
    spl92_5,
    inference(avatar_split_clause,[],[f1512,f2544]) ).

thf(f2544,plain,
    ( spl92_5
  <=> ( bot_bo1836341171_a_nat = vAPP(set_la1083530965_a_nat,set_Pr1987088711_a_nat,id_on_689842066_a_nat,bot_bo2122869057_a_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_5])]) ).

thf(f1512,plain,
    bot_bo1836341171_a_nat = vAPP(set_la1083530965_a_nat,set_Pr1987088711_a_nat,id_on_689842066_a_nat,bot_bo2122869057_a_nat),
    inference(cnf_transformation,[],[f146]) ).

thf(f146,axiom,
    bot_bo1836341171_a_nat = vAPP(set_la1083530965_a_nat,set_Pr1987088711_a_nat,id_on_689842066_a_nat,bot_bo2122869057_a_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Id__on__empty) ).

thf(f2542,plain,
    spl92_4,
    inference(avatar_split_clause,[],[f1511,f2539]) ).

thf(f2539,plain,
    ( spl92_4
  <=> ( bot_bo1343651123od_b_b = vAPP(set_b,set_Product_prod_b_b,id_on_b,bot_bot_set_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_4])]) ).

thf(f1511,plain,
    bot_bo1343651123od_b_b = vAPP(set_b,set_Product_prod_b_b,id_on_b,bot_bot_set_b),
    inference(cnf_transformation,[],[f147]) ).

thf(f147,axiom,
    bot_bo1343651123od_b_b = vAPP(set_b,set_Product_prod_b_b,id_on_b,bot_bot_set_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Id__on__empty) ).

thf(f2507,plain,
    spl92_3,
    inference(avatar_split_clause,[],[f363,f2505]) ).

thf(f363,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f2503,plain,
    ~ spl92_2,
    inference(avatar_split_clause,[],[f1510,f2500]) ).

thf(f1510,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true,
    inference(cnf_transformation,[],[f958]) ).

thf(f958,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true,
    inference(flattening,[],[f365]) ).

thf(f365,plain,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)) != $true,
    inference(fool_elimination,[],[f364]) ).

thf(f364,plain,
    ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    inference(rectify,[],[f361]) ).

thf(f361,negated_conjecture,
    ~ vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    inference(negated_conjecture,[],[f360]) ).

thf(f360,conjecture,
    vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,x),vAPP(labele1159362096nt_a_b,set_b,labele1424214014nt_a_b,g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f2498,plain,
    ~ spl92_1,
    inference(avatar_split_clause,[],[f362,f2495]) ).

thf(f2495,plain,
    ( spl92_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl92_1])]) ).

thf(f362,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : ITP177^1 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat May 18 18:28:53 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (3118)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.39  % (3121)WARNING: value z3 for option sas not known
% 0.20/0.39  % (3122)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39  % (3119)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39  % (3120)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39  % (3123)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)
% 0.20/0.39  % (3124)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)
% 0.20/0.39  % (3121)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)
% 0.20/0.39  % (3125)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)
% 0.20/0.44  % (3125)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.45  % Exception at run slice level
% 0.20/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.45  % Exception at run slice level
% 0.20/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.45  % Exception at run slice level
% 0.20/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.46  % (3126)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.46  % (3127)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)
% 0.20/0.46  % (3128)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)
% 0.20/0.50  % (3126)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.50  % (3127)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.51  % Exception at run slice level
% 0.20/0.51  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.51  % (3123)First to succeed.
% 0.20/0.52  % (3129)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)
% 0.20/0.52  % (3123)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3118"
% 0.20/0.52  % (3123)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (3123)------------------------------
% 0.20/0.53  % (3123)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.53  % (3123)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (3123)Memory used [KB]: 3321
% 0.20/0.53  % (3123)Time elapsed: 0.132 s
% 0.20/0.53  % (3123)Instructions burned: 356 (million)
% 0.20/0.53  % (3118)Success in time 0.165 s
%------------------------------------------------------------------------------