TSTP Solution File: SWW473+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n022.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 : 600s
% DateTime : Thu Jul 21 00:30:02 EDT 2022
% Result : Theorem 154.93s 155.25s
% Output : CNFRefutation 155.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 454
% Syntax : Number of formulae : 3625 ( 766 unt; 0 def)
% Number of atoms : 8730 (1407 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 8845 (3740 ~;4026 |; 209 &)
% ( 84 <=>; 786 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 258 ( 258 usr; 56 con; 0-3 aty)
% Number of variables : 7979 ( 879 sgn2908 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X9,X5)))
=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X9)),hAPP_pname_a(X9,X30)))))) ) ) ),
file('<stdin>',fact_175_pigeonhole__infinite) ).
fof(c_0_1,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X29)),hAPP_nat_fun_a_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X17)),hAPP_nat_fun_a_bool(X9,X28))) ) ),
file('<stdin>',fact_174_lift__Suc__mono__le) ).
fof(c_0_2,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X29)),hAPP_nat_nat(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X17)),hAPP_nat_nat(X9,X28))) ) ),
file('<stdin>',fact_173_lift__Suc__mono__le) ).
fof(c_0_3,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X29)),hAPP_n1025906991e_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X17)),hAPP_n1025906991e_bool(X9,X28))) ) ),
file('<stdin>',fact_172_lift__Suc__mono__le) ).
fof(c_0_4,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X29)),hAPP_n1699378549t_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X17)),hAPP_n1699378549t_bool(X9,X28))) ) ),
file('<stdin>',fact_171_lift__Suc__mono__le) ).
fof(c_0_5,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X30)),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),X10)) ),
file('<stdin>',fact_294_image__subsetI) ).
fof(c_0_6,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X25),X16)),hAPP_nat_nat(minus_minus_nat(X17),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ) ),
file('<stdin>',fact_162_le__diff__iff) ).
fof(c_0_7,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_a(X9,X27) ) ) ) ),
file('<stdin>',fact_170_finite__subset__image) ).
fof(c_0_8,axiom,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_a(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ) ),
file('<stdin>',fact_288_imageE) ).
fof(c_0_9,axiom,
! [X10,X9,X5] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
<=> ? [X38] :
( is_fun_pname_bool(X38)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X38),X5))
& X10 = image_pname_a(X9,X38) ) ) ),
file('<stdin>',fact_286_subset__image__iff) ).
fof(c_0_10,axiom,
! [X35,X9,X5] :
( is_a(X35)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X35),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X35 = hAPP_pname_a(X9,X30) ) ) ),
file('<stdin>',fact_260_image__iff) ).
fof(c_0_11,axiom,
! [X39,X13,X16] :
( hBOOL(hAPP_nat_bool(X13,X16))
=> ( ! [X29] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X29)))
=> hBOOL(hAPP_nat_bool(X13,X29)) )
=> hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(minus_minus_nat(X16),X39))) ) ),
file('<stdin>',fact_292_zero__induct__lemma) ).
fof(c_0_12,axiom,
! [X13,X12] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) ) ),
file('<stdin>',fact_134_finite__Collect__disjI) ).
fof(c_0_13,axiom,
! [X13,X12] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) ) ),
file('<stdin>',fact_133_finite__Collect__disjI) ).
fof(c_0_14,axiom,
! [X13,X12] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) ) ),
file('<stdin>',fact_132_finite__Collect__disjI) ).
fof(c_0_15,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) ) ),
file('<stdin>',fact_131_finite__Collect__disjI) ).
fof(c_0_16,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) ) ),
file('<stdin>',fact_130_finite__Collect__disjI) ).
fof(c_0_17,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) ) ),
file('<stdin>',fact_129_finite__Collect__disjI) ).
fof(c_0_18,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X10)),hAPP_fun_a_bool_nat(finite_card_a,X5)))
=> X5 = X10 ) ) ) ),
file('<stdin>',fact_90_card__seteq) ).
fof(c_0_19,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X10)),hAPP_f921600141ol_nat(finite_card_pname,X5)))
=> X5 = X10 ) ) ) ),
file('<stdin>',fact_89_card__seteq) ).
fof(c_0_20,axiom,
! [X5,X10] :
( ( is_fun949378684l_bool(X5)
& is_fun949378684l_bool(X10) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X10)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)))
=> X5 = X10 ) ) ) ),
file('<stdin>',fact_88_card__seteq) ).
fof(c_0_21,axiom,
! [X5,X10] :
( ( is_fun1661590463l_bool(X5)
& is_fun1661590463l_bool(X10) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X10)),hAPP_f55526627ol_nat(finite1340463720e_bool,X5)))
=> X5 = X10 ) ) ) ),
file('<stdin>',fact_87_card__seteq) ).
fof(c_0_22,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X10)),hAPP_f22106695ol_nat(finite_card_nat,X5)))
=> X5 = X10 ) ) ),
file('<stdin>',fact_91_card__seteq) ).
fof(c_0_23,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X10)),hAPP_f696928925ol_nat(finite346522414t_bool,X5)))
=> X5 = X10 ) ) ),
file('<stdin>',fact_86_card__seteq) ).
fof(c_0_24,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('<stdin>',fact_79_card__image__le) ).
fof(c_0_25,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('<stdin>',fact_78_card__image__le) ).
fof(c_0_26,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('<stdin>',fact_77_card__image__le) ).
fof(c_0_27,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('<stdin>',fact_76_card__image__le) ).
fof(c_0_28,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('<stdin>',fact_75_card__image__le) ).
fof(c_0_29,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('<stdin>',fact_74_card__image__le) ).
fof(c_0_30,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('<stdin>',fact_73_card__image__le) ).
fof(c_0_31,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_72_card__image__le) ).
fof(c_0_32,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_71_card__image__le) ).
fof(c_0_33,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_70_card__image__le) ).
fof(c_0_34,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_69_card__image__le) ).
fof(c_0_35,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('<stdin>',fact_68_card__image__le) ).
fof(c_0_36,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('<stdin>',fact_67_card__image__le) ).
fof(c_0_37,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('<stdin>',fact_66_card__image__le) ).
fof(c_0_38,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('<stdin>',fact_65_card__image__le) ).
fof(c_0_39,axiom,
! [X9,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X9,X5))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X5))) ),
file('<stdin>',fact_64_card__image__le) ).
fof(c_0_40,axiom,
! [X9,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X9,X5))),hAPP_f98387925ol_nat(finite269641166l_bool,X5))) ),
file('<stdin>',fact_63_card__image__le) ).
fof(c_0_41,axiom,
! [X9,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X9,X5))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X5))) ),
file('<stdin>',fact_62_card__image__le) ).
fof(c_0_42,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_61_card__image__le) ).
fof(c_0_43,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('<stdin>',fact_60_card__image__le) ).
fof(c_0_44,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('<stdin>',fact_59_card__image__le) ).
fof(c_0_45,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('<stdin>',fact_58_card__image__le) ).
fof(c_0_46,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('<stdin>',fact_57_card__image__le) ).
fof(c_0_47,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('<stdin>',fact_56_card__image__le) ).
fof(c_0_48,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('<stdin>',fact_55_card__image__le) ).
fof(c_0_49,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('<stdin>',fact_54_card__image__le) ).
fof(c_0_50,axiom,
! [X8,X13] : insert_fun_a_bool(X8,collect_fun_a_bool(X13)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8))),X13)),
file('<stdin>',fact_203_insert__Collect) ).
fof(c_0_51,axiom,
! [X8,X13] : insert1325755072e_bool(X8,collec1974731493e_bool(X13)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8))),X13)),
file('<stdin>',fact_202_insert__Collect) ).
fof(c_0_52,axiom,
! [X8,X13] : insert_fun_nat_bool(X8,collect_fun_nat_bool(X13)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8))),X13)),
file('<stdin>',fact_201_insert__Collect) ).
fof(c_0_53,axiom,
! [X8,X13] : insert_a(X8,collect_a(X13)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8))),X13)),
file('<stdin>',fact_200_insert__Collect) ).
fof(c_0_54,axiom,
! [X8,X13] : insert_pname(X8,collect_pname(X13)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8))),X13)),
file('<stdin>',fact_199_insert__Collect) ).
fof(c_0_55,axiom,
! [X8,X13] : insert_nat(X8,collect_nat(X13)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8))),X13)),
file('<stdin>',fact_198_insert__Collect) ).
fof(c_0_56,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X26),X14)),hAPP_nat_nat(minus_minus_nat(X26),X15))) ),
file('<stdin>',fact_167_diff__le__mono2) ).
fof(c_0_57,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X15),X26)),hAPP_nat_nat(minus_minus_nat(X14),X26))) ),
file('<stdin>',fact_166_diff__le__mono) ).
fof(c_0_58,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X11,X5)),X10))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
file('<stdin>',fact_274_insert__subset) ).
fof(c_0_59,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X11,X5)),X10))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
file('<stdin>',fact_273_insert__subset) ).
fof(c_0_60,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X11,X5)),X10))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
file('<stdin>',fact_272_insert__subset) ).
fof(c_0_61,axiom,
! [X17,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),hAPP_nat_nat(suc,X25)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X25)) ),
file('<stdin>',fact_156_Suc__le__mono) ).
fof(c_0_62,axiom,
! [X15,X14,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14)),hAPP_nat_nat(suc,X22)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X14)),X22),
file('<stdin>',fact_160_Suc__diff__diff) ).
fof(c_0_63,axiom,
! [X14,X22,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X22)),hAPP_nat_nat(minus_minus_nat(X14),X22)) = hAPP_nat_nat(minus_minus_nat(X15),X14) ) ),
file('<stdin>',fact_163_Nat_Odiff__diff__eq) ).
fof(c_0_64,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X13),X12)))) ),
file('<stdin>',fact_115_finite__Collect__conjI) ).
fof(c_0_65,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X13),X12)))) ),
file('<stdin>',fact_114_finite__Collect__conjI) ).
fof(c_0_66,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X13),X12)))) ),
file('<stdin>',fact_113_finite__Collect__conjI) ).
fof(c_0_67,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X13),X12)))) ),
file('<stdin>',fact_112_finite__Collect__conjI) ).
fof(c_0_68,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X13),X12)))) ),
file('<stdin>',fact_111_finite__Collect__conjI) ).
fof(c_0_69,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X13),X12)))) ),
file('<stdin>',fact_110_finite__Collect__conjI) ).
fof(c_0_70,axiom,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),X25)) ),
file('<stdin>',fact_158_not__less__eq__eq) ).
fof(c_0_71,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,X10))) ) ),
file('<stdin>',fact_85_card__mono) ).
fof(c_0_72,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,X10))) ) ),
file('<stdin>',fact_84_card__mono) ).
fof(c_0_73,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,X10))) ) ),
file('<stdin>',fact_83_card__mono) ).
fof(c_0_74,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X10))) ) ),
file('<stdin>',fact_82_card__mono) ).
fof(c_0_75,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,X10))) ) ),
file('<stdin>',fact_81_card__mono) ).
fof(c_0_76,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,X10))) ) ),
file('<stdin>',fact_80_card__mono) ).
fof(c_0_77,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)))) ),
file('<stdin>',fact_97_card__insert__le) ).
fof(c_0_78,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)))) ),
file('<stdin>',fact_96_card__insert__le) ).
fof(c_0_79,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)))) ),
file('<stdin>',fact_95_card__insert__le) ).
fof(c_0_80,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)))) ),
file('<stdin>',fact_94_card__insert__le) ).
fof(c_0_81,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)))) ),
file('<stdin>',fact_93_card__insert__le) ).
fof(c_0_82,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)))) ),
file('<stdin>',fact_92_card__insert__le) ).
fof(c_0_83,axiom,
! [X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X10)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
file('<stdin>',fact_291_subsetI) ).
fof(c_0_84,axiom,
! [X10,X5] :
( ! [X30] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
file('<stdin>',fact_290_subsetI) ).
fof(c_0_85,axiom,
! [X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X10)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
file('<stdin>',fact_289_subsetI) ).
fof(c_0_86,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),insert_a(X11,X10)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
file('<stdin>',fact_277_subset__insert) ).
fof(c_0_87,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X11,X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
file('<stdin>',fact_276_subset__insert) ).
fof(c_0_88,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),insert_nat(X11,X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
file('<stdin>',fact_275_subset__insert) ).
fof(c_0_89,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),image_pname_a(X9,X10))) ),
file('<stdin>',fact_287_image__mono) ).
fof(c_0_90,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X34),X37))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X34)),insert_a(X8,X37))) ),
file('<stdin>',fact_283_insert__mono) ).
fof(c_0_91,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X34),X37))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X8,X34)),insert_pname(X8,X37))) ),
file('<stdin>',fact_282_insert__mono) ).
fof(c_0_92,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X34),X37))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X8,X34)),insert_nat(X8,X37))) ),
file('<stdin>',fact_281_insert__mono) ).
fof(c_0_93,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5))) ),
file('<stdin>',fact_261_imageI) ).
fof(c_0_94,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('<stdin>',fact_153_Suc__leD) ).
fof(c_0_95,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X34))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X34)) ) ),
file('<stdin>',fact_248_subset__trans) ).
fof(c_0_96,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X34))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X34)) ) ),
file('<stdin>',fact_247_subset__trans) ).
fof(c_0_97,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X34))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X34)) ) ),
file('<stdin>',fact_246_subset__trans) ).
fof(c_0_98,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('<stdin>',fact_245_set__mp) ).
fof(c_0_99,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('<stdin>',fact_244_set__mp) ).
fof(c_0_100,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('<stdin>',fact_243_set__mp) ).
fof(c_0_101,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('<stdin>',fact_242_set__rev__mp) ).
fof(c_0_102,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('<stdin>',fact_241_set__rev__mp) ).
fof(c_0_103,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('<stdin>',fact_240_set__rev__mp) ).
fof(c_0_104,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('<stdin>',fact_239_in__mono) ).
fof(c_0_105,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('<stdin>',fact_238_in__mono) ).
fof(c_0_106,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('<stdin>',fact_237_in__mono) ).
fof(c_0_107,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
file('<stdin>',fact_182_subsetD) ).
fof(c_0_108,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
file('<stdin>',fact_181_subsetD) ).
fof(c_0_109,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
file('<stdin>',fact_180_subsetD) ).
fof(c_0_110,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X22)) ) ),
file('<stdin>',fact_124_le__trans) ).
fof(c_0_111,axiom,
! [X43] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43))
<=> ? [X41] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X41)) ) ),
file('<stdin>',fact_299_finite__nat__set__iff__bounded__le) ).
fof(c_0_112,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hAPP_nat_nat(minus_minus_nat(X25),X16) = hAPP_nat_nat(minus_minus_nat(X17),X16)
<=> X25 = X17 ) ) ),
file('<stdin>',fact_164_eq__diff__iff) ).
fof(c_0_113,axiom,
! [X14,X40] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X40))
=> ? [X41] : X40 = hAPP_nat_nat(suc,X41) ),
file('<stdin>',fact_293_Suc__le__D) ).
fof(c_0_114,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
file('<stdin>',fact_212_insert__iff) ).
fof(c_0_115,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
file('<stdin>',fact_211_insert__iff) ).
fof(c_0_116,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
file('<stdin>',fact_188_insertE) ).
fof(c_0_117,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
file('<stdin>',fact_187_insertE) ).
fof(c_0_118,axiom,
! [X30,X36] : insert_fun_a_bool(X30,X36) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X30)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X36))),
file('<stdin>',fact_268_insert__compr__raw) ).
fof(c_0_119,axiom,
! [X30,X36] : insert1325755072e_bool(X30,X36) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X30)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X36))),
file('<stdin>',fact_267_insert__compr__raw) ).
fof(c_0_120,axiom,
! [X30,X36] : insert_fun_nat_bool(X30,X36) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X30)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X36))),
file('<stdin>',fact_266_insert__compr__raw) ).
fof(c_0_121,axiom,
! [X30,X36] : insert_a(X30,X36) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X30)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X36))),
file('<stdin>',fact_265_insert__compr__raw) ).
fof(c_0_122,axiom,
! [X30,X36] : insert_pname(X30,X36) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X30)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X36))),
file('<stdin>',fact_264_insert__compr__raw) ).
fof(c_0_123,axiom,
! [X30,X36] : insert_nat(X30,X36) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X30)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X36))),
file('<stdin>',fact_263_insert__compr__raw) ).
fof(c_0_124,axiom,
! [X8,X10] : insert_fun_a_bool(X8,X10) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X10))),
file('<stdin>',fact_197_insert__compr) ).
fof(c_0_125,axiom,
! [X8,X10] : insert1325755072e_bool(X8,X10) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X10))),
file('<stdin>',fact_196_insert__compr) ).
fof(c_0_126,axiom,
! [X8,X10] : insert_fun_nat_bool(X8,X10) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X10))),
file('<stdin>',fact_195_insert__compr) ).
fof(c_0_127,axiom,
! [X8,X10] : insert_a(X8,X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10))),
file('<stdin>',fact_194_insert__compr) ).
fof(c_0_128,axiom,
! [X8,X10] : insert_pname(X8,X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10))),
file('<stdin>',fact_193_insert__compr) ).
fof(c_0_129,axiom,
! [X8,X10] : insert_nat(X8,X10) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X10))),
file('<stdin>',fact_192_insert__compr) ).
fof(c_0_130,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(suc,X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
| X25 = hAPP_nat_nat(suc,X17) ) ),
file('<stdin>',fact_157_le__Suc__eq) ).
fof(c_0_131,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> X15 = hAPP_nat_nat(suc,X14) ) ),
file('<stdin>',fact_154_le__SucE) ).
fof(c_0_132,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
file('<stdin>',fact_210_insert__iff) ).
fof(c_0_133,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
file('<stdin>',fact_186_insertE) ).
fof(c_0_134,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X31 = hAPP_pname_a(X9,X11)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
file('<stdin>',fact_262_rev__image__eqI) ).
fof(c_0_135,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_pname_a(X9,X11)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
file('<stdin>',fact_176_image__eqI) ).
fof(c_0_136,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('<stdin>',fact_169_finite__surj) ).
fof(c_0_137,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X14)),
file('<stdin>',fact_159_Suc__n__not__le__n) ).
fof(c_0_138,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ) ),
file('<stdin>',fact_230_set__eq__subset) ).
fof(c_0_139,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ) ),
file('<stdin>',fact_229_set__eq__subset) ).
fof(c_0_140,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5))
=> X5 = X10 ) ) ),
file('<stdin>',fact_179_equalityI) ).
fof(c_0_141,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5))
=> X5 = X10 ) ) ),
file('<stdin>',fact_178_equalityI) ).
fof(c_0_142,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),insert_a(X31,X10))) ),
file('<stdin>',fact_280_subset__insertI2) ).
fof(c_0_143,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X31,X10))) ),
file('<stdin>',fact_279_subset__insertI2) ).
fof(c_0_144,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),insert_nat(X31,X10))) ),
file('<stdin>',fact_278_subset__insertI2) ).
fof(c_0_145,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X10))) ),
file('<stdin>',fact_221_insertI2) ).
fof(c_0_146,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X10))) ),
file('<stdin>',fact_220_insertI2) ).
fof(c_0_147,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X10))) ),
file('<stdin>',fact_219_insertI2) ).
fof(c_0_148,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X10))) ),
file('<stdin>',fact_185_insertCI) ).
fof(c_0_149,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X10))) ),
file('<stdin>',fact_184_insertCI) ).
fof(c_0_150,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X10))) ),
file('<stdin>',fact_183_insertCI) ).
fof(c_0_151,axiom,
! [X5,X10] :
( X5 = X10
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
file('<stdin>',fact_228_set__eq__subset) ).
fof(c_0_152,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5))
=> X5 = X10 ) ),
file('<stdin>',fact_177_equalityI) ).
fof(c_0_153,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> X15 = X14 ) ),
file('<stdin>',fact_123_le__antisym) ).
fof(c_0_154,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14))) ),
file('<stdin>',fact_155_le__SucI) ).
fof(c_0_155,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X15),X14)) ),
file('<stdin>',fact_116_Suc__diff__le) ).
fof(c_0_156,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X15),X14)),X15)),
file('<stdin>',fact_168_diff__le__self) ).
fof(c_0_157,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_fun_a_bool_nat(finite_card_a,X5) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ) ),
file('<stdin>',fact_103_card__insert__if) ).
fof(c_0_158,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_f921600141ol_nat(finite_card_pname,X5) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
file('<stdin>',fact_102_card__insert__if) ).
fof(c_0_159,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_f22106695ol_nat(finite_card_nat,X5) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
file('<stdin>',fact_101_card__insert__if) ).
fof(c_0_160,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X5) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
file('<stdin>',fact_100_card__insert__if) ).
fof(c_0_161,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X5) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
file('<stdin>',fact_99_card__insert__if) ).
fof(c_0_162,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_f696928925ol_nat(finite346522414t_bool,X5) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
file('<stdin>',fact_98_card__insert__if) ).
fof(c_0_163,axiom,
! [X10,X11,X5] :
( ( is_fun_a_bool(X10)
& is_fun_a_bool(X5) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> ( insert_a(X11,X5) = insert_a(X11,X10)
<=> X5 = X10 ) ) ) ),
file('<stdin>',fact_218_insert__ident) ).
fof(c_0_164,axiom,
! [X10,X11,X5] :
( ( is_fun_pname_bool(X10)
& is_fun_pname_bool(X5) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> ( insert_pname(X11,X5) = insert_pname(X11,X10)
<=> X5 = X10 ) ) ) ),
file('<stdin>',fact_217_insert__ident) ).
fof(c_0_165,axiom,
! [X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X5)))) ),
file('<stdin>',fact_9_finite__Collect__subsets) ).
fof(c_0_166,axiom,
! [X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X5)))) ),
file('<stdin>',fact_8_finite__Collect__subsets) ).
fof(c_0_167,axiom,
! [X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X5)))) ),
file('<stdin>',fact_7_finite__Collect__subsets) ).
fof(c_0_168,axiom,
! [X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X5)))) ),
file('<stdin>',fact_6_finite__Collect__subsets) ).
fof(c_0_169,axiom,
! [X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X5)))) ),
file('<stdin>',fact_5_finite__Collect__subsets) ).
fof(c_0_170,axiom,
! [X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X5)))) ),
file('<stdin>',fact_4_finite__Collect__subsets) ).
fof(c_0_171,axiom,
! [X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X5)))) ),
file('<stdin>',fact_3_finite__Collect__subsets) ).
fof(c_0_172,axiom,
! [X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X5)))) ),
file('<stdin>',fact_2_finite__Collect__subsets) ).
fof(c_0_173,axiom,
! [X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X5)))) ),
file('<stdin>',fact_1_finite__Collect__subsets) ).
fof(c_0_174,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> insert_a(hAPP_pname_a(X9,X11),image_pname_a(X9,X5)) = image_pname_a(X9,X5) ),
file('<stdin>',fact_285_insert__image) ).
fof(c_0_175,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> ( insert_nat(X11,X5) = insert_nat(X11,X10)
<=> X5 = X10 ) ) ),
file('<stdin>',fact_216_insert__ident) ).
fof(c_0_176,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ),
file('<stdin>',fact_109_card__insert__disjoint) ).
fof(c_0_177,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
file('<stdin>',fact_108_card__insert__disjoint) ).
fof(c_0_178,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
file('<stdin>',fact_107_card__insert__disjoint) ).
fof(c_0_179,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
file('<stdin>',fact_106_card__insert__disjoint) ).
fof(c_0_180,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
file('<stdin>',fact_105_card__insert__disjoint) ).
fof(c_0_181,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
file('<stdin>',fact_104_card__insert__disjoint) ).
fof(c_0_182,axiom,
! [X23,X24,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X24)),X22) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X22)),X24),
file('<stdin>',fact_128_diff__commute) ).
fof(c_0_183,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
file('<stdin>',fact_152_rev__finite__subset) ).
fof(c_0_184,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
file('<stdin>',fact_151_rev__finite__subset) ).
fof(c_0_185,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
file('<stdin>',fact_150_rev__finite__subset) ).
fof(c_0_186,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
file('<stdin>',fact_149_rev__finite__subset) ).
fof(c_0_187,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
file('<stdin>',fact_148_rev__finite__subset) ).
fof(c_0_188,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
file('<stdin>',fact_147_rev__finite__subset) ).
fof(c_0_189,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
file('<stdin>',fact_146_finite__subset) ).
fof(c_0_190,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
file('<stdin>',fact_145_finite__subset) ).
fof(c_0_191,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
file('<stdin>',fact_144_finite__subset) ).
fof(c_0_192,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
file('<stdin>',fact_143_finite__subset) ).
fof(c_0_193,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
file('<stdin>',fact_142_finite__subset) ).
fof(c_0_194,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
file('<stdin>',fact_141_finite__subset) ).
fof(c_0_195,axiom,
! [X23,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X14))
=> hAPP_nat_nat(minus_minus_nat(X14),hAPP_nat_nat(minus_minus_nat(X14),X23)) = X23 ),
file('<stdin>',fact_165_diff__diff__cancel) ).
fof(c_0_196,axiom,
! [X33,X5,X11] :
( ( is_a(X33)
& is_a(X11) )
=> ( hBOOL(hAPP_a_bool(insert_a(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_a_bool(X5,X11)) ) ) ),
file('<stdin>',fact_215_insert__code) ).
fof(c_0_197,axiom,
! [X33,X5,X11] :
( ( is_pname(X33)
& is_pname(X11) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_pname_bool(X5,X11)) ) ) ),
file('<stdin>',fact_214_insert__code) ).
fof(c_0_198,axiom,
! [X16] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X16)))),
file('<stdin>',fact_117_finite__Collect__le__nat) ).
fof(c_0_199,axiom,
! [X3,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X4))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),X3)) ),
file('<stdin>',fact_0_assms_I1_J) ).
fof(c_0_200,axiom,
! [X33,X5,X11] :
( hBOOL(hAPP_nat_bool(insert_nat(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_nat_bool(X5,X11)) ) ),
file('<stdin>',fact_213_insert__code) ).
fof(c_0_201,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15)) ),
file('<stdin>',fact_126_nat__le__linear) ).
fof(c_0_202,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ),
file('<stdin>',fact_140_finite__insert) ).
fof(c_0_203,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ),
file('<stdin>',fact_139_finite__insert) ).
fof(c_0_204,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ),
file('<stdin>',fact_138_finite__insert) ).
fof(c_0_205,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ),
file('<stdin>',fact_137_finite__insert) ).
fof(c_0_206,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ),
file('<stdin>',fact_136_finite__insert) ).
fof(c_0_207,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ),
file('<stdin>',fact_135_finite__insert) ).
fof(c_0_208,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
<=> hBOOL(hAPP_pname_bool(X5,X11)) ),
file('<stdin>',fact_254_mem__def) ).
fof(c_0_209,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
<=> hBOOL(hAPP_a_bool(X5,X11)) ),
file('<stdin>',fact_253_mem__def) ).
fof(c_0_210,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
<=> hBOOL(hAPP_nat_bool(X5,X11)) ),
file('<stdin>',fact_252_mem__def) ).
fof(c_0_211,axiom,
! [X8,X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> insert_a(X8,X5) = X5 ) ),
file('<stdin>',fact_224_insert__absorb) ).
fof(c_0_212,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> insert_pname(X8,X5) = X5 ) ),
file('<stdin>',fact_223_insert__absorb) ).
fof(c_0_213,axiom,
! [X18,X19] :
( ( is_fun_pname_bool(X18)
& is_fun_pname_bool(X19) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19))
| X18 = X19 ) ),
file('<stdin>',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
fof(c_0_214,axiom,
! [X18,X19] :
( ( is_fun_a_bool(X18)
& is_fun_a_bool(X19) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19))
| X18 = X19 ) ),
file('<stdin>',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(c_0_215,axiom,
! [X18,X19] :
( ( is_pname(X18)
& is_pname(X19) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19))
| X18 = X19 ) ),
file('<stdin>',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
fof(c_0_216,axiom,
! [X18,X19] :
( ( is_a(X18)
& is_a(X19) )
=> ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19))
| X18 = X19 ) ),
file('<stdin>',help_fequal_1_1_fequal_000t__a_T) ).
fof(c_0_217,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
file('<stdin>',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
fof(c_0_218,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
file('<stdin>',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
fof(c_0_219,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> insert_nat(X8,X5) = X5 ),
file('<stdin>',fact_222_insert__absorb) ).
fof(c_0_220,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45))
| ~ hBOOL(X44)
| hBOOL(X45) ),
file('<stdin>',help_fimplies_3_1_U) ).
fof(c_0_221,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45))
| hBOOL(X44)
| hBOOL(X45) ),
file('<stdin>',help_fdisj_3_1_U) ).
fof(c_0_222,axiom,
! [X10,X8] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),insert_a(X8,X10))),
file('<stdin>',fact_271_subset__insertI) ).
fof(c_0_223,axiom,
! [X10,X8] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),insert_pname(X8,X10))),
file('<stdin>',fact_270_subset__insertI) ).
fof(c_0_224,axiom,
! [X10,X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),insert_nat(X8,X10))),
file('<stdin>',fact_269_subset__insertI) ).
fof(c_0_225,axiom,
! [X8,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X8,X10))),
file('<stdin>',fact_191_insertI1) ).
fof(c_0_226,axiom,
! [X8,X10] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X8,X10))),
file('<stdin>',fact_190_insertI1) ).
fof(c_0_227,axiom,
! [X8,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X8,X10))),
file('<stdin>',fact_189_insertI1) ).
fof(c_0_228,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X45) ),
file('<stdin>',help_fconj_3_1_U) ).
fof(c_0_229,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X44) ),
file('<stdin>',help_fconj_2_1_U) ).
fof(c_0_230,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5))) ),
file('<stdin>',fact_53_finite_OinsertI) ).
fof(c_0_231,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5))) ),
file('<stdin>',fact_52_finite_OinsertI) ).
fof(c_0_232,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5))) ),
file('<stdin>',fact_51_finite_OinsertI) ).
fof(c_0_233,axiom,
! [X8,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X8,X5))) ),
file('<stdin>',fact_50_finite_OinsertI) ).
fof(c_0_234,axiom,
! [X8,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X8,X5))) ),
file('<stdin>',fact_49_finite_OinsertI) ).
fof(c_0_235,axiom,
! [X8,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X8,X5))) ),
file('<stdin>',fact_48_finite_OinsertI) ).
fof(c_0_236,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5))) ),
file('<stdin>',fact_47_finite_OinsertI) ).
fof(c_0_237,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5))) ),
file('<stdin>',fact_46_finite_OinsertI) ).
fof(c_0_238,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5))) ),
file('<stdin>',fact_45_finite_OinsertI) ).
fof(c_0_239,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X6,X7))) ),
file('<stdin>',fact_44_finite__imageI) ).
fof(c_0_240,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X6,X7))) ),
file('<stdin>',fact_43_finite__imageI) ).
fof(c_0_241,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X6,X7))) ),
file('<stdin>',fact_42_finite__imageI) ).
fof(c_0_242,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X6,X7))) ),
file('<stdin>',fact_41_finite__imageI) ).
fof(c_0_243,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X6,X7))) ),
file('<stdin>',fact_40_finite__imageI) ).
fof(c_0_244,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X6,X7))) ),
file('<stdin>',fact_39_finite__imageI) ).
fof(c_0_245,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X6,X7))) ),
file('<stdin>',fact_38_finite__imageI) ).
fof(c_0_246,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X6,X7))) ),
file('<stdin>',fact_37_finite__imageI) ).
fof(c_0_247,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X6,X7))) ),
file('<stdin>',fact_36_finite__imageI) ).
fof(c_0_248,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X6,X7))) ),
file('<stdin>',fact_35_finite__imageI) ).
fof(c_0_249,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X6,X7))) ),
file('<stdin>',fact_34_finite__imageI) ).
fof(c_0_250,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X6,X7))) ),
file('<stdin>',fact_33_finite__imageI) ).
fof(c_0_251,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X6,X7))) ),
file('<stdin>',fact_32_finite__imageI) ).
fof(c_0_252,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X6,X7))) ),
file('<stdin>',fact_31_finite__imageI) ).
fof(c_0_253,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X6,X7))) ),
file('<stdin>',fact_30_finite__imageI) ).
fof(c_0_254,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X6,X7))) ),
file('<stdin>',fact_29_finite__imageI) ).
fof(c_0_255,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X6,X7))) ),
file('<stdin>',fact_28_finite__imageI) ).
fof(c_0_256,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X6,X7))) ),
file('<stdin>',fact_27_finite__imageI) ).
fof(c_0_257,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X6,X7))) ),
file('<stdin>',fact_26_finite__imageI) ).
fof(c_0_258,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X6,X7))) ),
file('<stdin>',fact_25_finite__imageI) ).
fof(c_0_259,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X6,X7))) ),
file('<stdin>',fact_24_finite__imageI) ).
fof(c_0_260,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X6,X7))) ),
file('<stdin>',fact_23_finite__imageI) ).
fof(c_0_261,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X6,X7))) ),
file('<stdin>',fact_22_finite__imageI) ).
fof(c_0_262,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X6,X7))) ),
file('<stdin>',fact_21_finite__imageI) ).
fof(c_0_263,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X6,X7))) ),
file('<stdin>',fact_20_finite__imageI) ).
fof(c_0_264,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X6,X7))) ),
file('<stdin>',fact_19_finite__imageI) ).
fof(c_0_265,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X6,X7))) ),
file('<stdin>',fact_18_finite__imageI) ).
fof(c_0_266,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X6,X7))) ),
file('<stdin>',fact_17_finite__imageI) ).
fof(c_0_267,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X6,X7))) ),
file('<stdin>',fact_16_finite__imageI) ).
fof(c_0_268,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X6,X7))) ),
file('<stdin>',fact_15_finite__imageI) ).
fof(c_0_269,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X6,X7))) ),
file('<stdin>',fact_14_finite__imageI) ).
fof(c_0_270,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X6,X7))) ),
file('<stdin>',fact_13_finite__imageI) ).
fof(c_0_271,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X6,X7))) ),
file('<stdin>',fact_12_finite__imageI) ).
fof(c_0_272,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X6,X7))) ),
file('<stdin>',fact_11_finite__imageI) ).
fof(c_0_273,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X6,X7))) ),
file('<stdin>',fact_10_finite__imageI) ).
fof(c_0_274,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19))
| X18 = X19 ),
file('<stdin>',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
fof(c_0_275,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19))
| X18 = X19 ),
file('<stdin>',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
fof(c_0_276,axiom,
! [X15,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(minus_minus_nat(X15),X14),
file('<stdin>',fact_161_diff__Suc__Suc) ).
fof(c_0_277,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1476298914l_bool(X44,X46),hAPP_f1664156314l_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
fof(c_0_278,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1748468828l_bool(X44,X46),hAPP_f54304608l_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
fof(c_0_279,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f198738859l_bool(X44,X46),hAPP_fun_a_bool_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
fof(c_0_280,axiom,
! [X44,X45,X46] : hAPP_pname_bool(cOMBS_568398431l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_p393069232l_bool(X44,X46),hAPP_pname_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(c_0_281,axiom,
! [X44,X45,X46] : hAPP_nat_bool(cOMBS_nat_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_n1006566506l_bool(X44,X46),hAPP_nat_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(c_0_282,axiom,
! [X44,X45,X46] : hAPP_a_bool(cOMBS_a_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X44,X46),hAPP_a_bool(X45,X46)),
file('<stdin>',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(c_0_283,axiom,
! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
file('<stdin>',fact_284_image__insert) ).
fof(c_0_284,axiom,
! [X17] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X17))) = hAPP_nat_nat(suc,X17),
file('<stdin>',fact_118_card__Collect__le__nat) ).
fof(c_0_285,axiom,
! [X44,X45,X46] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X44),X45),X46) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(c_0_286,axiom,
! [X44,X45,X46] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X44),X45),X46) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
fof(c_0_287,axiom,
! [X44,X45,X46] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X44),X45),X46) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
fof(c_0_288,axiom,
! [X44,X45,X46] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
fof(c_0_289,axiom,
! [X44,X45,X46] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
fof(c_0_290,axiom,
! [X44,X45,X46] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
fof(c_0_291,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012) ).
fof(c_0_292,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011) ).
fof(c_0_293,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
fof(c_0_294,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
fof(c_0_295,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
fof(c_0_296,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
fof(c_0_297,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
fof(c_0_298,axiom,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(c_0_299,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
fof(c_0_300,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X44),X45),X46) = hAPP_pname_bool(hAPP_p61793385e_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
fof(c_0_301,axiom,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X44),X45),X46) = hAPP_nat_bool(hAPP_n1699378549t_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
fof(c_0_302,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_p1534023578a_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
fof(c_0_303,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_a_fun_a_bool(X44,X46),X45),
file('<stdin>',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
fof(c_0_304,axiom,
! [X45,X44] :
( ~ hBOOL(X44)
| ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45)) ),
file('<stdin>',help_fconj_1_1_U) ).
fof(c_0_305,axiom,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
file('<stdin>',help_fimplies_2_1_U) ).
fof(c_0_306,axiom,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
file('<stdin>',help_fdisj_2_1_U) ).
fof(c_0_307,axiom,
! [X45,X44] :
( ~ hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
file('<stdin>',help_fdisj_1_1_U) ).
fof(c_0_308,axiom,
! [X45,X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
file('<stdin>',help_fimplies_1_1_U) ).
fof(c_0_309,axiom,
! [X44,X45,X46] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).
fof(c_0_310,axiom,
! [X44,X45,X46] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f54304608l_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).
fof(c_0_311,axiom,
! [X44,X45,X46] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).
fof(c_0_312,axiom,
! [X44,X45,X46] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_pname_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) ).
fof(c_0_313,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
fof(c_0_314,axiom,
! [X44,X45,X46] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_nat_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
fof(c_0_315,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f54304608l_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
fof(c_0_316,axiom,
! [X44,X45,X46] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_a_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
fof(c_0_317,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
fof(c_0_318,axiom,
! [X44,X45,X46] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X44,X45),X46) = hAPP_a_fun_a_bool(X44,hAPP_pname_a(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
fof(c_0_319,axiom,
! [X44,X45,X46] : hAPP_pname_bool(cOMBB_647938656_pname(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_pname_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
fof(c_0_320,axiom,
! [X44,X45,X46] : hAPP_nat_bool(cOMBB_bool_bool_nat(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_nat_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(c_0_321,axiom,
! [X44,X45,X46] : hAPP_a_bool(cOMBB_bool_bool_a(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_a_bool(X45,X46)),
file('<stdin>',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
fof(c_0_322,axiom,
! [X11,X33,X5] : insert_a(X11,insert_a(X33,X5)) = insert_a(X33,insert_a(X11,X5)),
file('<stdin>',fact_209_insert__commute) ).
fof(c_0_323,axiom,
! [X11,X33,X5] : insert_pname(X11,insert_pname(X33,X5)) = insert_pname(X33,insert_pname(X11,X5)),
file('<stdin>',fact_208_insert__commute) ).
fof(c_0_324,axiom,
! [X11,X33,X5] : insert_nat(X11,insert_nat(X33,X5)) = insert_nat(X33,insert_nat(X11,X5)),
file('<stdin>',fact_207_insert__commute) ).
fof(c_0_325,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
fof(c_0_326,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
fof(c_0_327,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(c_0_328,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
fof(c_0_329,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
fof(c_0_330,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19)) ),
file('<stdin>',help_fequal_2_1_fequal_000t__a_T) ).
fof(c_0_331,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ),
file('<stdin>',fact_251_equalityE) ).
fof(c_0_332,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ),
file('<stdin>',fact_250_equalityE) ).
fof(c_0_333,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
file('<stdin>',fact_249_equalityE) ).
fof(c_0_334,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ),
file('<stdin>',fact_236_equalityD2) ).
fof(c_0_335,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ),
file('<stdin>',fact_235_equalityD2) ).
fof(c_0_336,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ),
file('<stdin>',fact_234_equalityD2) ).
fof(c_0_337,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
file('<stdin>',fact_233_equalityD1) ).
fof(c_0_338,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
file('<stdin>',fact_232_equalityD1) ).
fof(c_0_339,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
file('<stdin>',fact_231_equalityD1) ).
fof(c_0_340,axiom,
! [X15,X14] :
( X15 = X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('<stdin>',fact_125_eq__imp__le) ).
fof(c_0_341,axiom,
! [X11] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X11)),
file('<stdin>',fact_298_order__refl) ).
fof(c_0_342,axiom,
! [X42] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X42),X42)),
file('<stdin>',fact_297_order__refl) ).
fof(c_0_343,axiom,
! [X11] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X11)),
file('<stdin>',fact_296_order__refl) ).
fof(c_0_344,axiom,
! [X11] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X11)),
file('<stdin>',fact_295_order__refl) ).
fof(c_0_345,axiom,
! [X5] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X5)),
file('<stdin>',fact_227_subset__refl) ).
fof(c_0_346,axiom,
! [X5] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X5)),
file('<stdin>',fact_226_subset__refl) ).
fof(c_0_347,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X5)),
file('<stdin>',fact_225_subset__refl) ).
fof(c_0_348,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X14)),
file('<stdin>',fact_127_le__refl) ).
fof(c_0_349,axiom,
! [X11,X5] : insert_a(X11,insert_a(X11,X5)) = insert_a(X11,X5),
file('<stdin>',fact_206_insert__absorb2) ).
fof(c_0_350,axiom,
! [X11,X5] : insert_pname(X11,insert_pname(X11,X5)) = insert_pname(X11,X5),
file('<stdin>',fact_205_insert__absorb2) ).
fof(c_0_351,axiom,
! [X11,X5] : insert_nat(X11,insert_nat(X11,X5)) = insert_nat(X11,X5),
file('<stdin>',fact_204_insert__absorb2) ).
fof(c_0_352,axiom,
! [X44] :
( ~ hBOOL(hAPP_bool_bool(fNot,X44))
| ~ hBOOL(X44) ),
file('<stdin>',help_fNot_1_1_U) ).
fof(c_0_353,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
file('<stdin>',gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_354,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
file('<stdin>',gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_355,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_pname(X2) )
=> is_bool(hAPP_pname_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
fof(c_0_356,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_a(X2) )
=> is_bool(hAPP_a_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
fof(c_0_357,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_fun1661590463l_bool(X2) )
=> is_fun1661590463l_bool(insert1325755072e_bool(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_358,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_fun949378684l_bool(X2) )
=> is_fun949378684l_bool(insert_fun_a_bool(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_359,axiom,
! [X1,X2] :
( ( is_pname(X1)
& is_fun_pname_bool(X2) )
=> is_fun_pname_bool(insert_pname(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
fof(c_0_360,axiom,
! [X20,X21] :
( hAPP_nat_nat(suc,X20) = hAPP_nat_nat(suc,X21)
<=> X20 = X21 ),
file('<stdin>',fact_120_nat_Oinject) ).
fof(c_0_361,axiom,
! [X18,X19] :
( hAPP_nat_nat(suc,X18) = hAPP_nat_nat(suc,X19)
=> X18 = X19 ),
file('<stdin>',fact_119_Suc__inject) ).
fof(c_0_362,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).
fof(c_0_363,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_bool(hAPP_f1935102916l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).
fof(c_0_364,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) ).
fof(c_0_365,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_bool(hAPP_f621171935l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).
fof(c_0_366,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).
fof(c_0_367,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
fof(c_0_368,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_369,axiom,
! [X1,X2] :
( is_bool(X2)
=> is_bool(hAPP_bool_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(c_0_370,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_371,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_372,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_373,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_374,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_pname_bool(image_1283814551_pname(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
fof(c_0_375,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_a_bool(image_876012084bool_a(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
fof(c_0_376,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_pname_bool(image_1854862208_pname(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(c_0_377,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_a_bool(image_fun_a_bool_a(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
fof(c_0_378,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(image_47868345e_bool(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
fof(c_0_379,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun949378684l_bool(image_112932426a_bool(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_380,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(image_pname_pname(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
fof(c_0_381,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_pname_bool(image_a_pname(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
fof(c_0_382,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(image_a_a(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000t__a_000t__a) ).
fof(c_0_383,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
fof(c_0_384,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).
fof(c_0_385,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(c_0_386,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBS_a_bool_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(c_0_387,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
fof(c_0_388,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2)) ),
file('<stdin>',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
fof(c_0_389,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBB_647938656_pname(X1,X2)) ),
file('<stdin>',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
fof(c_0_390,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBB_bool_bool_a(X1,X2)) ),
file('<stdin>',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
fof(c_0_391,axiom,
! [X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(fNot,X44)) ),
file('<stdin>',help_fNot_2_1_U) ).
fof(c_0_392,axiom,
! [X1,X2] : is_bool(hAPP_f1295398978l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(c_0_393,axiom,
! [X1,X2] : is_bool(hAPP_f595608956l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
fof(c_0_394,axiom,
! [X1,X2] : is_bool(hAPP_f1363661463l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) ).
fof(c_0_395,axiom,
! [X1,X2] : is_bool(hAPP_f937997336l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).
fof(c_0_396,axiom,
! [X1,X2] : is_bool(hAPP_f389811538l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).
fof(c_0_397,axiom,
! [X1,X2] : is_bool(hAPP_f292226953l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
fof(c_0_398,axiom,
! [X1,X2] : is_bool(hAPP_f1637334154l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
fof(c_0_399,axiom,
! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(c_0_400,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_401,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_402,axiom,
! [X1,X2] : is_fun_pname_bool(image_1604018183_pname(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) ).
fof(c_0_403,axiom,
! [X1,X2] : is_fun_a_bool(image_526090948bool_a(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) ).
fof(c_0_404,axiom,
! [X1,X2] : is_fun_pname_bool(image_1705983821_pname(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) ).
fof(c_0_405,axiom,
! [X1,X2] : is_fun_a_bool(image_349102846bool_a(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).
fof(c_0_406,axiom,
! [X1,X2] : is_fun_pname_bool(image_990671762_pname(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) ).
fof(c_0_407,axiom,
! [X1,X2] : is_fun_a_bool(image_573985017bool_a(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) ).
fof(c_0_408,axiom,
! [X1,X2] : is_fun_pname_bool(image_1921560913_pname(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(c_0_409,axiom,
! [X1,X2] : is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
fof(c_0_410,axiom,
! [X1,X2] : is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_411,axiom,
! [X1,X2] : is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_412,axiom,
! [X1,X2] : is_fun_pname_bool(image_nat_pname(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
fof(c_0_413,axiom,
! [X1,X2] : is_fun_a_bool(image_nat_a(X1,X2)),
file('<stdin>',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
fof(c_0_414,axiom,
! [X14] : X14 != hAPP_nat_nat(suc,X14),
file('<stdin>',fact_122_n__not__Suc__n) ).
fof(c_0_415,axiom,
! [X14] : hAPP_nat_nat(suc,X14) != X14,
file('<stdin>',fact_121_Suc__n__not__n) ).
fof(c_0_416,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(p(X1)) ),
file('<stdin>',gsy_v_P) ).
fof(c_0_417,axiom,
! [X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(collec1974731493e_bool(X1)) ),
file('<stdin>',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(c_0_418,axiom,
! [X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(collect_fun_a_bool(X1)) ),
file('<stdin>',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(c_0_419,axiom,
! [X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(collect_pname(X1)) ),
file('<stdin>',gsy_c_Set_OCollect_000tc__Com__Opname) ).
fof(c_0_420,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(collect_a(X1)) ),
file('<stdin>',gsy_c_Set_OCollect_000t__a) ).
fof(c_0_421,axiom,
! [X13] :
( is_fun949378684l_bool(X13)
=> collect_fun_a_bool(X13) = X13 ),
file('<stdin>',fact_258_Collect__def) ).
fof(c_0_422,axiom,
! [X13] :
( is_fun1661590463l_bool(X13)
=> collec1974731493e_bool(X13) = X13 ),
file('<stdin>',fact_257_Collect__def) ).
fof(c_0_423,axiom,
! [X13] :
( is_fun_pname_bool(X13)
=> collect_pname(X13) = X13 ),
file('<stdin>',fact_255_Collect__def) ).
fof(c_0_424,axiom,
is_pname(undefined_pname(pname)),
file('<stdin>',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
fof(c_0_425,axiom,
is_a(undefined_a(x_a)),
file('<stdin>',gsy_c_HOL_Oundefined_000t__a) ).
fof(c_0_426,axiom,
! [X13] : collect_nat(X13) = X13,
file('<stdin>',fact_259_Collect__def) ).
fof(c_0_427,axiom,
! [X13] : collect_fun_nat_bool(X13) = X13,
file('<stdin>',fact_256_Collect__def) ).
fof(c_0_428,axiom,
is_fun949378684l_bool(finite_finite_a),
file('<stdin>',gsy_c_Finite__Set_Ofinite_000t__a) ).
fof(c_0_429,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X9,X5)))
=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X9)),hAPP_pname_a(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_430,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X29)),hAPP_nat_fun_a_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X17)),hAPP_nat_fun_a_bool(X9,X28))) ) ),
c_0_1 ).
fof(c_0_431,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X29)),hAPP_nat_nat(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X17)),hAPP_nat_nat(X9,X28))) ) ),
c_0_2 ).
fof(c_0_432,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X29)),hAPP_n1025906991e_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X17)),hAPP_n1025906991e_bool(X9,X28))) ) ),
c_0_3 ).
fof(c_0_433,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X29)),hAPP_n1699378549t_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X17)),hAPP_n1699378549t_bool(X9,X28))) ) ),
c_0_4 ).
fof(c_0_434,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X30)),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),X10)) ),
c_0_5 ).
fof(c_0_435,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X25),X16)),hAPP_nat_nat(minus_minus_nat(X17),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ) ),
c_0_6 ).
fof(c_0_436,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_a(X9,X27) ) ) ) ),
c_0_7 ).
fof(c_0_437,plain,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_a(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_438,axiom,
! [X10,X9,X5] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
<=> ? [X38] :
( is_fun_pname_bool(X38)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X38),X5))
& X10 = image_pname_a(X9,X38) ) ) ),
c_0_9 ).
fof(c_0_439,axiom,
! [X35,X9,X5] :
( is_a(X35)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X35),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X35 = hAPP_pname_a(X9,X30) ) ) ),
c_0_10 ).
fof(c_0_440,axiom,
! [X39,X13,X16] :
( hBOOL(hAPP_nat_bool(X13,X16))
=> ( ! [X29] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X29)))
=> hBOOL(hAPP_nat_bool(X13,X29)) )
=> hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(minus_minus_nat(X16),X39))) ) ),
c_0_11 ).
fof(c_0_441,axiom,
! [X13,X12] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) ) ),
c_0_12 ).
fof(c_0_442,axiom,
! [X13,X12] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) ) ),
c_0_13 ).
fof(c_0_443,axiom,
! [X13,X12] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) ) ),
c_0_14 ).
fof(c_0_444,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) ) ),
c_0_15 ).
fof(c_0_445,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) ) ),
c_0_16 ).
fof(c_0_446,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) ) ),
c_0_17 ).
fof(c_0_447,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X10)),hAPP_fun_a_bool_nat(finite_card_a,X5)))
=> X5 = X10 ) ) ) ),
c_0_18 ).
fof(c_0_448,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X10)),hAPP_f921600141ol_nat(finite_card_pname,X5)))
=> X5 = X10 ) ) ) ),
c_0_19 ).
fof(c_0_449,axiom,
! [X5,X10] :
( ( is_fun949378684l_bool(X5)
& is_fun949378684l_bool(X10) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X10)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)))
=> X5 = X10 ) ) ) ),
c_0_20 ).
fof(c_0_450,axiom,
! [X5,X10] :
( ( is_fun1661590463l_bool(X5)
& is_fun1661590463l_bool(X10) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X10)),hAPP_f55526627ol_nat(finite1340463720e_bool,X5)))
=> X5 = X10 ) ) ) ),
c_0_21 ).
fof(c_0_451,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X10)),hAPP_f22106695ol_nat(finite_card_nat,X5)))
=> X5 = X10 ) ) ),
c_0_22 ).
fof(c_0_452,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X10)),hAPP_f696928925ol_nat(finite346522414t_bool,X5)))
=> X5 = X10 ) ) ),
c_0_23 ).
fof(c_0_453,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
c_0_24 ).
fof(c_0_454,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
c_0_25 ).
fof(c_0_455,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
c_0_26 ).
fof(c_0_456,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
c_0_27 ).
fof(c_0_457,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
c_0_28 ).
fof(c_0_458,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
c_0_29 ).
fof(c_0_459,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
c_0_30 ).
fof(c_0_460,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_31 ).
fof(c_0_461,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_32 ).
fof(c_0_462,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_33 ).
fof(c_0_463,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_34 ).
fof(c_0_464,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
c_0_35 ).
fof(c_0_465,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
c_0_36 ).
fof(c_0_466,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
c_0_37 ).
fof(c_0_467,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
c_0_38 ).
fof(c_0_468,axiom,
! [X9,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X9,X5))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X5))) ),
c_0_39 ).
fof(c_0_469,axiom,
! [X9,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X9,X5))),hAPP_f98387925ol_nat(finite269641166l_bool,X5))) ),
c_0_40 ).
fof(c_0_470,axiom,
! [X9,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X9,X5))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X5))) ),
c_0_41 ).
fof(c_0_471,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_42 ).
fof(c_0_472,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
c_0_43 ).
fof(c_0_473,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
c_0_44 ).
fof(c_0_474,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
c_0_45 ).
fof(c_0_475,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
c_0_46 ).
fof(c_0_476,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
c_0_47 ).
fof(c_0_477,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
c_0_48 ).
fof(c_0_478,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
c_0_49 ).
fof(c_0_479,axiom,
! [X8,X13] : insert_fun_a_bool(X8,collect_fun_a_bool(X13)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8))),X13)),
c_0_50 ).
fof(c_0_480,axiom,
! [X8,X13] : insert1325755072e_bool(X8,collec1974731493e_bool(X13)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8))),X13)),
c_0_51 ).
fof(c_0_481,axiom,
! [X8,X13] : insert_fun_nat_bool(X8,collect_fun_nat_bool(X13)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8))),X13)),
c_0_52 ).
fof(c_0_482,axiom,
! [X8,X13] : insert_a(X8,collect_a(X13)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8))),X13)),
c_0_53 ).
fof(c_0_483,axiom,
! [X8,X13] : insert_pname(X8,collect_pname(X13)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8))),X13)),
c_0_54 ).
fof(c_0_484,axiom,
! [X8,X13] : insert_nat(X8,collect_nat(X13)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8))),X13)),
c_0_55 ).
fof(c_0_485,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X26),X14)),hAPP_nat_nat(minus_minus_nat(X26),X15))) ),
c_0_56 ).
fof(c_0_486,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X15),X26)),hAPP_nat_nat(minus_minus_nat(X14),X26))) ),
c_0_57 ).
fof(c_0_487,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X11,X5)),X10))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
c_0_58 ).
fof(c_0_488,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X11,X5)),X10))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
c_0_59 ).
fof(c_0_489,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X11,X5)),X10))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
c_0_60 ).
fof(c_0_490,axiom,
! [X17,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),hAPP_nat_nat(suc,X25)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X25)) ),
c_0_61 ).
fof(c_0_491,axiom,
! [X15,X14,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14)),hAPP_nat_nat(suc,X22)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X14)),X22),
c_0_62 ).
fof(c_0_492,axiom,
! [X14,X22,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X22)),hAPP_nat_nat(minus_minus_nat(X14),X22)) = hAPP_nat_nat(minus_minus_nat(X15),X14) ) ),
c_0_63 ).
fof(c_0_493,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X13),X12)))) ),
c_0_64 ).
fof(c_0_494,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X13),X12)))) ),
c_0_65 ).
fof(c_0_495,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X13),X12)))) ),
c_0_66 ).
fof(c_0_496,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X13),X12)))) ),
c_0_67 ).
fof(c_0_497,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X13),X12)))) ),
c_0_68 ).
fof(c_0_498,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X13),X12)))) ),
c_0_69 ).
fof(c_0_499,plain,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),X25)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_500,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,X10))) ) ),
c_0_71 ).
fof(c_0_501,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,X10))) ) ),
c_0_72 ).
fof(c_0_502,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,X10))) ) ),
c_0_73 ).
fof(c_0_503,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X10))) ) ),
c_0_74 ).
fof(c_0_504,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,X10))) ) ),
c_0_75 ).
fof(c_0_505,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,X10))) ) ),
c_0_76 ).
fof(c_0_506,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)))) ),
c_0_77 ).
fof(c_0_507,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)))) ),
c_0_78 ).
fof(c_0_508,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)))) ),
c_0_79 ).
fof(c_0_509,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)))) ),
c_0_80 ).
fof(c_0_510,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)))) ),
c_0_81 ).
fof(c_0_511,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)))) ),
c_0_82 ).
fof(c_0_512,axiom,
! [X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X10)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
c_0_83 ).
fof(c_0_513,axiom,
! [X10,X5] :
( ! [X30] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
c_0_84 ).
fof(c_0_514,axiom,
! [X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X10)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
c_0_85 ).
fof(c_0_515,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),insert_a(X11,X10)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_516,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X11,X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_517,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),insert_nat(X11,X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_518,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),image_pname_a(X9,X10))) ),
c_0_89 ).
fof(c_0_519,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X34),X37))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X34)),insert_a(X8,X37))) ),
c_0_90 ).
fof(c_0_520,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X34),X37))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X8,X34)),insert_pname(X8,X37))) ),
c_0_91 ).
fof(c_0_521,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X34),X37))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X8,X34)),insert_nat(X8,X37))) ),
c_0_92 ).
fof(c_0_522,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5))) ),
c_0_93 ).
fof(c_0_523,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
c_0_94 ).
fof(c_0_524,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X34))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X34)) ) ),
c_0_95 ).
fof(c_0_525,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X34))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X34)) ) ),
c_0_96 ).
fof(c_0_526,axiom,
! [X34,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X34))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X34)) ) ),
c_0_97 ).
fof(c_0_527,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
c_0_98 ).
fof(c_0_528,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
c_0_99 ).
fof(c_0_529,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
c_0_100 ).
fof(c_0_530,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
c_0_101 ).
fof(c_0_531,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
c_0_102 ).
fof(c_0_532,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
c_0_103 ).
fof(c_0_533,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
c_0_104 ).
fof(c_0_534,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
c_0_105 ).
fof(c_0_535,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
c_0_106 ).
fof(c_0_536,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
c_0_107 ).
fof(c_0_537,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
c_0_108 ).
fof(c_0_538,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
c_0_109 ).
fof(c_0_539,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X22)) ) ),
c_0_110 ).
fof(c_0_540,axiom,
! [X43] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43))
<=> ? [X41] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X41)) ) ),
c_0_111 ).
fof(c_0_541,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hAPP_nat_nat(minus_minus_nat(X25),X16) = hAPP_nat_nat(minus_minus_nat(X17),X16)
<=> X25 = X17 ) ) ),
c_0_112 ).
fof(c_0_542,axiom,
! [X14,X40] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X40))
=> ? [X41] : X40 = hAPP_nat_nat(suc,X41) ),
c_0_113 ).
fof(c_0_543,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
c_0_114 ).
fof(c_0_544,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
c_0_115 ).
fof(c_0_545,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
c_0_116 ).
fof(c_0_546,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
c_0_117 ).
fof(c_0_547,axiom,
! [X30,X36] : insert_fun_a_bool(X30,X36) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X30)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X36))),
c_0_118 ).
fof(c_0_548,axiom,
! [X30,X36] : insert1325755072e_bool(X30,X36) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X30)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X36))),
c_0_119 ).
fof(c_0_549,axiom,
! [X30,X36] : insert_fun_nat_bool(X30,X36) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X30)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X36))),
c_0_120 ).
fof(c_0_550,axiom,
! [X30,X36] : insert_a(X30,X36) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X30)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X36))),
c_0_121 ).
fof(c_0_551,axiom,
! [X30,X36] : insert_pname(X30,X36) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X30)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X36))),
c_0_122 ).
fof(c_0_552,axiom,
! [X30,X36] : insert_nat(X30,X36) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X30)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X36))),
c_0_123 ).
fof(c_0_553,axiom,
! [X8,X10] : insert_fun_a_bool(X8,X10) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X10))),
c_0_124 ).
fof(c_0_554,axiom,
! [X8,X10] : insert1325755072e_bool(X8,X10) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X10))),
c_0_125 ).
fof(c_0_555,axiom,
! [X8,X10] : insert_fun_nat_bool(X8,X10) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X10))),
c_0_126 ).
fof(c_0_556,axiom,
! [X8,X10] : insert_a(X8,X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10))),
c_0_127 ).
fof(c_0_557,axiom,
! [X8,X10] : insert_pname(X8,X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10))),
c_0_128 ).
fof(c_0_558,axiom,
! [X8,X10] : insert_nat(X8,X10) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X10))),
c_0_129 ).
fof(c_0_559,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(suc,X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
| X25 = hAPP_nat_nat(suc,X17) ) ),
c_0_130 ).
fof(c_0_560,plain,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> X15 = hAPP_nat_nat(suc,X14) ) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_561,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
c_0_132 ).
fof(c_0_562,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
c_0_133 ).
fof(c_0_563,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X31 = hAPP_pname_a(X9,X11)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
c_0_134 ).
fof(c_0_564,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_pname_a(X9,X11)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
c_0_135 ).
fof(c_0_565,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
c_0_136 ).
fof(c_0_566,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X14)),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_567,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ) ),
c_0_138 ).
fof(c_0_568,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ) ),
c_0_139 ).
fof(c_0_569,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5))
=> X5 = X10 ) ) ),
c_0_140 ).
fof(c_0_570,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5))
=> X5 = X10 ) ) ),
c_0_141 ).
fof(c_0_571,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),insert_a(X31,X10))) ),
c_0_142 ).
fof(c_0_572,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X31,X10))) ),
c_0_143 ).
fof(c_0_573,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),insert_nat(X31,X10))) ),
c_0_144 ).
fof(c_0_574,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X10))) ),
c_0_145 ).
fof(c_0_575,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X10))) ),
c_0_146 ).
fof(c_0_576,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X10))) ),
c_0_147 ).
fof(c_0_577,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X31,X10))) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_578,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X31,X10))) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_579,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X31,X10))) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_580,axiom,
! [X5,X10] :
( X5 = X10
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
c_0_151 ).
fof(c_0_581,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5))
=> X5 = X10 ) ),
c_0_152 ).
fof(c_0_582,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> X15 = X14 ) ),
c_0_153 ).
fof(c_0_583,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14))) ),
c_0_154 ).
fof(c_0_584,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X15),X14)) ),
c_0_155 ).
fof(c_0_585,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X15),X14)),X15)),
c_0_156 ).
fof(c_0_586,plain,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_fun_a_bool_nat(finite_card_a,X5) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_587,plain,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_f921600141ol_nat(finite_card_pname,X5) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_588,plain,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_f22106695ol_nat(finite_card_nat,X5) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_589,plain,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X5) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_590,plain,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X5) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_591,plain,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_f696928925ol_nat(finite346522414t_bool,X5) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_592,plain,
! [X10,X11,X5] :
( ( is_fun_a_bool(X10)
& is_fun_a_bool(X5) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> ( insert_a(X11,X5) = insert_a(X11,X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_593,plain,
! [X10,X11,X5] :
( ( is_fun_pname_bool(X10)
& is_fun_pname_bool(X5) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> ( insert_pname(X11,X5) = insert_pname(X11,X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_594,axiom,
! [X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X5)))) ),
c_0_165 ).
fof(c_0_595,axiom,
! [X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X5)))) ),
c_0_166 ).
fof(c_0_596,axiom,
! [X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X5)))) ),
c_0_167 ).
fof(c_0_597,axiom,
! [X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X5)))) ),
c_0_168 ).
fof(c_0_598,axiom,
! [X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X5)))) ),
c_0_169 ).
fof(c_0_599,axiom,
! [X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X5)))) ),
c_0_170 ).
fof(c_0_600,axiom,
! [X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X5)))) ),
c_0_171 ).
fof(c_0_601,axiom,
! [X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X5)))) ),
c_0_172 ).
fof(c_0_602,axiom,
! [X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X5)))) ),
c_0_173 ).
fof(c_0_603,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> insert_a(hAPP_pname_a(X9,X11),image_pname_a(X9,X5)) = image_pname_a(X9,X5) ),
c_0_174 ).
fof(c_0_604,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> ( insert_nat(X11,X5) = insert_nat(X11,X10)
<=> X5 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_605,plain,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_606,plain,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_607,plain,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_608,plain,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_609,plain,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_610,plain,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_611,axiom,
! [X23,X24,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X24)),X22) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X22)),X24),
c_0_182 ).
fof(c_0_612,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
c_0_183 ).
fof(c_0_613,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
c_0_184 ).
fof(c_0_614,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
c_0_185 ).
fof(c_0_615,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
c_0_186 ).
fof(c_0_616,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
c_0_187 ).
fof(c_0_617,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
c_0_188 ).
fof(c_0_618,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
c_0_189 ).
fof(c_0_619,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
c_0_190 ).
fof(c_0_620,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
c_0_191 ).
fof(c_0_621,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
c_0_192 ).
fof(c_0_622,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
c_0_193 ).
fof(c_0_623,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
c_0_194 ).
fof(c_0_624,axiom,
! [X23,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X14))
=> hAPP_nat_nat(minus_minus_nat(X14),hAPP_nat_nat(minus_minus_nat(X14),X23)) = X23 ),
c_0_195 ).
fof(c_0_625,axiom,
! [X33,X5,X11] :
( ( is_a(X33)
& is_a(X11) )
=> ( hBOOL(hAPP_a_bool(insert_a(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_a_bool(X5,X11)) ) ) ),
c_0_196 ).
fof(c_0_626,axiom,
! [X33,X5,X11] :
( ( is_pname(X33)
& is_pname(X11) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_pname_bool(X5,X11)) ) ) ),
c_0_197 ).
fof(c_0_627,axiom,
! [X16] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X16)))),
c_0_198 ).
fof(c_0_628,axiom,
! [X3,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X4))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),X3)) ),
c_0_199 ).
fof(c_0_629,axiom,
! [X33,X5,X11] :
( hBOOL(hAPP_nat_bool(insert_nat(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_nat_bool(X5,X11)) ) ),
c_0_200 ).
fof(c_0_630,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15)) ),
c_0_201 ).
fof(c_0_631,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ),
c_0_202 ).
fof(c_0_632,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ),
c_0_203 ).
fof(c_0_633,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ),
c_0_204 ).
fof(c_0_634,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ),
c_0_205 ).
fof(c_0_635,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ),
c_0_206 ).
fof(c_0_636,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ),
c_0_207 ).
fof(c_0_637,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
<=> hBOOL(hAPP_pname_bool(X5,X11)) ),
c_0_208 ).
fof(c_0_638,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
<=> hBOOL(hAPP_a_bool(X5,X11)) ),
c_0_209 ).
fof(c_0_639,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
<=> hBOOL(hAPP_nat_bool(X5,X11)) ),
c_0_210 ).
fof(c_0_640,axiom,
! [X8,X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> insert_a(X8,X5) = X5 ) ),
c_0_211 ).
fof(c_0_641,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> insert_pname(X8,X5) = X5 ) ),
c_0_212 ).
fof(c_0_642,plain,
! [X18,X19] :
( ( is_fun_pname_bool(X18)
& is_fun_pname_bool(X19) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_643,plain,
! [X18,X19] :
( ( is_fun_a_bool(X18)
& is_fun_a_bool(X19) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_644,plain,
! [X18,X19] :
( ( is_pname(X18)
& is_pname(X19) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_645,plain,
! [X18,X19] :
( ( is_a(X18)
& is_a(X19) )
=> ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_646,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
c_0_217 ).
fof(c_0_647,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
c_0_218 ).
fof(c_0_648,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> insert_nat(X8,X5) = X5 ),
c_0_219 ).
fof(c_0_649,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45))
| ~ hBOOL(X44)
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_650,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45))
| hBOOL(X44)
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_651,axiom,
! [X10,X8] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),insert_a(X8,X10))),
c_0_222 ).
fof(c_0_652,axiom,
! [X10,X8] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),insert_pname(X8,X10))),
c_0_223 ).
fof(c_0_653,axiom,
! [X10,X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),insert_nat(X8,X10))),
c_0_224 ).
fof(c_0_654,axiom,
! [X8,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X8,X10))),
c_0_225 ).
fof(c_0_655,axiom,
! [X8,X10] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X8,X10))),
c_0_226 ).
fof(c_0_656,axiom,
! [X8,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X8,X10))),
c_0_227 ).
fof(c_0_657,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_658,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X44) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_659,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5))) ),
c_0_230 ).
fof(c_0_660,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5))) ),
c_0_231 ).
fof(c_0_661,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5))) ),
c_0_232 ).
fof(c_0_662,axiom,
! [X8,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X8,X5))) ),
c_0_233 ).
fof(c_0_663,axiom,
! [X8,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X8,X5))) ),
c_0_234 ).
fof(c_0_664,axiom,
! [X8,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X8,X5))) ),
c_0_235 ).
fof(c_0_665,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5))) ),
c_0_236 ).
fof(c_0_666,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5))) ),
c_0_237 ).
fof(c_0_667,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5))) ),
c_0_238 ).
fof(c_0_668,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X6,X7))) ),
c_0_239 ).
fof(c_0_669,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X6,X7))) ),
c_0_240 ).
fof(c_0_670,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X6,X7))) ),
c_0_241 ).
fof(c_0_671,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X6,X7))) ),
c_0_242 ).
fof(c_0_672,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X6,X7))) ),
c_0_243 ).
fof(c_0_673,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X6,X7))) ),
c_0_244 ).
fof(c_0_674,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X6,X7))) ),
c_0_245 ).
fof(c_0_675,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X6,X7))) ),
c_0_246 ).
fof(c_0_676,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X6,X7))) ),
c_0_247 ).
fof(c_0_677,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X6,X7))) ),
c_0_248 ).
fof(c_0_678,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X6,X7))) ),
c_0_249 ).
fof(c_0_679,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X6,X7))) ),
c_0_250 ).
fof(c_0_680,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X6,X7))) ),
c_0_251 ).
fof(c_0_681,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X6,X7))) ),
c_0_252 ).
fof(c_0_682,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X6,X7))) ),
c_0_253 ).
fof(c_0_683,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X6,X7))) ),
c_0_254 ).
fof(c_0_684,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X6,X7))) ),
c_0_255 ).
fof(c_0_685,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X6,X7))) ),
c_0_256 ).
fof(c_0_686,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X6,X7))) ),
c_0_257 ).
fof(c_0_687,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X6,X7))) ),
c_0_258 ).
fof(c_0_688,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X6,X7))) ),
c_0_259 ).
fof(c_0_689,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X6,X7))) ),
c_0_260 ).
fof(c_0_690,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X6,X7))) ),
c_0_261 ).
fof(c_0_691,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X6,X7))) ),
c_0_262 ).
fof(c_0_692,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X6,X7))) ),
c_0_263 ).
fof(c_0_693,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X6,X7))) ),
c_0_264 ).
fof(c_0_694,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X6,X7))) ),
c_0_265 ).
fof(c_0_695,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X6,X7))) ),
c_0_266 ).
fof(c_0_696,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X6,X7))) ),
c_0_267 ).
fof(c_0_697,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X6,X7))) ),
c_0_268 ).
fof(c_0_698,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X6,X7))) ),
c_0_269 ).
fof(c_0_699,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X6,X7))) ),
c_0_270 ).
fof(c_0_700,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X6,X7))) ),
c_0_271 ).
fof(c_0_701,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X6,X7))) ),
c_0_272 ).
fof(c_0_702,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X6,X7))) ),
c_0_273 ).
fof(c_0_703,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_704,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_705,axiom,
! [X15,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(minus_minus_nat(X15),X14),
c_0_276 ).
fof(c_0_706,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1476298914l_bool(X44,X46),hAPP_f1664156314l_bool(X45,X46)),
c_0_277 ).
fof(c_0_707,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1748468828l_bool(X44,X46),hAPP_f54304608l_bool(X45,X46)),
c_0_278 ).
fof(c_0_708,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f198738859l_bool(X44,X46),hAPP_fun_a_bool_bool(X45,X46)),
c_0_279 ).
fof(c_0_709,axiom,
! [X44,X45,X46] : hAPP_pname_bool(cOMBS_568398431l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_p393069232l_bool(X44,X46),hAPP_pname_bool(X45,X46)),
c_0_280 ).
fof(c_0_710,axiom,
! [X44,X45,X46] : hAPP_nat_bool(cOMBS_nat_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_n1006566506l_bool(X44,X46),hAPP_nat_bool(X45,X46)),
c_0_281 ).
fof(c_0_711,axiom,
! [X44,X45,X46] : hAPP_a_bool(cOMBS_a_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X44,X46),hAPP_a_bool(X45,X46)),
c_0_282 ).
fof(c_0_712,axiom,
! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
c_0_283 ).
fof(c_0_713,axiom,
! [X17] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X17))) = hAPP_nat_nat(suc,X17),
c_0_284 ).
fof(c_0_714,axiom,
! [X44,X45,X46] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X44),X45),X46) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X44,X46),X45),
c_0_285 ).
fof(c_0_715,axiom,
! [X44,X45,X46] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X44),X45),X46) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X44,X46),X45),
c_0_286 ).
fof(c_0_716,axiom,
! [X44,X45,X46] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X44),X45),X46) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X44,X46),X45),
c_0_287 ).
fof(c_0_717,axiom,
! [X44,X45,X46] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X44,X46),X45),
c_0_288 ).
fof(c_0_718,axiom,
! [X44,X45,X46] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X44,X46),X45),
c_0_289 ).
fof(c_0_719,axiom,
! [X44,X45,X46] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X44,X46),X45),
c_0_290 ).
fof(c_0_720,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X44,X46),X45),
c_0_291 ).
fof(c_0_721,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X44,X46),X45),
c_0_292 ).
fof(c_0_722,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X44,X46),X45),
c_0_293 ).
fof(c_0_723,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X44,X46),X45),
c_0_294 ).
fof(c_0_724,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X44,X46),X45),
c_0_295 ).
fof(c_0_725,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X44,X46),X45),
c_0_296 ).
fof(c_0_726,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X44,X46),X45),
c_0_297 ).
fof(c_0_727,axiom,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X44,X46),X45),
c_0_298 ).
fof(c_0_728,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X44,X46),X45),
c_0_299 ).
fof(c_0_729,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X44),X45),X46) = hAPP_pname_bool(hAPP_p61793385e_bool(X44,X46),X45),
c_0_300 ).
fof(c_0_730,axiom,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X44),X45),X46) = hAPP_nat_bool(hAPP_n1699378549t_bool(X44,X46),X45),
c_0_301 ).
fof(c_0_731,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_p1534023578a_bool(X44,X46),X45),
c_0_302 ).
fof(c_0_732,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_a_fun_a_bool(X44,X46),X45),
c_0_303 ).
fof(c_0_733,plain,
! [X45,X44] :
( ~ hBOOL(X44)
| ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_734,plain,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_735,plain,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_736,plain,
! [X45,X44] :
( ~ hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_737,axiom,
! [X45,X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
c_0_308 ).
fof(c_0_738,axiom,
! [X44,X45,X46] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
c_0_309 ).
fof(c_0_739,axiom,
! [X44,X45,X46] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f54304608l_bool(X45,X46)),
c_0_310 ).
fof(c_0_740,axiom,
! [X44,X45,X46] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
c_0_311 ).
fof(c_0_741,axiom,
! [X44,X45,X46] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_pname_bool(X45,X46)),
c_0_312 ).
fof(c_0_742,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
c_0_313 ).
fof(c_0_743,axiom,
! [X44,X45,X46] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_nat_bool(X45,X46)),
c_0_314 ).
fof(c_0_744,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f54304608l_bool(X45,X46)),
c_0_315 ).
fof(c_0_745,axiom,
! [X44,X45,X46] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_a_bool(X45,X46)),
c_0_316 ).
fof(c_0_746,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
c_0_317 ).
fof(c_0_747,axiom,
! [X44,X45,X46] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X44,X45),X46) = hAPP_a_fun_a_bool(X44,hAPP_pname_a(X45,X46)),
c_0_318 ).
fof(c_0_748,axiom,
! [X44,X45,X46] : hAPP_pname_bool(cOMBB_647938656_pname(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_pname_bool(X45,X46)),
c_0_319 ).
fof(c_0_749,axiom,
! [X44,X45,X46] : hAPP_nat_bool(cOMBB_bool_bool_nat(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_nat_bool(X45,X46)),
c_0_320 ).
fof(c_0_750,axiom,
! [X44,X45,X46] : hAPP_a_bool(cOMBB_bool_bool_a(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_a_bool(X45,X46)),
c_0_321 ).
fof(c_0_751,axiom,
! [X11,X33,X5] : insert_a(X11,insert_a(X33,X5)) = insert_a(X33,insert_a(X11,X5)),
c_0_322 ).
fof(c_0_752,axiom,
! [X11,X33,X5] : insert_pname(X11,insert_pname(X33,X5)) = insert_pname(X33,insert_pname(X11,X5)),
c_0_323 ).
fof(c_0_753,axiom,
! [X11,X33,X5] : insert_nat(X11,insert_nat(X33,X5)) = insert_nat(X33,insert_nat(X11,X5)),
c_0_324 ).
fof(c_0_754,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19)) ),
c_0_325 ).
fof(c_0_755,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19)) ),
c_0_326 ).
fof(c_0_756,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19)) ),
c_0_327 ).
fof(c_0_757,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19)) ),
c_0_328 ).
fof(c_0_758,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19)) ),
c_0_329 ).
fof(c_0_759,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19)) ),
c_0_330 ).
fof(c_0_760,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_761,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_762,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_763,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ),
c_0_334 ).
fof(c_0_764,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ),
c_0_335 ).
fof(c_0_765,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ),
c_0_336 ).
fof(c_0_766,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
c_0_337 ).
fof(c_0_767,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
c_0_338 ).
fof(c_0_768,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
c_0_339 ).
fof(c_0_769,axiom,
! [X15,X14] :
( X15 = X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
c_0_340 ).
fof(c_0_770,axiom,
! [X11] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X11)),
c_0_341 ).
fof(c_0_771,axiom,
! [X42] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X42),X42)),
c_0_342 ).
fof(c_0_772,axiom,
! [X11] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X11)),
c_0_343 ).
fof(c_0_773,axiom,
! [X11] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X11)),
c_0_344 ).
fof(c_0_774,axiom,
! [X5] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X5)),
c_0_345 ).
fof(c_0_775,axiom,
! [X5] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X5)),
c_0_346 ).
fof(c_0_776,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X5)),
c_0_347 ).
fof(c_0_777,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X14)),
c_0_348 ).
fof(c_0_778,axiom,
! [X11,X5] : insert_a(X11,insert_a(X11,X5)) = insert_a(X11,X5),
c_0_349 ).
fof(c_0_779,axiom,
! [X11,X5] : insert_pname(X11,insert_pname(X11,X5)) = insert_pname(X11,X5),
c_0_350 ).
fof(c_0_780,axiom,
! [X11,X5] : insert_nat(X11,insert_nat(X11,X5)) = insert_nat(X11,X5),
c_0_351 ).
fof(c_0_781,plain,
! [X44] :
( ~ hBOOL(hAPP_bool_bool(fNot,X44))
| ~ hBOOL(X44) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_782,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
c_0_353 ).
fof(c_0_783,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
c_0_354 ).
fof(c_0_784,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_pname(X2) )
=> is_bool(hAPP_pname_bool(X1,X2)) ),
c_0_355 ).
fof(c_0_785,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_a(X2) )
=> is_bool(hAPP_a_bool(X1,X2)) ),
c_0_356 ).
fof(c_0_786,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_fun1661590463l_bool(X2) )
=> is_fun1661590463l_bool(insert1325755072e_bool(X1,X2)) ),
c_0_357 ).
fof(c_0_787,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_fun949378684l_bool(X2) )
=> is_fun949378684l_bool(insert_fun_a_bool(X1,X2)) ),
c_0_358 ).
fof(c_0_788,axiom,
! [X1,X2] :
( ( is_pname(X1)
& is_fun_pname_bool(X2) )
=> is_fun_pname_bool(insert_pname(X1,X2)) ),
c_0_359 ).
fof(c_0_789,axiom,
! [X20,X21] :
( hAPP_nat_nat(suc,X20) = hAPP_nat_nat(suc,X21)
<=> X20 = X21 ),
c_0_360 ).
fof(c_0_790,axiom,
! [X18,X19] :
( hAPP_nat_nat(suc,X18) = hAPP_nat_nat(suc,X19)
=> X18 = X19 ),
c_0_361 ).
fof(c_0_791,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2)) ),
c_0_362 ).
fof(c_0_792,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_bool(hAPP_f1935102916l_bool(X1,X2)) ),
c_0_363 ).
fof(c_0_793,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2)) ),
c_0_364 ).
fof(c_0_794,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_bool(hAPP_f621171935l_bool(X1,X2)) ),
c_0_365 ).
fof(c_0_795,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2)) ),
c_0_366 ).
fof(c_0_796,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2)) ),
c_0_367 ).
fof(c_0_797,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2)) ),
c_0_368 ).
fof(c_0_798,axiom,
! [X1,X2] :
( is_bool(X2)
=> is_bool(hAPP_bool_bool(X1,X2)) ),
c_0_369 ).
fof(c_0_799,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2)) ),
c_0_370 ).
fof(c_0_800,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
c_0_371 ).
fof(c_0_801,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2)) ),
c_0_372 ).
fof(c_0_802,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
c_0_373 ).
fof(c_0_803,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_pname_bool(image_1283814551_pname(X1,X2)) ),
c_0_374 ).
fof(c_0_804,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_a_bool(image_876012084bool_a(X1,X2)) ),
c_0_375 ).
fof(c_0_805,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_pname_bool(image_1854862208_pname(X1,X2)) ),
c_0_376 ).
fof(c_0_806,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_a_bool(image_fun_a_bool_a(X1,X2)) ),
c_0_377 ).
fof(c_0_807,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(image_47868345e_bool(X1,X2)) ),
c_0_378 ).
fof(c_0_808,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun949378684l_bool(image_112932426a_bool(X1,X2)) ),
c_0_379 ).
fof(c_0_809,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(image_pname_pname(X1,X2)) ),
c_0_380 ).
fof(c_0_810,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_pname_bool(image_a_pname(X1,X2)) ),
c_0_381 ).
fof(c_0_811,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(image_a_a(X1,X2)) ),
c_0_382 ).
fof(c_0_812,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2)) ),
c_0_383 ).
fof(c_0_813,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2)) ),
c_0_384 ).
fof(c_0_814,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2)) ),
c_0_385 ).
fof(c_0_815,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBS_a_bool_bool(X1,X2)) ),
c_0_386 ).
fof(c_0_816,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2)) ),
c_0_387 ).
fof(c_0_817,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2)) ),
c_0_388 ).
fof(c_0_818,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBB_647938656_pname(X1,X2)) ),
c_0_389 ).
fof(c_0_819,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBB_bool_bool_a(X1,X2)) ),
c_0_390 ).
fof(c_0_820,axiom,
! [X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(fNot,X44)) ),
c_0_391 ).
fof(c_0_821,axiom,
! [X1,X2] : is_bool(hAPP_f1295398978l_bool(X1,X2)),
c_0_392 ).
fof(c_0_822,axiom,
! [X1,X2] : is_bool(hAPP_f595608956l_bool(X1,X2)),
c_0_393 ).
fof(c_0_823,axiom,
! [X1,X2] : is_bool(hAPP_f1363661463l_bool(X1,X2)),
c_0_394 ).
fof(c_0_824,axiom,
! [X1,X2] : is_bool(hAPP_f937997336l_bool(X1,X2)),
c_0_395 ).
fof(c_0_825,axiom,
! [X1,X2] : is_bool(hAPP_f389811538l_bool(X1,X2)),
c_0_396 ).
fof(c_0_826,axiom,
! [X1,X2] : is_bool(hAPP_f292226953l_bool(X1,X2)),
c_0_397 ).
fof(c_0_827,axiom,
! [X1,X2] : is_bool(hAPP_f1637334154l_bool(X1,X2)),
c_0_398 ).
fof(c_0_828,axiom,
! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
c_0_399 ).
fof(c_0_829,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
c_0_400 ).
fof(c_0_830,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
c_0_401 ).
fof(c_0_831,axiom,
! [X1,X2] : is_fun_pname_bool(image_1604018183_pname(X1,X2)),
c_0_402 ).
fof(c_0_832,axiom,
! [X1,X2] : is_fun_a_bool(image_526090948bool_a(X1,X2)),
c_0_403 ).
fof(c_0_833,axiom,
! [X1,X2] : is_fun_pname_bool(image_1705983821_pname(X1,X2)),
c_0_404 ).
fof(c_0_834,axiom,
! [X1,X2] : is_fun_a_bool(image_349102846bool_a(X1,X2)),
c_0_405 ).
fof(c_0_835,axiom,
! [X1,X2] : is_fun_pname_bool(image_990671762_pname(X1,X2)),
c_0_406 ).
fof(c_0_836,axiom,
! [X1,X2] : is_fun_a_bool(image_573985017bool_a(X1,X2)),
c_0_407 ).
fof(c_0_837,axiom,
! [X1,X2] : is_fun_pname_bool(image_1921560913_pname(X1,X2)),
c_0_408 ).
fof(c_0_838,axiom,
! [X1,X2] : is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
c_0_409 ).
fof(c_0_839,axiom,
! [X1,X2] : is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
c_0_410 ).
fof(c_0_840,axiom,
! [X1,X2] : is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
c_0_411 ).
fof(c_0_841,axiom,
! [X1,X2] : is_fun_pname_bool(image_nat_pname(X1,X2)),
c_0_412 ).
fof(c_0_842,axiom,
! [X1,X2] : is_fun_a_bool(image_nat_a(X1,X2)),
c_0_413 ).
fof(c_0_843,axiom,
! [X14] : X14 != hAPP_nat_nat(suc,X14),
c_0_414 ).
fof(c_0_844,axiom,
! [X14] : hAPP_nat_nat(suc,X14) != X14,
c_0_415 ).
fof(c_0_845,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(p(X1)) ),
c_0_416 ).
fof(c_0_846,axiom,
! [X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(collec1974731493e_bool(X1)) ),
c_0_417 ).
fof(c_0_847,axiom,
! [X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(collect_fun_a_bool(X1)) ),
c_0_418 ).
fof(c_0_848,axiom,
! [X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(collect_pname(X1)) ),
c_0_419 ).
fof(c_0_849,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(collect_a(X1)) ),
c_0_420 ).
fof(c_0_850,axiom,
! [X13] :
( is_fun949378684l_bool(X13)
=> collect_fun_a_bool(X13) = X13 ),
c_0_421 ).
fof(c_0_851,axiom,
! [X13] :
( is_fun1661590463l_bool(X13)
=> collec1974731493e_bool(X13) = X13 ),
c_0_422 ).
fof(c_0_852,axiom,
! [X13] :
( is_fun_pname_bool(X13)
=> collect_pname(X13) = X13 ),
c_0_423 ).
fof(c_0_853,axiom,
is_pname(undefined_pname(pname)),
c_0_424 ).
fof(c_0_854,axiom,
is_a(undefined_a(x_a)),
c_0_425 ).
fof(c_0_855,axiom,
! [X13] : collect_nat(X13) = X13,
c_0_426 ).
fof(c_0_856,axiom,
! [X13] : collect_fun_nat_bool(X13) = X13,
c_0_427 ).
fof(c_0_857,axiom,
is_fun949378684l_bool(finite_finite_a),
c_0_428 ).
fof(c_0_858,plain,
! [X31,X32] :
( ( is_pname(esk6_2(X31,X32))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X31,X32)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X32)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk6_2(X31,X32)),X32))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X31,X32)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X32)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X32)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X31)),hAPP_pname_a(X31,esk6_2(X31,X32)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X31,X32)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X32)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_429])])])]) ).
fof(c_0_859,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X32,esk5_3(X30,X31,X32))),hAPP_nat_fun_a_bool(X32,hAPP_nat_nat(suc,esk5_3(X30,X31,X32)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X32,X30)),hAPP_nat_fun_a_bool(X32,X31))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_430])])]) ).
fof(c_0_860,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X32,esk4_3(X30,X31,X32))),hAPP_nat_nat(X32,hAPP_nat_nat(suc,esk4_3(X30,X31,X32)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X32,X30)),hAPP_nat_nat(X32,X31))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_431])])]) ).
fof(c_0_861,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X32,esk3_3(X30,X31,X32))),hAPP_n1025906991e_bool(X32,hAPP_nat_nat(suc,esk3_3(X30,X31,X32)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X32,X30)),hAPP_n1025906991e_bool(X32,X31))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_432])])]) ).
fof(c_0_862,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X32,esk2_3(X30,X31,X32))),hAPP_n1699378549t_bool(X32,hAPP_nat_nat(suc,esk2_3(X30,X31,X32)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X32,X30)),hAPP_n1699378549t_bool(X32,X31))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_433])])]) ).
fof(c_0_863,plain,
! [X31,X32,X33] :
( ( is_pname(esk15_3(X31,X32,X33))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X31,X33)),X32)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk15_3(X31,X32,X33)),X33))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X31,X33)),X32)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X31,esk15_3(X31,X32,X33))),X32))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X31,X33)),X32)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_434])])])]) ).
fof(c_0_864,plain,
! [X26,X27,X28] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X28),X27)),hAPP_nat_nat(minus_minus_nat(X26),X27)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X28)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X28),X27)),hAPP_nat_nat(minus_minus_nat(X26),X27)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X28)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_435])])]) ).
fof(c_0_865,plain,
! [X28,X29,X30] :
( ( is_fun_pname_bool(esk1_3(X28,X29,X30))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X30),image_pname_a(X28,X29)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X30))
| ~ is_fun_a_bool(X30) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk1_3(X28,X29,X30)),X29))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X30),image_pname_a(X28,X29)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X30))
| ~ is_fun_a_bool(X30) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk1_3(X28,X29,X30)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X30),image_pname_a(X28,X29)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X30))
| ~ is_fun_a_bool(X30) )
& ( X30 = image_pname_a(X28,esk1_3(X28,X29,X30))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X30),image_pname_a(X28,X29)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X30))
| ~ is_fun_a_bool(X30) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_436])])])]) ).
fof(c_0_866,plain,
! [X32,X33,X34] :
( ( is_pname(esk9_3(X32,X33,X34))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),image_pname_a(X33,X34)))
| ~ is_a(X32) )
& ( X32 = hAPP_pname_a(X33,esk9_3(X32,X33,X34))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),image_pname_a(X33,X34)))
| ~ is_a(X32) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk9_3(X32,X33,X34)),X34))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),image_pname_a(X33,X34)))
| ~ is_a(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_437])])])])])]) ).
fof(c_0_867,plain,
! [X39,X40,X41,X43,X44,X45] :
( ( is_fun_pname_bool(esk8_3(X39,X40,X41))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),image_pname_a(X40,X41)))
| ~ is_fun_a_bool(X39) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk8_3(X39,X40,X41)),X41))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),image_pname_a(X40,X41)))
| ~ is_fun_a_bool(X39) )
& ( X39 = image_pname_a(X40,esk8_3(X39,X40,X41))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),image_pname_a(X40,X41)))
| ~ is_fun_a_bool(X39) )
& ( ~ is_fun_pname_bool(X45)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X45),X44))
| X39 != image_pname_a(X43,X45)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),image_pname_a(X43,X44)))
| ~ is_fun_a_bool(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_438])])])])])]) ).
fof(c_0_868,plain,
! [X36,X37,X38,X40,X41,X42] :
( ( is_pname(esk7_3(X36,X37,X38))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X36),image_pname_a(X37,X38)))
| ~ is_a(X36) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk7_3(X36,X37,X38)),X38))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X36),image_pname_a(X37,X38)))
| ~ is_a(X36) )
& ( X36 = hAPP_pname_a(X37,esk7_3(X36,X37,X38))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X36),image_pname_a(X37,X38)))
| ~ is_a(X36) )
& ( ~ is_pname(X42)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X42),X41))
| X36 != hAPP_pname_a(X40,X42)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X36),image_pname_a(X40,X41)))
| ~ is_a(X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_439])])])])])]) ).
fof(c_0_869,plain,
! [X40,X41,X42] :
( ( hBOOL(hAPP_nat_bool(X41,hAPP_nat_nat(suc,esk13_3(X40,X41,X42))))
| hBOOL(hAPP_nat_bool(X41,hAPP_nat_nat(minus_minus_nat(X42),X40)))
| ~ hBOOL(hAPP_nat_bool(X41,X42)) )
& ( ~ hBOOL(hAPP_nat_bool(X41,esk13_3(X40,X41,X42)))
| hBOOL(hAPP_nat_bool(X41,hAPP_nat_nat(minus_minus_nat(X42),X40)))
| ~ hBOOL(hAPP_nat_bool(X41,X42)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_440])])])]) ).
fof(c_0_870,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X14)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X15)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X16)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X17)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_441])])])])]) ).
fof(c_0_871,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X14)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X15)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X16)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X17)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_442])])])])]) ).
fof(c_0_872,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X14)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X15)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X16)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X17)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_443])])])])]) ).
fof(c_0_873,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X14)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X15)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X16)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X17)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_444])])])])]) ).
fof(c_0_874,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X14)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X15)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X16)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X17)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_445])])])])]) ).
fof(c_0_875,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X14)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X14),X15)))) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X15)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X14),X15)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X16)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X17)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X16),X17)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_446])])])])]) ).
fof(c_0_876,plain,
! [X11,X12] :
( ~ is_fun_a_bool(X11)
| ~ is_fun_a_bool(X12)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X12)),hAPP_fun_a_bool_nat(finite_card_a,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_447])]) ).
fof(c_0_877,plain,
! [X11,X12] :
( ~ is_fun_pname_bool(X11)
| ~ is_fun_pname_bool(X12)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X12))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X12)),hAPP_f921600141ol_nat(finite_card_pname,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_448])]) ).
fof(c_0_878,plain,
! [X11,X12] :
( ~ is_fun949378684l_bool(X11)
| ~ is_fun949378684l_bool(X12)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X12))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X12)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_449])]) ).
fof(c_0_879,plain,
! [X11,X12] :
( ~ is_fun1661590463l_bool(X11)
| ~ is_fun1661590463l_bool(X12)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X12))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X12)),hAPP_f55526627ol_nat(finite1340463720e_bool,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_450])]) ).
fof(c_0_880,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X12))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X12)),hAPP_f22106695ol_nat(finite_card_nat,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_451])]) ).
fof(c_0_881,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X12))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X11),X12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X12)),hAPP_f696928925ol_nat(finite346522414t_bool,X11)))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_452])]) ).
fof(c_0_882,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X10,X11))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_453])]) ).
fof(c_0_883,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X10,X11))),hAPP_f55526627ol_nat(finite1340463720e_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_454])]) ).
fof(c_0_884,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X10,X11))),hAPP_f696928925ol_nat(finite346522414t_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_455])]) ).
fof(c_0_885,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X10,X11))),hAPP_f22106695ol_nat(finite_card_nat,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_456])]) ).
fof(c_0_886,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X10,X11))),hAPP_f22106695ol_nat(finite_card_nat,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_457])]) ).
fof(c_0_887,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X10,X11))),hAPP_f22106695ol_nat(finite_card_nat,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_458])]) ).
fof(c_0_888,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X10,X11))),hAPP_f22106695ol_nat(finite_card_nat,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_459])]) ).
fof(c_0_889,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_460])]) ).
fof(c_0_890,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_461])]) ).
fof(c_0_891,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_462])]) ).
fof(c_0_892,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_463])]) ).
fof(c_0_893,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X10,X11))),hAPP_fun_a_bool_nat(finite_card_a,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_464])]) ).
fof(c_0_894,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X10,X11))),hAPP_f696928925ol_nat(finite346522414t_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_465])]) ).
fof(c_0_895,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X10,X11))),hAPP_f55526627ol_nat(finite1340463720e_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_466])]) ).
fof(c_0_896,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X10,X11))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_467])]) ).
fof(c_0_897,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X10,X11))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_468])]) ).
fof(c_0_898,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X10,X11))),hAPP_f98387925ol_nat(finite269641166l_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_469])]) ).
fof(c_0_899,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X10,X11))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_470])]) ).
fof(c_0_900,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_471])]) ).
fof(c_0_901,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X10,X11))),hAPP_f22106695ol_nat(finite_card_nat,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_472])]) ).
fof(c_0_902,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X10,X11))),hAPP_fun_a_bool_nat(finite_card_a,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_473])]) ).
fof(c_0_903,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X10,X11))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_474])]) ).
fof(c_0_904,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X10,X11))),hAPP_f55526627ol_nat(finite1340463720e_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_475])]) ).
fof(c_0_905,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X10,X11))),hAPP_f696928925ol_nat(finite346522414t_bool,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_476])]) ).
fof(c_0_906,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X10,X11))),hAPP_fun_a_bool_nat(finite_card_a,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_477])]) ).
fof(c_0_907,plain,
! [X10,X11] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X10,X11))),hAPP_f921600141ol_nat(finite_card_pname,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_478])]) ).
fof(c_0_908,plain,
! [X14,X15] : insert_fun_a_bool(X14,collect_fun_a_bool(X15)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_909,plain,
! [X14,X15] : insert1325755072e_bool(X14,collec1974731493e_bool(X15)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_910,plain,
! [X14,X15] : insert_fun_nat_bool(X14,collect_fun_nat_bool(X15)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_911,plain,
! [X14,X15] : insert_a(X14,collect_a(X15)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_912,plain,
! [X14,X15] : insert_pname(X14,collect_pname(X15)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_913,plain,
! [X14,X15] : insert_nat(X14,collect_nat(X15)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X14))),X15)),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_914,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X27),X29)),hAPP_nat_nat(minus_minus_nat(X27),X28))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_485])]) ).
fof(c_0_915,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X28),X27)),hAPP_nat_nat(minus_minus_nat(X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_486])]) ).
fof(c_0_916,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X14))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X12,X13)),X14)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X13),X14))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X12,X13)),X14)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X15),X17))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X16),X17))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X15,X16)),X17)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_487])])])])]) ).
fof(c_0_917,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X14))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X12,X13)),X14)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X13),X14))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X12,X13)),X14)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X15),X17))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X16),X17))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X15,X16)),X17)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_488])])])])]) ).
fof(c_0_918,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X12,X13)),X14)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X12,X13)),X14)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X15),X17))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X16),X17))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X15,X16)),X17)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_489])])])])]) ).
fof(c_0_919,plain,
! [X26,X27,X28,X29] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X26)),hAPP_nat_nat(suc,X27)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X27)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X28)),hAPP_nat_nat(suc,X29))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_490])])])]) ).
fof(c_0_920,plain,
! [X23,X24,X25] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X23)),X24)),hAPP_nat_nat(suc,X25)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X24)),X25),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_921,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X25))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X23))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X25),X24)),hAPP_nat_nat(minus_minus_nat(X23),X24)) = hAPP_nat_nat(minus_minus_nat(X25),X23) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_492])]) ).
fof(c_0_922,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X15)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X14)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_493])])]) ).
fof(c_0_923,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X15)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X14)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_494])])]) ).
fof(c_0_924,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X15)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X14)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_495])])]) ).
fof(c_0_925,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X15)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X14)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_496])])]) ).
fof(c_0_926,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X15)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X14)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_497])])]) ).
fof(c_0_927,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X15)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X15),X14)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X14)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X15),X14)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_498])])]) ).
fof(c_0_928,plain,
! [X26,X27,X28,X29] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X27))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)),X26)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X29)),X28))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X29)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_499])])])]) ).
fof(c_0_929,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X12))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X11)),hAPP_f22106695ol_nat(finite_card_nat,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_500])]) ).
fof(c_0_930,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X11)),hAPP_fun_a_bool_nat(finite_card_a,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_501])]) ).
fof(c_0_931,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X12))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X11)),hAPP_f921600141ol_nat(finite_card_pname,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_502])]) ).
fof(c_0_932,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X12))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X11)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_503])]) ).
fof(c_0_933,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X12))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X11)),hAPP_f55526627ol_nat(finite1340463720e_bool,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_504])]) ).
fof(c_0_934,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X12))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X11)),hAPP_f696928925ol_nat(finite346522414t_bool,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_505])]) ).
fof(c_0_935,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X13)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_506])]) ).
fof(c_0_936,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X13)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_507])]) ).
fof(c_0_937,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X13)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_508])]) ).
fof(c_0_938,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X13)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_509])]) ).
fof(c_0_939,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X13)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_510])]) ).
fof(c_0_940,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X13)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_511])]) ).
fof(c_0_941,plain,
! [X31,X32] :
( ( is_pname(esk12_2(X31,X32))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X32),X31)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X31,X32)),X32))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X32),X31)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X31,X32)),X31))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X32),X31)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_512])])])]) ).
fof(c_0_942,plain,
! [X31,X32] :
( ( is_a(esk11_2(X31,X32))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X32),X31)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X31,X32)),X32))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X32),X31)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X31,X32)),X31))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X32),X31)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_513])])])]) ).
fof(c_0_943,plain,
! [X31,X32] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X31,X32)),X32))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X32),X31)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X31,X32)),X31))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X32),X31)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_514])])])]) ).
fof(c_0_944,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X14),insert_a(X13,X12)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X14),X12))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X14)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X14),X12))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X14),insert_a(X13,X12)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_515])])]) ).
fof(c_0_945,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X14),insert_pname(X13,X12)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X14),X12))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X14),X12))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X14),insert_pname(X13,X12)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_516])])]) ).
fof(c_0_946,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),insert_nat(X13,X12)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),X12))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X14)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),X12))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),insert_nat(X13,X12)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_517])])]) ).
fof(c_0_947,plain,
! [X11,X12,X13] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X11,X12)),image_pname_a(X11,X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_518])]) ).
fof(c_0_948,plain,
! [X38,X39,X40] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X40))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X38,X39)),insert_a(X38,X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_519])]) ).
fof(c_0_949,plain,
! [X38,X39,X40] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X39),X40))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X38,X39)),insert_pname(X38,X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_520])]) ).
fof(c_0_950,plain,
! [X38,X39,X40] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X40))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X38,X39)),insert_nat(X38,X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_521])]) ).
fof(c_0_951,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X12,X13)),image_pname_a(X12,X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_522])]) ).
fof(c_0_952,plain,
! [X16,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X16)),X17))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_523])]) ).
fof(c_0_953,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X37))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X37),X35))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_524])]) ).
fof(c_0_954,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X37))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X37),X35))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_525])]) ).
fof(c_0_955,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X37))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X37),X35))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_526])]) ).
fof(c_0_956,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X13),X14))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_527])]) ).
fof(c_0_957,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X13),X14))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_528])]) ).
fof(c_0_958,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_529])]) ).
fof(c_0_959,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X14),X12))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_530])]) ).
fof(c_0_960,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X14))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X14),X12))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_531])]) ).
fof(c_0_961,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),X12))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_532])]) ).
fof(c_0_962,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X13),X14))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_533])]) ).
fof(c_0_963,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X13),X14))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_534])]) ).
fof(c_0_964,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_535])]) ).
fof(c_0_965,plain,
! [X33,X34,X35] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X34),X35))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),X34))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_536])]) ).
fof(c_0_966,plain,
! [X33,X34,X35] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X34),X35))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),X34))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_537])]) ).
fof(c_0_967,plain,
! [X33,X34,X35] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X34),X35))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),X34))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_538])]) ).
fof(c_0_968,plain,
! [X25,X26,X27] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X27))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X25))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_539])]) ).
fof(c_0_969,plain,
! [X44,X46,X47,X48] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X44))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X46),X44))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X46),esk16_1(X44))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk17_2(X47,X48)),X47))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X47)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk17_2(X47,X48)),X48))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X47)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_540])])])])])]) ).
fof(c_0_970,plain,
! [X26,X27,X28] :
( ( hAPP_nat_nat(minus_minus_nat(X28),X27) != hAPP_nat_nat(minus_minus_nat(X26),X27)
| X28 = X26
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X28)) )
& ( X28 != X26
| hAPP_nat_nat(minus_minus_nat(X28),X27) = hAPP_nat_nat(minus_minus_nat(X26),X27)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X28)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_541])])]) ).
fof(c_0_971,plain,
! [X42,X43] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X42)),X43))
| X43 = hAPP_nat_nat(suc,esk14_2(X42,X43)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_542])])]) ).
fof(c_0_972,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),insert_a(X33,X34)))
| X32 = X33
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X34))
| ~ is_a(X32)
| ~ is_a(X33) )
& ( X32 != X33
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),insert_a(X33,X35)))
| ~ is_a(X32)
| ~ is_a(X33) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X35))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),insert_a(X33,X35)))
| ~ is_a(X32)
| ~ is_a(X33) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_543])])])])]) ).
fof(c_0_973,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),insert_pname(X33,X34)))
| X32 = X33
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X34))
| ~ is_pname(X32)
| ~ is_pname(X33) )
& ( X32 != X33
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),insert_pname(X33,X35)))
| ~ is_pname(X32)
| ~ is_pname(X33) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X35))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),insert_pname(X33,X35)))
| ~ is_pname(X32)
| ~ is_pname(X33) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_544])])])])]) ).
fof(c_0_974,plain,
! [X32,X33,X34] :
( ~ is_a(X32)
| ~ is_a(X33)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),insert_a(X33,X34)))
| X32 = X33
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_545])])])]) ).
fof(c_0_975,plain,
! [X32,X33,X34] :
( ~ is_pname(X32)
| ~ is_pname(X33)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),insert_pname(X33,X34)))
| X32 = X33
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_546])])])]) ).
fof(c_0_976,plain,
! [X37,X38] : insert_fun_a_bool(X37,X38) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X37)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X38))),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_977,plain,
! [X37,X38] : insert1325755072e_bool(X37,X38) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X37)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X38))),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_978,plain,
! [X37,X38] : insert_fun_nat_bool(X37,X38) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X37)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X38))),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_979,plain,
! [X37,X38] : insert_a(X37,X38) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X37)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X38))),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_980,plain,
! [X37,X38] : insert_pname(X37,X38) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X37)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X38))),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_981,plain,
! [X37,X38] : insert_nat(X37,X38) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X37)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X38))),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_982,plain,
! [X11,X12] : insert_fun_a_bool(X11,X12) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X11)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X12))),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_983,plain,
! [X11,X12] : insert1325755072e_bool(X11,X12) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X11)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X12))),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_984,plain,
! [X11,X12] : insert_fun_nat_bool(X11,X12) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X11)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X12))),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_985,plain,
! [X11,X12] : insert_a(X11,X12) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X11)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X12))),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_986,plain,
! [X11,X12] : insert_pname(X11,X12) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X11)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X12))),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_987,plain,
! [X11,X12] : insert_nat(X11,X12) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X11)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X12))),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_988,plain,
! [X26,X27,X28,X29] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),hAPP_nat_nat(suc,X27)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X27))
| X26 = hAPP_nat_nat(suc,X27) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),hAPP_nat_nat(suc,X29))) )
& ( X28 != hAPP_nat_nat(suc,X29)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X28),hAPP_nat_nat(suc,X29))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_559])])])])]) ).
fof(c_0_989,plain,
! [X16,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(suc,X17)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
| X16 = hAPP_nat_nat(suc,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_560])]) ).
fof(c_0_990,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),insert_nat(X33,X34)))
| X32 = X33
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X34)) )
& ( X35 != X36
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X35),insert_nat(X36,X37))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X35),X37))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X35),insert_nat(X36,X37))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_561])])])])]) ).
fof(c_0_991,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),insert_nat(X33,X34)))
| X32 = X33
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X34)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_562])]) ).
fof(c_0_992,plain,
! [X32,X33,X34,X35] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X34),X35))
| X32 != hAPP_pname_a(X33,X34)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),image_pname_a(X33,X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_563])]) ).
fof(c_0_993,plain,
! [X32,X33,X34,X35] :
( X33 != hAPP_pname_a(X34,X35)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X35),X32))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),image_pname_a(X34,X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_564])]) ).
fof(c_0_994,plain,
! [X11,X12,X13] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X13))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),image_pname_a(X12,X13)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_565])]) ).
fof(c_0_995,plain,
! [X15] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X15)),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_996,plain,
! [X11,X12] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| X11 != X12
| ~ is_fun_a_bool(X11)
| ~ is_fun_a_bool(X12) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X11))
| X11 != X12
| ~ is_fun_a_bool(X11)
| ~ is_fun_a_bool(X12) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X11))
| X11 = X12
| ~ is_fun_a_bool(X11)
| ~ is_fun_a_bool(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_567])])]) ).
fof(c_0_997,plain,
! [X11,X12] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| X11 != X12
| ~ is_fun_pname_bool(X11)
| ~ is_fun_pname_bool(X12) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X11))
| X11 != X12
| ~ is_fun_pname_bool(X11)
| ~ is_fun_pname_bool(X12) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X11))
| X11 = X12
| ~ is_fun_pname_bool(X11)
| ~ is_fun_pname_bool(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_568])])]) ).
fof(c_0_998,plain,
! [X11,X12] :
( ~ is_fun_a_bool(X11)
| ~ is_fun_a_bool(X12)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X11))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_569])]) ).
fof(c_0_999,plain,
! [X11,X12] :
( ~ is_fun_pname_bool(X11)
| ~ is_fun_pname_bool(X12)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X11))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_570])]) ).
fof(c_0_1000,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X33),X34))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X33),insert_a(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_571])]) ).
fof(c_0_1001,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X33),X34))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X33),insert_pname(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_572])]) ).
fof(c_0_1002,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X33),X34))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X33),insert_nat(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_573])]) ).
fof(c_0_1003,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),X34))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),insert_a(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_574])]) ).
fof(c_0_1004,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),X34))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),insert_pname(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_575])]) ).
fof(c_0_1005,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),X34))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),insert_nat(X32,X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_576])]) ).
fof(c_0_1006,plain,
! [X32,X33,X34] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),X34))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),insert_a(X32,X34))) )
& ( X33 != X32
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X33),insert_a(X32,X34))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_577])])]) ).
fof(c_0_1007,plain,
! [X32,X33,X34] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),X34))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),insert_pname(X32,X34))) )
& ( X33 != X32
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X33),insert_pname(X32,X34))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_578])])]) ).
fof(c_0_1008,plain,
! [X32,X33,X34] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),X34))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),insert_nat(X32,X34))) )
& ( X33 != X32
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X33),insert_nat(X32,X34))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_579])])]) ).
fof(c_0_1009,plain,
! [X11,X12,X13,X14] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| X11 != X12 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X11))
| X11 != X12 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X13),X14))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X14),X13))
| X13 = X14 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_580])])])])]) ).
fof(c_0_1010,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X11))
| X11 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_581])]) ).
fof(c_0_1011,plain,
! [X16,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X16))
| X16 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_582])]) ).
fof(c_0_1012,plain,
! [X16,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(suc,X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_583])]) ).
fof(c_0_1013,plain,
! [X16,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X17)),X16) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_584])]) ).
fof(c_0_1014,plain,
! [X16,X17] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X16),X17)),X16)),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1015,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X12,X13)) = hAPP_fun_a_bool_nat(finite_card_a,X13)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X13)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X12,X13)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X13))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_586])])]) ).
fof(c_0_1016,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X12,X13)) = hAPP_f921600141ol_nat(finite_card_pname,X13)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X13)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X12,X13)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X13))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_587])])]) ).
fof(c_0_1017,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X12,X13)) = hAPP_f22106695ol_nat(finite_card_nat,X13)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X13)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X12,X13)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X13))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_588])])]) ).
fof(c_0_1018,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X12),X13))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X12,X13)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X13)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X13)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X12),X13))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X13))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_589])])]) ).
fof(c_0_1019,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X12),X13))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X12,X13)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X13)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X13)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X12),X13))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X13))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_590])])]) ).
fof(c_0_1020,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X12),X13))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X12,X13)) = hAPP_f696928925ol_nat(finite346522414t_bool,X13)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X13)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X12),X13))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X13))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_591])])]) ).
fof(c_0_1021,plain,
! [X12,X13,X14] :
( ( insert_a(X13,X14) != insert_a(X13,X12)
| X14 = X12
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X12))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X14))
| ~ is_fun_a_bool(X12)
| ~ is_fun_a_bool(X14) )
& ( X14 != X12
| insert_a(X13,X14) = insert_a(X13,X12)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X12))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X13),X14))
| ~ is_fun_a_bool(X12)
| ~ is_fun_a_bool(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_592])])]) ).
fof(c_0_1022,plain,
! [X12,X13,X14] :
( ( insert_pname(X13,X14) != insert_pname(X13,X12)
| X14 = X12
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X12))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14))
| ~ is_fun_pname_bool(X12)
| ~ is_fun_pname_bool(X14) )
& ( X14 != X12
| insert_pname(X13,X14) = insert_pname(X13,X12)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X12))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14))
| ~ is_fun_pname_bool(X12)
| ~ is_fun_pname_bool(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_593])])]) ).
fof(c_0_1023,plain,
! [X6] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X6))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_594])]) ).
fof(c_0_1024,plain,
! [X6] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X6))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_595])]) ).
fof(c_0_1025,plain,
! [X6] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X6))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_596])]) ).
fof(c_0_1026,plain,
! [X6] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X6))
| hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_597])]) ).
fof(c_0_1027,plain,
! [X6] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X6))
| hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_598])]) ).
fof(c_0_1028,plain,
! [X6] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X6))
| hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_599])]) ).
fof(c_0_1029,plain,
! [X6] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X6))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_600])]) ).
fof(c_0_1030,plain,
! [X6] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X6))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_601])]) ).
fof(c_0_1031,plain,
! [X6] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_602])]) ).
fof(c_0_1032,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X13),X14))
| insert_a(hAPP_pname_a(X12,X13),image_pname_a(X12,X14)) = image_pname_a(X12,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_603])]) ).
fof(c_0_1033,plain,
! [X12,X13,X14] :
( ( insert_nat(X13,X14) != insert_nat(X13,X12)
| X14 = X12
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X12))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X14)) )
& ( X14 != X12
| insert_nat(X13,X14) = insert_nat(X13,X12)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X12))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X13),X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_604])])]) ).
fof(c_0_1034,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X12,X13)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_605])]) ).
fof(c_0_1035,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X13))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X12,X13)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_606])]) ).
fof(c_0_1036,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X13))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X12,X13)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_607])]) ).
fof(c_0_1037,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X13))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X12),X13))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_608])]) ).
fof(c_0_1038,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X13))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X12),X13))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_609])]) ).
fof(c_0_1039,plain,
! [X12,X13] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X13))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X12),X13))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X12,X13)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_610])]) ).
fof(c_0_1040,plain,
! [X25,X26,X27] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X25),X26)),X27) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X25),X27)),X26),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1041,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X12))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_612])]) ).
fof(c_0_1042,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X12))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_613])]) ).
fof(c_0_1043,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X12))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X11),X12))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_614])]) ).
fof(c_0_1044,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_615])]) ).
fof(c_0_1045,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X12))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X11),X12))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_616])]) ).
fof(c_0_1046,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X12))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X11),X12))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_617])]) ).
fof(c_0_1047,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X12))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_618])]) ).
fof(c_0_1048,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X12))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_619])]) ).
fof(c_0_1049,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X11),X12))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X12))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_620])]) ).
fof(c_0_1050,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X12))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_621])]) ).
fof(c_0_1051,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X11),X12))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X12))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_622])]) ).
fof(c_0_1052,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X11),X12))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X12))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_623])]) ).
fof(c_0_1053,plain,
! [X24,X25] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X25))
| hAPP_nat_nat(minus_minus_nat(X25),hAPP_nat_nat(minus_minus_nat(X25),X24)) = X24 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_624])]) ).
fof(c_0_1054,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP_a_bool(insert_a(X34,X35),X36))
| X34 = X36
| hBOOL(hAPP_a_bool(X35,X36))
| ~ is_a(X34)
| ~ is_a(X36) )
& ( X34 != X36
| hBOOL(hAPP_a_bool(insert_a(X34,X35),X36))
| ~ is_a(X34)
| ~ is_a(X36) )
& ( ~ hBOOL(hAPP_a_bool(X35,X36))
| hBOOL(hAPP_a_bool(insert_a(X34,X35),X36))
| ~ is_a(X34)
| ~ is_a(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_625])])]) ).
fof(c_0_1055,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP_pname_bool(insert_pname(X34,X35),X36))
| X34 = X36
| hBOOL(hAPP_pname_bool(X35,X36))
| ~ is_pname(X34)
| ~ is_pname(X36) )
& ( X34 != X36
| hBOOL(hAPP_pname_bool(insert_pname(X34,X35),X36))
| ~ is_pname(X34)
| ~ is_pname(X36) )
& ( ~ hBOOL(hAPP_pname_bool(X35,X36))
| hBOOL(hAPP_pname_bool(insert_pname(X34,X35),X36))
| ~ is_pname(X34)
| ~ is_pname(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_626])])]) ).
fof(c_0_1056,plain,
! [X17] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X17)))),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1057,plain,
! [X5,X6] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X6))
| hBOOL(hAPP_fun_a_bool_bool(p(X6),X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_628])]) ).
fof(c_0_1058,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP_nat_bool(insert_nat(X34,X35),X36))
| X34 = X36
| hBOOL(hAPP_nat_bool(X35,X36)) )
& ( X37 != X39
| hBOOL(hAPP_nat_bool(insert_nat(X37,X38),X39)) )
& ( ~ hBOOL(hAPP_nat_bool(X38,X39))
| hBOOL(hAPP_nat_bool(insert_nat(X37,X38),X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_629])])])])]) ).
fof(c_0_1059,plain,
! [X16,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1060,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X9,X10)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X12))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_631])])])]) ).
fof(c_0_1061,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X9,X10)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X12))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_632])])])]) ).
fof(c_0_1062,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X9,X10)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X12))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_633])])])]) ).
fof(c_0_1063,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X9,X10)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X12))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_634])])])]) ).
fof(c_0_1064,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X9,X10)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X12))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_635])])])]) ).
fof(c_0_1065,plain,
! [X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X9,X10)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X12))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X11,X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_636])])])]) ).
fof(c_0_1066,plain,
! [X12,X13,X14,X15] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X12),X13))
| hBOOL(hAPP_pname_bool(X13,X12)) )
& ( ~ hBOOL(hAPP_pname_bool(X15,X14))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X14),X15)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_637])])])]) ).
fof(c_0_1067,plain,
! [X12,X13,X14,X15] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X12),X13))
| hBOOL(hAPP_a_bool(X13,X12)) )
& ( ~ hBOOL(hAPP_a_bool(X15,X14))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X14),X15)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_638])])])]) ).
fof(c_0_1068,plain,
! [X12,X13,X14,X15] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X12),X13))
| hBOOL(hAPP_nat_bool(X13,X12)) )
& ( ~ hBOOL(hAPP_nat_bool(X15,X14))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X14),X15)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_639])])])]) ).
fof(c_0_1069,plain,
! [X9,X10] :
( ~ is_fun_a_bool(X10)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X9),X10))
| insert_a(X9,X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_640])]) ).
fof(c_0_1070,plain,
! [X9,X10] :
( ~ is_fun_pname_bool(X10)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X9),X10))
| insert_pname(X9,X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_641])]) ).
fof(c_0_1071,plain,
! [X20,X21] :
( ~ is_fun_pname_bool(X20)
| ~ is_fun_pname_bool(X21)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_642])]) ).
fof(c_0_1072,plain,
! [X20,X21] :
( ~ is_fun_a_bool(X20)
| ~ is_fun_a_bool(X21)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_643])]) ).
fof(c_0_1073,plain,
! [X20,X21] :
( ~ is_pname(X20)
| ~ is_pname(X21)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_644])]) ).
fof(c_0_1074,plain,
! [X20,X21] :
( ~ is_a(X20)
| ~ is_a(X21)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_645])]) ).
fof(c_0_1075,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
c_0_646 ).
fof(c_0_1076,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
c_0_647 ).
fof(c_0_1077,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X9),X10))
| insert_nat(X9,X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_648])]) ).
fof(c_0_1078,plain,
! [X46,X47] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X46),X47))
| ~ hBOOL(X46)
| hBOOL(X47) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1079,plain,
! [X46,X47] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X46),X47))
| hBOOL(X46)
| hBOOL(X47) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1080,plain,
! [X11,X12] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),insert_a(X12,X11))),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1081,plain,
! [X11,X12] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),insert_pname(X12,X11))),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1082,plain,
! [X11,X12] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),insert_nat(X12,X11))),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1083,plain,
! [X11,X12] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),insert_a(X11,X12))),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1084,plain,
! [X11,X12] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),insert_pname(X11,X12))),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1085,plain,
! [X11,X12] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),insert_nat(X11,X12))),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1086,plain,
! [X46,X47] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X46),X47))
| hBOOL(X47) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1087,plain,
! [X46,X47] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X46),X47))
| hBOOL(X46) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_658])])]) ).
fof(c_0_1088,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_659])]) ).
fof(c_0_1089,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_660])]) ).
fof(c_0_1090,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_661])]) ).
fof(c_0_1091,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X10))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_662])]) ).
fof(c_0_1092,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X10))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_663])]) ).
fof(c_0_1093,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X10))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_664])]) ).
fof(c_0_1094,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_665])]) ).
fof(c_0_1095,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_666])]) ).
fof(c_0_1096,plain,
! [X9,X10] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X9,X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_667])]) ).
fof(c_0_1097,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_668])]) ).
fof(c_0_1098,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_669])]) ).
fof(c_0_1099,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_670])]) ).
fof(c_0_1100,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_671])]) ).
fof(c_0_1101,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_672])]) ).
fof(c_0_1102,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_673])]) ).
fof(c_0_1103,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_674])]) ).
fof(c_0_1104,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_675])]) ).
fof(c_0_1105,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_676])]) ).
fof(c_0_1106,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_677])]) ).
fof(c_0_1107,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_678])]) ).
fof(c_0_1108,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_679])]) ).
fof(c_0_1109,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_680])]) ).
fof(c_0_1110,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_681])]) ).
fof(c_0_1111,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_682])]) ).
fof(c_0_1112,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_683])]) ).
fof(c_0_1113,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_684])]) ).
fof(c_0_1114,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_685])]) ).
fof(c_0_1115,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_686])]) ).
fof(c_0_1116,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X9))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_687])]) ).
fof(c_0_1117,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_688])]) ).
fof(c_0_1118,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_689])]) ).
fof(c_0_1119,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_690])]) ).
fof(c_0_1120,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_691])]) ).
fof(c_0_1121,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_692])]) ).
fof(c_0_1122,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_693])]) ).
fof(c_0_1123,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X9))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_694])]) ).
fof(c_0_1124,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_695])]) ).
fof(c_0_1125,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_696])]) ).
fof(c_0_1126,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_697])]) ).
fof(c_0_1127,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_698])]) ).
fof(c_0_1128,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_699])]) ).
fof(c_0_1129,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_700])]) ).
fof(c_0_1130,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X9))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_701])]) ).
fof(c_0_1131,plain,
! [X8,X9] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X9))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X8,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_702])]) ).
fof(c_0_1132,plain,
! [X20,X21] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1133,plain,
! [X20,X21] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X20),X21))
| X20 = X21 ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1134,plain,
! [X16,X17] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X16)),hAPP_nat_nat(suc,X17)) = hAPP_nat_nat(minus_minus_nat(X16),X17),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1135,plain,
! [X47,X48,X49] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_f1476298914l_bool(X47,X49),hAPP_f1664156314l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1136,plain,
! [X47,X48,X49] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_f1748468828l_bool(X47,X49),hAPP_f54304608l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1137,plain,
! [X47,X48,X49] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_f198738859l_bool(X47,X49),hAPP_fun_a_bool_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1138,plain,
! [X47,X48,X49] : hAPP_pname_bool(cOMBS_568398431l_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_p393069232l_bool(X47,X49),hAPP_pname_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1139,plain,
! [X47,X48,X49] : hAPP_nat_bool(cOMBS_nat_bool_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_n1006566506l_bool(X47,X49),hAPP_nat_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1140,plain,
! [X47,X48,X49] : hAPP_a_bool(cOMBS_a_bool_bool(X47,X48),X49) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X47,X49),hAPP_a_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1141,plain,
! [X11,X12,X13] : image_pname_a(X11,insert_pname(X12,X13)) = insert_a(hAPP_pname_a(X11,X12),image_pname_a(X11,X13)),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1142,plain,
! [X18] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X18))) = hAPP_nat_nat(suc,X18),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1143,plain,
! [X47,X48,X49] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X47),X48),X49) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1144,plain,
! [X47,X48,X49] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X47),X48),X49) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1145,plain,
! [X47,X48,X49] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X47),X48),X49) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1146,plain,
! [X47,X48,X49] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X47),X48),X49) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1147,plain,
! [X47,X48,X49] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X47),X48),X49) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1148,plain,
! [X47,X48,X49] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X47),X48),X49) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1149,plain,
! [X47,X48,X49] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X47),X48),X49) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1150,plain,
! [X47,X48,X49] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X47),X48),X49) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1151,plain,
! [X47,X48,X49] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X47),X48),X49) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1152,plain,
! [X47,X48,X49] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X47),X48),X49) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1153,plain,
! [X47,X48,X49] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X47),X48),X49) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1154,plain,
! [X47,X48,X49] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X47),X48),X49) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1155,plain,
! [X47,X48,X49] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X47),X48),X49) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1156,plain,
! [X47,X48,X49] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X47),X48),X49) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1157,plain,
! [X47,X48,X49] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X47),X48),X49) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1158,plain,
! [X47,X48,X49] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X47),X48),X49) = hAPP_pname_bool(hAPP_p61793385e_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1159,plain,
! [X47,X48,X49] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X47),X48),X49) = hAPP_nat_bool(hAPP_n1699378549t_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1160,plain,
! [X47,X48,X49] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X47),X48),X49) = hAPP_a_bool(hAPP_p1534023578a_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1161,plain,
! [X47,X48,X49] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X47),X48),X49) = hAPP_a_bool(hAPP_a_fun_a_bool(X47,X49),X48),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1162,plain,
! [X46,X47] :
( ~ hBOOL(X47)
| ~ hBOOL(X46)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1163,plain,
! [X46,X47] :
( ~ hBOOL(X47)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X46),X47)) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1164,plain,
! [X46,X47] :
( ~ hBOOL(X47)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X46),X47)) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1165,plain,
! [X46,X47] :
( ~ hBOOL(X47)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1166,plain,
! [X46,X47] :
( hBOOL(X47)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1167,plain,
! [X47,X48,X49] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_f1664156314l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1168,plain,
! [X47,X48,X49] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_f54304608l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1169,plain,
! [X47,X48,X49] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_fun_a_bool_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1170,plain,
! [X47,X48,X49] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_pname_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1171,plain,
! [X47,X48,X49] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_f1664156314l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1172,plain,
! [X47,X48,X49] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_nat_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1173,plain,
! [X47,X48,X49] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_f54304608l_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1174,plain,
! [X47,X48,X49] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X47,X48),X49) = hAPP_b589554111l_bool(X47,hAPP_a_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1175,plain,
! [X47,X48,X49] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_fun_a_bool_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1176,plain,
! [X47,X48,X49] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X47,X48),X49) = hAPP_a_fun_a_bool(X47,hAPP_pname_a(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1177,plain,
! [X47,X48,X49] : hAPP_pname_bool(cOMBB_647938656_pname(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_pname_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1178,plain,
! [X47,X48,X49] : hAPP_nat_bool(cOMBB_bool_bool_nat(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_nat_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1179,plain,
! [X47,X48,X49] : hAPP_a_bool(cOMBB_bool_bool_a(X47,X48),X49) = hAPP_bool_bool(X47,hAPP_a_bool(X48,X49)),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1180,plain,
! [X34,X35,X36] : insert_a(X34,insert_a(X35,X36)) = insert_a(X35,insert_a(X34,X36)),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1181,plain,
! [X34,X35,X36] : insert_pname(X34,insert_pname(X35,X36)) = insert_pname(X35,insert_pname(X34,X36)),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1182,plain,
! [X34,X35,X36] : insert_nat(X34,insert_nat(X35,X36)) = insert_nat(X35,insert_nat(X34,X36)),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1183,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1184,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1185,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1186,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1187,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1188,plain,
! [X20,X21] :
( X20 != X21
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1189,plain,
! [X11,X12] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12))
| X11 != X12 )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X11))
| X11 != X12 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_760])])]) ).
fof(c_0_1190,plain,
! [X11,X12] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12))
| X11 != X12 )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X11))
| X11 != X12 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_761])])]) ).
fof(c_0_1191,plain,
! [X11,X12] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12))
| X11 != X12 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X11))
| X11 != X12 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_762])])]) ).
fof(c_0_1192,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_763])]) ).
fof(c_0_1193,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_764])]) ).
fof(c_0_1194,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_765])]) ).
fof(c_0_1195,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_766])]) ).
fof(c_0_1196,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_767])]) ).
fof(c_0_1197,plain,
! [X11,X12] :
( X11 != X12
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_768])]) ).
fof(c_0_1198,plain,
! [X16,X17] :
( X16 != X17
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_769])]) ).
fof(c_0_1199,plain,
! [X12] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X12),X12)),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1200,plain,
! [X43] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X43),X43)),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1201,plain,
! [X12] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X12),X12)),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1202,plain,
! [X12] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X12),X12)),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1203,plain,
! [X6] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X6),X6)),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1204,plain,
! [X6] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X6),X6)),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1205,plain,
! [X6] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6),X6)),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1206,plain,
! [X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X15)),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1207,plain,
! [X12,X13] : insert_a(X12,insert_a(X12,X13)) = insert_a(X12,X13),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1208,plain,
! [X12,X13] : insert_pname(X12,insert_pname(X12,X13)) = insert_pname(X12,X13),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1209,plain,
! [X12,X13] : insert_nat(X12,insert_nat(X12,X13)) = insert_nat(X12,X13),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1210,plain,
! [X45] :
( ~ hBOOL(hAPP_bool_bool(fNot,X45))
| ~ hBOOL(X45) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1211,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
c_0_782 ).
fof(c_0_1212,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
c_0_783 ).
fof(c_0_1213,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X3)
| ~ is_pname(X4)
| is_bool(hAPP_pname_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_784])]) ).
fof(c_0_1214,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X3)
| ~ is_a(X4)
| is_bool(hAPP_a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_785])]) ).
fof(c_0_1215,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X3)
| ~ is_fun1661590463l_bool(X4)
| is_fun1661590463l_bool(insert1325755072e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_786])]) ).
fof(c_0_1216,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X3)
| ~ is_fun949378684l_bool(X4)
| is_fun949378684l_bool(insert_fun_a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_787])]) ).
fof(c_0_1217,plain,
! [X3,X4] :
( ~ is_pname(X3)
| ~ is_fun_pname_bool(X4)
| is_fun_pname_bool(insert_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_788])]) ).
fof(c_0_1218,plain,
! [X22,X23,X24,X25] :
( ( hAPP_nat_nat(suc,X22) != hAPP_nat_nat(suc,X23)
| X22 = X23 )
& ( X24 != X25
| hAPP_nat_nat(suc,X24) = hAPP_nat_nat(suc,X25) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_789])])])]) ).
fof(c_0_1219,plain,
! [X20,X21] :
( hAPP_nat_nat(suc,X20) != hAPP_nat_nat(suc,X21)
| X20 = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_790])]) ).
fof(c_0_1220,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_fun1661590463l_bool(hAPP_f559147733l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_791])]) ).
fof(c_0_1221,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_bool(hAPP_f1935102916l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_792])]) ).
fof(c_0_1222,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_fun949378684l_bool(hAPP_f2117159681l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_793])]) ).
fof(c_0_1223,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_bool(hAPP_f621171935l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_794])]) ).
fof(c_0_1224,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun1661590463l_bool(hAPP_f434788991l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_795])]) ).
fof(c_0_1225,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun_pname_bool(hAPP_f759274231e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_796])]) ).
fof(c_0_1226,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun_a_bool(hAPP_f2050579477a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_797])]) ).
fof(c_0_1227,plain,
! [X3,X4] :
( ~ is_bool(X4)
| is_bool(hAPP_bool_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_798])]) ).
fof(c_0_1228,plain,
! [X3,X4] :
( ~ is_pname(X4)
| is_fun_pname_bool(hAPP_p61793385e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_799])]) ).
fof(c_0_1229,plain,
! [X3,X4] :
( ~ is_pname(X4)
| is_fun_a_bool(hAPP_p1534023578a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_800])]) ).
fof(c_0_1230,plain,
! [X3,X4] :
( ~ is_a(X4)
| is_fun_pname_bool(hAPP_a93125764e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_801])]) ).
fof(c_0_1231,plain,
! [X3,X4] :
( ~ is_a(X4)
| is_fun_a_bool(hAPP_a_fun_a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_802])]) ).
fof(c_0_1232,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_fun_pname_bool(image_1283814551_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_803])]) ).
fof(c_0_1233,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_fun_a_bool(image_876012084bool_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_804])]) ).
fof(c_0_1234,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_fun_pname_bool(image_1854862208_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_805])]) ).
fof(c_0_1235,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_fun_a_bool(image_fun_a_bool_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_806])]) ).
fof(c_0_1236,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun1661590463l_bool(image_47868345e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_807])]) ).
fof(c_0_1237,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun949378684l_bool(image_112932426a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_808])]) ).
fof(c_0_1238,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun_pname_bool(image_pname_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_809])]) ).
fof(c_0_1239,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun_pname_bool(image_a_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_810])]) ).
fof(c_0_1240,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun_a_bool(image_a_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_811])]) ).
fof(c_0_1241,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_fun1661590463l_bool(cOMBS_350070575l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_812])]) ).
fof(c_0_1242,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_fun949378684l_bool(cOMBS_1035972772l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_813])]) ).
fof(c_0_1243,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun_pname_bool(cOMBS_568398431l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_814])]) ).
fof(c_0_1244,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun_a_bool(cOMBS_a_bool_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_815])]) ).
fof(c_0_1245,plain,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X4)
| is_fun1661590463l_bool(cOMBB_307249310e_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_816])]) ).
fof(c_0_1246,plain,
! [X3,X4] :
( ~ is_fun949378684l_bool(X4)
| is_fun949378684l_bool(cOMBB_2140588453a_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_817])]) ).
fof(c_0_1247,plain,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun_pname_bool(cOMBB_647938656_pname(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_818])]) ).
fof(c_0_1248,plain,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun_a_bool(cOMBB_bool_bool_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_819])]) ).
fof(c_0_1249,plain,
! [X45] :
( hBOOL(X45)
| hBOOL(hAPP_bool_bool(fNot,X45)) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1250,plain,
! [X3,X4] : is_bool(hAPP_f1295398978l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1251,plain,
! [X3,X4] : is_bool(hAPP_f595608956l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1252,plain,
! [X3,X4] : is_bool(hAPP_f1363661463l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1253,plain,
! [X3,X4] : is_bool(hAPP_f937997336l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1254,plain,
! [X3,X4] : is_bool(hAPP_f389811538l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1255,plain,
! [X3,X4] : is_bool(hAPP_f292226953l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1256,plain,
! [X3,X4] : is_bool(hAPP_f1637334154l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1257,plain,
! [X3,X4] : is_bool(hAPP_f54304608l_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1258,plain,
! [X3,X4] : is_fun_pname_bool(hAPP_n1025906991e_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1259,plain,
! [X3,X4] : is_fun_a_bool(hAPP_nat_fun_a_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1260,plain,
! [X3,X4] : is_fun_pname_bool(image_1604018183_pname(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1261,plain,
! [X3,X4] : is_fun_a_bool(image_526090948bool_a(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1262,plain,
! [X3,X4] : is_fun_pname_bool(image_1705983821_pname(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1263,plain,
! [X3,X4] : is_fun_a_bool(image_349102846bool_a(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1264,plain,
! [X3,X4] : is_fun_pname_bool(image_990671762_pname(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1265,plain,
! [X3,X4] : is_fun_a_bool(image_573985017bool_a(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1266,plain,
! [X3,X4] : is_fun_pname_bool(image_1921560913_pname(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1267,plain,
! [X3,X4] : is_fun_a_bool(image_fun_nat_bool_a(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1268,plain,
! [X3,X4] : is_fun1661590463l_bool(image_1655916159e_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1269,plain,
! [X3,X4] : is_fun949378684l_bool(image_nat_fun_a_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1270,plain,
! [X3,X4] : is_fun_pname_bool(image_nat_pname(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1271,plain,
! [X3,X4] : is_fun_a_bool(image_nat_a(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1272,plain,
! [X15] : X15 != hAPP_nat_nat(suc,X15),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1273,plain,
! [X15] : hAPP_nat_nat(suc,X15) != X15,
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1274,plain,
! [X2] :
( ~ is_fun_a_bool(X2)
| is_fun949378684l_bool(p(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_845])]) ).
fof(c_0_1275,plain,
! [X2] :
( ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(collec1974731493e_bool(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_846])]) ).
fof(c_0_1276,plain,
! [X2] :
( ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(collect_fun_a_bool(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_847])]) ).
fof(c_0_1277,plain,
! [X2] :
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(collect_pname(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_848])]) ).
fof(c_0_1278,plain,
! [X2] :
( ~ is_fun_a_bool(X2)
| is_fun_a_bool(collect_a(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_849])]) ).
fof(c_0_1279,plain,
! [X14] :
( ~ is_fun949378684l_bool(X14)
| collect_fun_a_bool(X14) = X14 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_850])]) ).
fof(c_0_1280,plain,
! [X14] :
( ~ is_fun1661590463l_bool(X14)
| collec1974731493e_bool(X14) = X14 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_851])]) ).
fof(c_0_1281,plain,
! [X14] :
( ~ is_fun_pname_bool(X14)
| collect_pname(X14) = X14 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_852])]) ).
fof(c_0_1282,axiom,
is_pname(undefined_pname(pname)),
c_0_853 ).
fof(c_0_1283,axiom,
is_a(undefined_a(x_a)),
c_0_854 ).
fof(c_0_1284,plain,
! [X14] : collect_nat(X14) = X14,
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1285,plain,
! [X14] : collect_fun_nat_bool(X14) = X14,
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1286,axiom,
is_fun949378684l_bool(finite_finite_a),
c_0_857 ).
cnf(c_0_1287,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,esk6_2(X2,X1))))))) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1288,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,esk5_3(X2,X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1289,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk4_3(X2,X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1290,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,esk3_3(X2,X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1291,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,esk2_3(X2,X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1292,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,esk15_3(X1,X3,X2))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1293,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1294,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk1_3(X2,X3,X1)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1295,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk9_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1296,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk8_3(X1,X2,X3)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1297,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk7_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1298,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk15_3(X1,X3,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1299,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1300,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk13_3(X3,X1,X2))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1301,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1302,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1303,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1304,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1305,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1306,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1307,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1308,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1309,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1310,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1311,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1312,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1313,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,esk13_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1314,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1315,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1316,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1317,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1318,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1319,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1320,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk1_3(X2,X3,X1)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1321,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1322,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1323,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1324,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1325,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1326,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1327,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1328,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1329,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1330,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1331,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1332,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1333,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1334,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1335,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1336,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X2))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1337,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X2))),hAPP_f98387925ol_nat(finite269641166l_bool,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1338,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X2))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1339,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1340,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1341,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1342,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1343,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1344,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1345,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1346,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1347,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1348,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1349,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1350,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1351,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1352,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1353,plain,
insert_fun_a_bool(X1,collect_fun_a_bool(X2)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1354,plain,
insert1325755072e_bool(X1,collec1974731493e_bool(X2)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1355,plain,
insert_fun_nat_bool(X1,collect_fun_nat_bool(X2)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1356,plain,
insert_a(X1,collect_a(X2)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1357,plain,
insert_pname(X1,collect_pname(X2)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1358,plain,
insert_nat(X1,collect_nat(X2)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1359,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1360,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1361,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1362,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1363,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1364,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1365,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1366,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1367,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1368,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1369,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1370,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1371,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1372,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1373,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1374,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1375,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1376,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1377,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1378,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1379,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1380,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1381,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1382,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1383,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1384,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1385,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1386,plain,
( X1 = image_pname_a(X2,esk1_3(X2,X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1387,plain,
( is_fun_pname_bool(esk1_3(X2,X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1388,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1389,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1390,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1391,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1392,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1393,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1394,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1395,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1396,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1397,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1398,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1399,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1400,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1401,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1402,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1403,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1404,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1405,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1406,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1407,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1408,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1409,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1410,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1411,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1412,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1413,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk6_2(X2,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1414,plain,
( X1 = hAPP_pname_a(X2,esk9_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1415,plain,
( X1 = image_pname_a(X2,esk8_3(X1,X2,X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1416,plain,
( X1 = hAPP_pname_a(X2,esk7_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1417,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1418,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1419,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1420,plain,
( is_pname(esk9_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1421,plain,
( is_fun_pname_bool(esk8_3(X1,X2,X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1422,plain,
( is_pname(esk7_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1423,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1424,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1425,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1426,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1427,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1428,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1429,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1430,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1431,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1432,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1433,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1434,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1435,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1436,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1437,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1438,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1439,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk17_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1440,plain,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1441,plain,
( X1 = hAPP_nat_nat(suc,esk14_2(X2,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1442,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1443,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1444,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ is_a(X3)
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1445,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ is_pname(X3)
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1446,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| is_pname(esk15_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1447,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| X1 != image_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| ~ is_fun_pname_bool(X4) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1448,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| ~ is_pname(X4) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1449,plain,
( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1450,plain,
insert_fun_a_bool(X1,X2) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1451,plain,
insert1325755072e_bool(X1,X2) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1452,plain,
insert_fun_nat_bool(X1,X2) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1453,plain,
insert_a(X1,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1454,plain,
insert_pname(X1,X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1455,plain,
insert_nat(X1,X2) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1456,plain,
insert_fun_a_bool(X1,X2) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1457,plain,
insert1325755072e_bool(X1,X2) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1458,plain,
insert_fun_nat_bool(X1,X2) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1459,plain,
insert_a(X1,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1460,plain,
insert_pname(X1,X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1461,plain,
insert_nat(X1,X2) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1462,plain,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1463,plain,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1464,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1465,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1466,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1467,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1468,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1469,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1470,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1471,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1472,plain,
( X2 = X1
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1473,plain,
( X2 = X1
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1474,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1475,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1476,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X2,X1)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1477,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X2,X1)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1478,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X2,X1)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1479,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk16_1(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1480,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1481,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1482,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1483,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1484,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1485,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1486,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1487,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1488,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1489,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1490,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1491,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1492,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1493,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1494,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1495,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1496,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1497,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1498,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_fun_a_bool_nat(finite_card_a,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1499,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_f921600141ol_nat(finite_card_pname,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1500,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_f22106695ol_nat(finite_card_nat,X1)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1501,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1502,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1503,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1504,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1505,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1506,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1507,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1508,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1509,plain,
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1510,plain,
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1511,plain,
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1512,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1513,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1514,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1515,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk17_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1516,plain,
( insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1517,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| X2 = X3
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1518,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| insert_a(X3,X1) = insert_a(X3,X2)
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1519,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| insert_pname(X3,X1) = insert_pname(X3,X2)
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1520,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1521,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1522,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1523,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1524,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1525,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1526,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1527,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1528,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1529,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1530,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1531,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1532,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X3)),X2),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1533,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1534,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1535,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1536,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1537,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1538,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1539,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1540,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1541,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1542,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1543,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1544,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1545,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| insert_nat(X1,X2) = insert_nat(X1,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1546,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_pname(esk6_2(X2,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1547,plain,
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1548,plain,
( hBOOL(hAPP_a_bool(X3,X1))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1549,plain,
( hBOOL(hAPP_pname_bool(X3,X1))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1550,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1)))),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1551,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1552,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1553,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1554,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1555,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1556,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1557,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1558,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1559,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1560,plain,
( hBOOL(hAPP_pname_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1561,plain,
( hBOOL(hAPP_a_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1562,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1563,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1564,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1565,plain,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1566,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1567,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1568,plain,
( insert_a(X1,X2) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1569,plain,
( insert_pname(X1,X2) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1570,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1571,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1572,plain,
( X1 = X2
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1573,plain,
( X1 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1574,plain,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1575,plain,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1576,plain,
( insert_nat(X1,X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1577,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1578,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1579,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1580,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1581,plain,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1582,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1583,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1584,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1585,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1586,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1587,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1588,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1589,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1590,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1591,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1592,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1593,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_a_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1594,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1595,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1596,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1597,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1598,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1599,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1600,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1601,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1602,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1603,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1604,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1605,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1606,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1607,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1608,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1609,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1610,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1611,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1612,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1613,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1614,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1615,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1616,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1617,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1618,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1619,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1620,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1621,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1622,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1623,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1624,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1625,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1626,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1627,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1628,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1629,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1630,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1631,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1632,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1633,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1634,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1635,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1636,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1637,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1638,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1639,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1640,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1641,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1642,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1643,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1644,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1645,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1646,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1647,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1648,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| is_pname(esk12_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1649,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk11_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1650,plain,
hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f1476298914l_bool(X1,X3),hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1651,plain,
hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f1748468828l_bool(X1,X3),hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1652,plain,
hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f198738859l_bool(X1,X3),hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1653,plain,
hAPP_pname_bool(cOMBS_568398431l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_p393069232l_bool(X1,X3),hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1654,plain,
hAPP_nat_bool(cOMBS_nat_bool_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_n1006566506l_bool(X1,X3),hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1655,plain,
hAPP_a_bool(cOMBS_a_bool_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X1,X3),hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1656,plain,
image_pname_a(X1,insert_pname(X2,X3)) = insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1657,plain,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1658,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1659,plain,
hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1))) = hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1660,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1661,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1662,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1663,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1664,plain,
hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X1),X2),X3) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1665,plain,
hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X1),X2),X3) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1666,plain,
hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X1),X2),X3) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1667,plain,
hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1668,plain,
hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1669,plain,
hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1670,plain,
hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1671,plain,
hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1672,plain,
hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1673,plain,
hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1674,plain,
hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1675,plain,
hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1676,plain,
hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1677,plain,
hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1678,plain,
hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1679,plain,
hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_p61793385e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1680,plain,
hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1681,plain,
hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_p1534023578a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1682,plain,
hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_a_fun_a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1683,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1684,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1685,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1686,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1687,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1688,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1689,plain,
hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1690,plain,
hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1691,plain,
hAPP_f198738859l_bool(cOMBB_338059395a_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1692,plain,
hAPP_p393069232l_bool(cOMBB_675860798_pname(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1693,plain,
hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1694,plain,
hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1695,plain,
hAPP_f54304608l_bool(cOMBB_238756964t_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1696,plain,
hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1697,plain,
hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1698,plain,
hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1699,plain,
hAPP_pname_bool(cOMBB_647938656_pname(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1700,plain,
hAPP_nat_bool(cOMBB_bool_bool_nat(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1701,plain,
hAPP_a_bool(cOMBB_bool_bool_a(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1702,plain,
insert_a(X1,insert_a(X2,X3)) = insert_a(X2,insert_a(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1703,plain,
insert_pname(X1,insert_pname(X2,X3)) = insert_pname(X2,insert_pname(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1704,plain,
insert_nat(X1,insert_nat(X2,X3)) = insert_nat(X2,insert_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1705,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1706,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1707,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1708,plain,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1709,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1710,plain,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1711,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1712,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1713,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1714,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1715,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1716,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1717,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1718,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1719,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1720,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1721,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1722,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1723,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1724,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1725,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1726,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1727,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1728,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1729,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1730,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1731,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1732,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1733,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1734,plain,
insert_a(X1,insert_a(X1,X2)) = insert_a(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1735,plain,
insert_pname(X1,insert_pname(X1,X2)) = insert_pname(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1736,plain,
insert_nat(X1,insert_nat(X1,X2)) = insert_nat(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1737,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1738,plain,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1739,plain,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1740,plain,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1741,plain,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1742,plain,
( is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1743,plain,
( is_fun949378684l_bool(insert_fun_a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1744,plain,
( is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1745,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1746,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1747,plain,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1748,plain,
( is_bool(hAPP_f1935102916l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1749,plain,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1750,plain,
( is_bool(hAPP_f621171935l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1751,plain,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1752,plain,
( is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1753,plain,
( is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1754,plain,
( is_bool(hAPP_bool_bool(X1,X2))
| ~ is_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1755,plain,
( is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1756,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1757,plain,
( is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1758,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1759,plain,
( is_fun_pname_bool(image_1283814551_pname(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1760,plain,
( is_fun_a_bool(image_876012084bool_a(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1761,plain,
( is_fun_pname_bool(image_1854862208_pname(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1762,plain,
( is_fun_a_bool(image_fun_a_bool_a(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1763,plain,
( is_fun1661590463l_bool(image_47868345e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1764,plain,
( is_fun949378684l_bool(image_112932426a_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1765,plain,
( is_fun_pname_bool(image_pname_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1766,plain,
( is_fun_pname_bool(image_a_pname(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1767,plain,
( is_fun_a_bool(image_a_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1768,plain,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1769,plain,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1770,plain,
( is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1771,plain,
( is_fun_a_bool(cOMBS_a_bool_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1772,plain,
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1773,plain,
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1774,plain,
( is_fun_pname_bool(cOMBB_647938656_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1775,plain,
( is_fun_a_bool(cOMBB_bool_bool_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1776,plain,
( hBOOL(hAPP_bool_bool(fNot,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1777,plain,
is_bool(hAPP_f1295398978l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1778,plain,
is_bool(hAPP_f595608956l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1251]) ).
cnf(c_0_1779,plain,
is_bool(hAPP_f1363661463l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1780,plain,
is_bool(hAPP_f937997336l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1781,plain,
is_bool(hAPP_f389811538l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1782,plain,
is_bool(hAPP_f292226953l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1783,plain,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1784,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1785,plain,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1786,plain,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1787,plain,
is_fun_pname_bool(image_1604018183_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1788,plain,
is_fun_a_bool(image_526090948bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1261]) ).
cnf(c_0_1789,plain,
is_fun_pname_bool(image_1705983821_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1790,plain,
is_fun_a_bool(image_349102846bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1791,plain,
is_fun_pname_bool(image_990671762_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1792,plain,
is_fun_a_bool(image_573985017bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1793,plain,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1794,plain,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1795,plain,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1796,plain,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1797,plain,
is_fun_pname_bool(image_nat_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1798,plain,
is_fun_a_bool(image_nat_a(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1799,plain,
( hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1800,plain,
X1 != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1801,plain,
hAPP_nat_nat(suc,X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1802,plain,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1803,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1804,plain,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1805,plain,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1806,plain,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1807,plain,
( collect_fun_a_bool(X1) = X1
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1808,plain,
( collec1974731493e_bool(X1) = X1
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1809,plain,
( collect_pname(X1) = X1
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1810,plain,
is_pname(undefined_pname(pname)),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1811,plain,
is_a(undefined_a(x_a)),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1812,plain,
collect_nat(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1813,plain,
collect_fun_nat_bool(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1814,plain,
is_fun949378684l_bool(finite_finite_a),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1815,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,esk6_2(X2,X1))))))) ),
c_0_1287,
[final] ).
cnf(c_0_1816,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,esk5_3(X2,X3,X1))))) ),
c_0_1288,
[final] ).
cnf(c_0_1817,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk4_3(X2,X3,X1))))) ),
c_0_1289,
[final] ).
cnf(c_0_1818,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,esk3_3(X2,X3,X1))))) ),
c_0_1290,
[final] ).
cnf(c_0_1819,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,esk2_3(X2,X3,X1))))) ),
c_0_1291,
[final] ).
cnf(c_0_1820,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,esk15_3(X1,X3,X2))),X3)) ),
c_0_1292,
[final] ).
cnf(c_0_1821,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
c_0_1293,
[final] ).
cnf(c_0_1822,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk1_3(X2,X3,X1)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1294,
[final] ).
cnf(c_0_1823,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk9_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1295,
[final] ).
cnf(c_0_1824,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk8_3(X1,X2,X3)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1296,
[final] ).
cnf(c_0_1825,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk7_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1297,
[final] ).
cnf(c_0_1826,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk15_3(X1,X3,X2)),X2)) ),
c_0_1298,
[final] ).
cnf(c_0_1827,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_1299,
[final] ).
cnf(c_0_1828,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk13_3(X3,X1,X2))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
c_0_1300,
[final] ).
cnf(c_0_1829,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
c_0_1301,
[final] ).
cnf(c_0_1830,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
c_0_1302,
[final] ).
cnf(c_0_1831,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
c_0_1303,
[final] ).
cnf(c_0_1832,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
c_0_1304,
[final] ).
cnf(c_0_1833,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
c_0_1305,
[final] ).
cnf(c_0_1834,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
c_0_1306,
[final] ).
cnf(c_0_1835,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
c_0_1307,
[final] ).
cnf(c_0_1836,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
c_0_1308,
[final] ).
cnf(c_0_1837,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
c_0_1309,
[final] ).
cnf(c_0_1838,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
c_0_1310,
[final] ).
cnf(c_0_1839,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
c_0_1311,
[final] ).
cnf(c_0_1840,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
c_0_1312,
[final] ).
cnf(c_0_1841,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,esk13_3(X3,X1,X2))) ),
c_0_1313,
[final] ).
cnf(c_0_1842,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
c_0_1314,
[final] ).
cnf(c_0_1843,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
c_0_1315,
[final] ).
cnf(c_0_1844,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
c_0_1316,
[final] ).
cnf(c_0_1845,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
c_0_1317,
[final] ).
cnf(c_0_1846,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1318,
[final] ).
cnf(c_0_1847,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1319,
[final] ).
cnf(c_0_1848,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk1_3(X2,X3,X1)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1320,
[final] ).
cnf(c_0_1849,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1321,
[final] ).
cnf(c_0_1850,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1322,
[final] ).
cnf(c_0_1851,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1323,
[final] ).
cnf(c_0_1852,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1324,
[final] ).
cnf(c_0_1853,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1325,
[final] ).
cnf(c_0_1854,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1326,
[final] ).
cnf(c_0_1855,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1327,
[final] ).
cnf(c_0_1856,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1328,
[final] ).
cnf(c_0_1857,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1329,
[final] ).
cnf(c_0_1858,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1330,
[final] ).
cnf(c_0_1859,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1331,
[final] ).
cnf(c_0_1860,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1332,
[final] ).
cnf(c_0_1861,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1333,
[final] ).
cnf(c_0_1862,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1334,
[final] ).
cnf(c_0_1863,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1335,
[final] ).
cnf(c_0_1864,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X2))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
c_0_1336,
[final] ).
cnf(c_0_1865,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X2))),hAPP_f98387925ol_nat(finite269641166l_bool,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
c_0_1337,
[final] ).
cnf(c_0_1866,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X2))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
c_0_1338,
[final] ).
cnf(c_0_1867,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1339,
[final] ).
cnf(c_0_1868,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1340,
[final] ).
cnf(c_0_1869,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1341,
[final] ).
cnf(c_0_1870,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1342,
[final] ).
cnf(c_0_1871,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1343,
[final] ).
cnf(c_0_1872,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1344,
[final] ).
cnf(c_0_1873,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1345,
[final] ).
cnf(c_0_1874,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1346,
[final] ).
cnf(c_0_1875,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
c_0_1347,
[final] ).
cnf(c_0_1876,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
c_0_1348,
[final] ).
cnf(c_0_1877,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
c_0_1349,
[final] ).
cnf(c_0_1878,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
c_0_1350,
[final] ).
cnf(c_0_1879,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
c_0_1351,
[final] ).
cnf(c_0_1880,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
c_0_1352,
[final] ).
cnf(c_0_1881,plain,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))),X2)) = insert_fun_a_bool(X1,collect_fun_a_bool(X2)),
c_0_1353,
[final] ).
cnf(c_0_1882,plain,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))),X2)) = insert1325755072e_bool(X1,collec1974731493e_bool(X2)),
c_0_1354,
[final] ).
cnf(c_0_1883,plain,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X2)) = insert_fun_nat_bool(X1,collect_fun_nat_bool(X2)),
c_0_1355,
[final] ).
cnf(c_0_1884,plain,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))),X2)) = insert_a(X1,collect_a(X2)),
c_0_1356,
[final] ).
cnf(c_0_1885,plain,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),X2)) = insert_pname(X1,collect_pname(X2)),
c_0_1357,
[final] ).
cnf(c_0_1886,plain,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)) = insert_nat(X1,collect_nat(X2)),
c_0_1358,
[final] ).
cnf(c_0_1887,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_1359,
[final] ).
cnf(c_0_1888,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_1360,
[final] ).
cnf(c_0_1889,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
c_0_1361,
[final] ).
cnf(c_0_1890,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
c_0_1362,
[final] ).
cnf(c_0_1891,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
c_0_1363,
[final] ).
cnf(c_0_1892,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
c_0_1364,
[final] ).
cnf(c_0_1893,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3),
c_0_1365,
[final] ).
cnf(c_0_1894,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_1366,
[final] ).
cnf(c_0_1895,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
c_0_1367,
[final] ).
cnf(c_0_1896,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2))) ),
c_0_1368,
[final] ).
cnf(c_0_1897,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
c_0_1369,
[final] ).
cnf(c_0_1898,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2))) ),
c_0_1370,
[final] ).
cnf(c_0_1899,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
c_0_1371,
[final] ).
cnf(c_0_1900,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2))) ),
c_0_1372,
[final] ).
cnf(c_0_1901,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
c_0_1373,
[final] ).
cnf(c_0_1902,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2))) ),
c_0_1374,
[final] ).
cnf(c_0_1903,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
c_0_1375,
[final] ).
cnf(c_0_1904,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2))) ),
c_0_1376,
[final] ).
cnf(c_0_1905,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
c_0_1377,
[final] ).
cnf(c_0_1906,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2))) ),
c_0_1378,
[final] ).
cnf(c_0_1907,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
c_0_1379,
[final] ).
cnf(c_0_1908,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1380,
[final] ).
cnf(c_0_1909,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1381,
[final] ).
cnf(c_0_1910,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1382,
[final] ).
cnf(c_0_1911,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1383,
[final] ).
cnf(c_0_1912,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1384,
[final] ).
cnf(c_0_1913,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1385,
[final] ).
cnf(c_0_1914,plain,
( image_pname_a(X2,esk1_3(X2,X3,X1)) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1386,
[final] ).
cnf(c_0_1915,plain,
( is_fun_pname_bool(esk1_3(X2,X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1387,
[final] ).
cnf(c_0_1916,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
c_0_1388,
[final] ).
cnf(c_0_1917,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
c_0_1389,
[final] ).
cnf(c_0_1918,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
c_0_1390,
[final] ).
cnf(c_0_1919,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
c_0_1391,
[final] ).
cnf(c_0_1920,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
c_0_1392,
[final] ).
cnf(c_0_1921,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
c_0_1393,
[final] ).
cnf(c_0_1922,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X2,X1)),X2)) ),
c_0_1394,
[final] ).
cnf(c_0_1923,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X2,X1)),X2)) ),
c_0_1395,
[final] ).
cnf(c_0_1924,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X2,X1)),X2)) ),
c_0_1396,
[final] ).
cnf(c_0_1925,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
c_0_1397,
[final] ).
cnf(c_0_1926,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
c_0_1398,
[final] ).
cnf(c_0_1927,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
c_0_1399,
[final] ).
cnf(c_0_1928,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
c_0_1400,
[final] ).
cnf(c_0_1929,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
c_0_1401,
[final] ).
cnf(c_0_1930,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
c_0_1402,
[final] ).
cnf(c_0_1931,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3))) ),
c_0_1403,
[final] ).
cnf(c_0_1932,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3))) ),
c_0_1404,
[final] ).
cnf(c_0_1933,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3))) ),
c_0_1405,
[final] ).
cnf(c_0_1934,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
c_0_1406,
[final] ).
cnf(c_0_1935,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
c_0_1407,
[final] ).
cnf(c_0_1936,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
c_0_1408,
[final] ).
cnf(c_0_1937,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
c_0_1409,
[final] ).
cnf(c_0_1938,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
c_0_1410,
[final] ).
cnf(c_0_1939,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
c_0_1411,
[final] ).
cnf(c_0_1940,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_1412,
[final] ).
cnf(c_0_1941,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk6_2(X2,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
c_0_1413,
[final] ).
cnf(c_0_1942,plain,
( hAPP_pname_a(X2,esk9_3(X1,X2,X3)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1414,
[final] ).
cnf(c_0_1943,plain,
( image_pname_a(X2,esk8_3(X1,X2,X3)) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1415,
[final] ).
cnf(c_0_1944,plain,
( hAPP_pname_a(X2,esk7_3(X1,X2,X3)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1416,
[final] ).
cnf(c_0_1945,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
c_0_1417,
[final] ).
cnf(c_0_1946,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
c_0_1418,
[final] ).
cnf(c_0_1947,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
c_0_1419,
[final] ).
cnf(c_0_1948,plain,
( is_pname(esk9_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1420,
[final] ).
cnf(c_0_1949,plain,
( is_fun_pname_bool(esk8_3(X1,X2,X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
c_0_1421,
[final] ).
cnf(c_0_1950,plain,
( is_pname(esk7_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
c_0_1422,
[final] ).
cnf(c_0_1951,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
c_0_1423,
[final] ).
cnf(c_0_1952,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
c_0_1424,
[final] ).
cnf(c_0_1953,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
c_0_1425,
[final] ).
cnf(c_0_1954,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
c_0_1426,
[final] ).
cnf(c_0_1955,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
c_0_1427,
[final] ).
cnf(c_0_1956,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
c_0_1428,
[final] ).
cnf(c_0_1957,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
c_0_1429,
[final] ).
cnf(c_0_1958,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
c_0_1430,
[final] ).
cnf(c_0_1959,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
c_0_1431,
[final] ).
cnf(c_0_1960,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
c_0_1432,
[final] ).
cnf(c_0_1961,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
c_0_1433,
[final] ).
cnf(c_0_1962,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
c_0_1434,
[final] ).
cnf(c_0_1963,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
c_0_1435,
[final] ).
cnf(c_0_1964,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
c_0_1436,
[final] ).
cnf(c_0_1965,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
c_0_1437,
[final] ).
cnf(c_0_1966,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_1438,
[final] ).
cnf(c_0_1967,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk17_2(X1,X2)),X2)) ),
c_0_1439,
[final] ).
cnf(c_0_1968,plain,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1) ),
c_0_1440,
[final] ).
cnf(c_0_1969,plain,
( hAPP_nat_nat(suc,esk14_2(X2,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
c_0_1441,
[final] ).
cnf(c_0_1970,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
c_0_1442,
[final] ).
cnf(c_0_1971,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
c_0_1443,
[final] ).
cnf(c_0_1972,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ is_a(X3)
| ~ is_a(X1) ),
c_0_1444,
[final] ).
cnf(c_0_1973,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ is_pname(X3)
| ~ is_pname(X1) ),
c_0_1445,
[final] ).
cnf(c_0_1974,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| is_pname(esk15_3(X1,X3,X2)) ),
c_0_1446,
[final] ).
cnf(c_0_1975,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| X1 != image_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| ~ is_fun_pname_bool(X4) ),
c_0_1447,
[final] ).
cnf(c_0_1976,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| ~ is_pname(X4) ),
c_0_1448,
[final] ).
cnf(c_0_1977,plain,
( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
c_0_1449,
[final] ).
cnf(c_0_1978,plain,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))) = insert_fun_a_bool(X1,X2),
c_0_1450,
[final] ).
cnf(c_0_1979,plain,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))) = insert1325755072e_bool(X1,X2),
c_0_1451,
[final] ).
cnf(c_0_1980,plain,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = insert_fun_nat_bool(X1,X2),
c_0_1452,
[final] ).
cnf(c_0_1981,plain,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))) = insert_a(X1,X2),
c_0_1453,
[final] ).
cnf(c_0_1982,plain,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = insert_pname(X1,X2),
c_0_1454,
[final] ).
cnf(c_0_1983,plain,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))) = insert_nat(X1,X2),
c_0_1455,
[final] ).
cnf(c_0_1984,plain,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))) = insert_fun_a_bool(X1,X2),
c_0_1456,
[final] ).
cnf(c_0_1985,plain,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))) = insert1325755072e_bool(X1,X2),
c_0_1457,
[final] ).
cnf(c_0_1986,plain,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = insert_fun_nat_bool(X1,X2),
c_0_1458,
[final] ).
cnf(c_0_1987,plain,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))) = insert_a(X1,X2),
c_0_1459,
[final] ).
cnf(c_0_1988,plain,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = insert_pname(X1,X2),
c_0_1460,
[final] ).
cnf(c_0_1989,plain,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))) = insert_nat(X1,X2),
c_0_1461,
[final] ).
cnf(c_0_1990,plain,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
c_0_1462,
[final] ).
cnf(c_0_1991,plain,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
c_0_1463,
[final] ).
cnf(c_0_1992,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
c_0_1464,
[final] ).
cnf(c_0_1993,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
c_0_1465,
[final] ).
cnf(c_0_1994,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3)) ),
c_0_1466,
[final] ).
cnf(c_0_1995,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4) ),
c_0_1467,
[final] ).
cnf(c_0_1996,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
c_0_1468,
[final] ).
cnf(c_0_1997,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
c_0_1469,
[final] ).
cnf(c_0_1998,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
c_0_1470,
[final] ).
cnf(c_0_1999,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
c_0_1471,
[final] ).
cnf(c_0_2000,plain,
( X2 = X1
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
c_0_1472,
[final] ).
cnf(c_0_2001,plain,
( X2 = X1
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
c_0_1473,
[final] ).
cnf(c_0_2002,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
c_0_1474,
[final] ).
cnf(c_0_2003,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
c_0_1475,
[final] ).
cnf(c_0_2004,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X2,X1)),X1)) ),
c_0_1476,
[final] ).
cnf(c_0_2005,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X2,X1)),X1)) ),
c_0_1477,
[final] ).
cnf(c_0_2006,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X2,X1)),X1)) ),
c_0_1478,
[final] ).
cnf(c_0_2007,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk16_1(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1479,
[final] ).
cnf(c_0_2008,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
c_0_1480,
[final] ).
cnf(c_0_2009,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
c_0_1481,
[final] ).
cnf(c_0_2010,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
c_0_1482,
[final] ).
cnf(c_0_2011,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
c_0_1483,
[final] ).
cnf(c_0_2012,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
c_0_1484,
[final] ).
cnf(c_0_2013,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
c_0_1485,
[final] ).
cnf(c_0_2014,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
c_0_1486,
[final] ).
cnf(c_0_2015,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
c_0_1487,
[final] ).
cnf(c_0_2016,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
c_0_1488,
[final] ).
cnf(c_0_2017,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
c_0_1489,
[final] ).
cnf(c_0_2018,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_1490,
[final] ).
cnf(c_0_2019,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
c_0_1491,
[final] ).
cnf(c_0_2020,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
c_0_1492,
[final] ).
cnf(c_0_2021,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_1493,
[final] ).
cnf(c_0_2022,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_1494,
[final] ).
cnf(c_0_2023,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_1495,
[final] ).
cnf(c_0_2024,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_1496,
[final] ).
cnf(c_0_2025,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X1)),
c_0_1497,
[final] ).
cnf(c_0_2026,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_fun_a_bool_nat(finite_card_a,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
c_0_1498,
[final] ).
cnf(c_0_2027,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_f921600141ol_nat(finite_card_pname,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
c_0_1499,
[final] ).
cnf(c_0_2028,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_f22106695ol_nat(finite_card_nat,X1)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
c_0_1500,
[final] ).
cnf(c_0_2029,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1)) ),
c_0_1501,
[final] ).
cnf(c_0_2030,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1)) ),
c_0_1502,
[final] ).
cnf(c_0_2031,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1)) ),
c_0_1503,
[final] ).
cnf(c_0_2032,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
c_0_1504,
[final] ).
cnf(c_0_2033,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
c_0_1505,
[final] ).
cnf(c_0_2034,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
c_0_1506,
[final] ).
cnf(c_0_2035,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
c_0_1507,
[final] ).
cnf(c_0_2036,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
c_0_1508,
[final] ).
cnf(c_0_2037,plain,
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
c_0_1509,
[final] ).
cnf(c_0_2038,plain,
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
c_0_1510,
[final] ).
cnf(c_0_2039,plain,
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
c_0_1511,
[final] ).
cnf(c_0_2040,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
c_0_1512,
[final] ).
cnf(c_0_2041,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
c_0_1513,
[final] ).
cnf(c_0_2042,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
c_0_1514,
[final] ).
cnf(c_0_2043,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk17_2(X1,X2)),X1)) ),
c_0_1515,
[final] ).
cnf(c_0_2044,plain,
( insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
c_0_1516,
[final] ).
cnf(c_0_2045,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| X2 = X3
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
c_0_1517,
[final] ).
cnf(c_0_2046,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| insert_a(X3,X1) = insert_a(X3,X2)
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
c_0_1518,
[final] ).
cnf(c_0_2047,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| insert_pname(X3,X1) = insert_pname(X3,X2)
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
c_0_1519,
[final] ).
cnf(c_0_2048,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1520,
[final] ).
cnf(c_0_2049,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1521,
[final] ).
cnf(c_0_2050,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1522,
[final] ).
cnf(c_0_2051,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1523,
[final] ).
cnf(c_0_2052,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1524,
[final] ).
cnf(c_0_2053,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1525,
[final] ).
cnf(c_0_2054,plain,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
c_0_1526,
[final] ).
cnf(c_0_2055,plain,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
c_0_1527,
[final] ).
cnf(c_0_2056,plain,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
c_0_1528,
[final] ).
cnf(c_0_2057,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
c_0_1529,
[final] ).
cnf(c_0_2058,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
c_0_1530,
[final] ).
cnf(c_0_2059,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
c_0_1531,
[final] ).
cnf(c_0_2060,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X3)),X2),
c_0_1532,
[final] ).
cnf(c_0_2061,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1533,
[final] ).
cnf(c_0_2062,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1534,
[final] ).
cnf(c_0_2063,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1535,
[final] ).
cnf(c_0_2064,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1536,
[final] ).
cnf(c_0_2065,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1537,
[final] ).
cnf(c_0_2066,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1538,
[final] ).
cnf(c_0_2067,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
c_0_1539,
[final] ).
cnf(c_0_2068,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
c_0_1540,
[final] ).
cnf(c_0_2069,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2)) ),
c_0_1541,
[final] ).
cnf(c_0_2070,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
c_0_1542,
[final] ).
cnf(c_0_2071,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2)) ),
c_0_1543,
[final] ).
cnf(c_0_2072,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2)) ),
c_0_1544,
[final] ).
cnf(c_0_2073,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| insert_nat(X1,X2) = insert_nat(X1,X3)
| X2 != X3 ),
c_0_1545,
[final] ).
cnf(c_0_2074,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_pname(esk6_2(X2,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
c_0_1546,
[final] ).
cnf(c_0_2075,plain,
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_1547,
[final] ).
cnf(c_0_2076,plain,
( hBOOL(hAPP_a_bool(X3,X1))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
c_0_1548,
[final] ).
cnf(c_0_2077,plain,
( hBOOL(hAPP_pname_bool(X3,X1))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
c_0_1549,
[final] ).
cnf(c_0_2078,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1)))),
c_0_1550,
[final] ).
cnf(c_0_2079,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
c_0_1551,
[final] ).
cnf(c_0_2080,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2)) ),
c_0_1552,
[final] ).
cnf(c_0_2081,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_1553,
[final] ).
cnf(c_0_2082,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1))) ),
c_0_1554,
[final] ).
cnf(c_0_2083,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1))) ),
c_0_1555,
[final] ).
cnf(c_0_2084,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1))) ),
c_0_1556,
[final] ).
cnf(c_0_2085,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1))) ),
c_0_1557,
[final] ).
cnf(c_0_2086,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1))) ),
c_0_1558,
[final] ).
cnf(c_0_2087,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1))) ),
c_0_1559,
[final] ).
cnf(c_0_2088,plain,
( hBOOL(hAPP_pname_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
c_0_1560,
[final] ).
cnf(c_0_2089,plain,
( hBOOL(hAPP_a_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
c_0_1561,
[final] ).
cnf(c_0_2090,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
c_0_1562,
[final] ).
cnf(c_0_2091,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
c_0_1563,
[final] ).
cnf(c_0_2092,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
c_0_1564,
[final] ).
cnf(c_0_2093,plain,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X3,X1)) ),
c_0_1565,
[final] ).
cnf(c_0_2094,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X3,X1)) ),
c_0_1566,
[final] ).
cnf(c_0_2095,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != hAPP_nat_nat(suc,X2) ),
c_0_1567,
[final] ).
cnf(c_0_2096,plain,
( insert_a(X1,X2) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_fun_a_bool(X2) ),
c_0_1568,
[final] ).
cnf(c_0_2097,plain,
( insert_pname(X1,X2) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1569,
[final] ).
cnf(c_0_2098,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
c_0_1570,
[final] ).
cnf(c_0_2099,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
c_0_1571,
[final] ).
cnf(c_0_2100,plain,
( X1 = X2
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X1) ),
c_0_1572,
[final] ).
cnf(c_0_2101,plain,
( X1 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| ~ is_a(X2)
| ~ is_a(X1) ),
c_0_1573,
[final] ).
cnf(c_0_2102,plain,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
c_0_1574,
[final] ).
cnf(c_0_2103,plain,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
c_0_1575,
[final] ).
cnf(c_0_2104,plain,
( insert_nat(X1,X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
c_0_1576,
[final] ).
cnf(c_0_2105,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
c_0_1577,
[final] ).
cnf(c_0_2106,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| X1 != X2 ),
c_0_1578,
[final] ).
cnf(c_0_2107,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2 ),
c_0_1579,
[final] ).
cnf(c_0_2108,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
c_0_1580,
[final] ).
cnf(c_0_2109,plain,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1)) ),
c_0_1581,
[final] ).
cnf(c_0_2110,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(X2,X3)) ),
c_0_1582,
[final] ).
cnf(c_0_2111,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1)) ),
c_0_1583,
[final] ).
cnf(c_0_2112,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X1))),
c_0_1584,
[final] ).
cnf(c_0_2113,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X1))),
c_0_1585,
[final] ).
cnf(c_0_2114,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X1))),
c_0_1586,
[final] ).
cnf(c_0_2115,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X1,X2))),
c_0_1587,
[final] ).
cnf(c_0_2116,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X1,X2))),
c_0_1588,
[final] ).
cnf(c_0_2117,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X1,X2))),
c_0_1589,
[final] ).
cnf(c_0_2118,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X2),X1)) ),
c_0_1590,
[final] ).
cnf(c_0_2119,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
c_0_1591,
[final] ).
cnf(c_0_2120,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X2,X1)) ),
c_0_1592,
[final] ).
cnf(c_0_2121,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_a_bool(X2,X1)) ),
c_0_1593,
[final] ).
cnf(c_0_2122,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
c_0_1594,
[final] ).
cnf(c_0_2123,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1595,
[final] ).
cnf(c_0_2124,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1596,
[final] ).
cnf(c_0_2125,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1597,
[final] ).
cnf(c_0_2126,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1598,
[final] ).
cnf(c_0_2127,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1599,
[final] ).
cnf(c_0_2128,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1600,
[final] ).
cnf(c_0_2129,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1601,
[final] ).
cnf(c_0_2130,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1602,
[final] ).
cnf(c_0_2131,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1603,
[final] ).
cnf(c_0_2132,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
c_0_1604,
[final] ).
cnf(c_0_2133,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
c_0_1605,
[final] ).
cnf(c_0_2134,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
c_0_1606,
[final] ).
cnf(c_0_2135,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1607,
[final] ).
cnf(c_0_2136,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1608,
[final] ).
cnf(c_0_2137,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1609,
[final] ).
cnf(c_0_2138,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1610,
[final] ).
cnf(c_0_2139,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1611,
[final] ).
cnf(c_0_2140,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1612,
[final] ).
cnf(c_0_2141,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1613,
[final] ).
cnf(c_0_2142,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1614,
[final] ).
cnf(c_0_2143,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1615,
[final] ).
cnf(c_0_2144,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1616,
[final] ).
cnf(c_0_2145,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1617,
[final] ).
cnf(c_0_2146,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1618,
[final] ).
cnf(c_0_2147,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1619,
[final] ).
cnf(c_0_2148,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1620,
[final] ).
cnf(c_0_2149,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1621,
[final] ).
cnf(c_0_2150,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1622,
[final] ).
cnf(c_0_2151,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1623,
[final] ).
cnf(c_0_2152,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1624,
[final] ).
cnf(c_0_2153,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1625,
[final] ).
cnf(c_0_2154,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1626,
[final] ).
cnf(c_0_2155,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1627,
[final] ).
cnf(c_0_2156,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1628,
[final] ).
cnf(c_0_2157,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
c_0_1629,
[final] ).
cnf(c_0_2158,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1630,
[final] ).
cnf(c_0_2159,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1631,
[final] ).
cnf(c_0_2160,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1632,
[final] ).
cnf(c_0_2161,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1633,
[final] ).
cnf(c_0_2162,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
c_0_1634,
[final] ).
cnf(c_0_2163,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
c_0_1635,
[final] ).
cnf(c_0_2164,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
c_0_1636,
[final] ).
cnf(c_0_2165,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
c_0_1637,
[final] ).
cnf(c_0_2166,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
c_0_1638,
[final] ).
cnf(c_0_2167,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
c_0_1639,
[final] ).
cnf(c_0_2168,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
c_0_1640,
[final] ).
cnf(c_0_2169,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
c_0_1641,
[final] ).
cnf(c_0_2170,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
c_0_1642,
[final] ).
cnf(c_0_2171,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
c_0_1643,
[final] ).
cnf(c_0_2172,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
c_0_1644,
[final] ).
cnf(c_0_2173,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
c_0_1645,
[final] ).
cnf(c_0_2174,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
c_0_1646,
[final] ).
cnf(c_0_2175,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
c_0_1647,
[final] ).
cnf(c_0_2176,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| is_pname(esk12_2(X2,X1)) ),
c_0_1648,
[final] ).
cnf(c_0_2177,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk11_2(X2,X1)) ),
c_0_1649,
[final] ).
cnf(c_0_2178,plain,
hAPP_bool_bool(hAPP_f1476298914l_bool(X1,X3),hAPP_f1664156314l_bool(X2,X3)) = hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X1,X2),X3),
c_0_1650,
[final] ).
cnf(c_0_2179,plain,
hAPP_bool_bool(hAPP_f1748468828l_bool(X1,X3),hAPP_f54304608l_bool(X2,X3)) = hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1,X2),X3),
c_0_1651,
[final] ).
cnf(c_0_2180,plain,
hAPP_bool_bool(hAPP_f198738859l_bool(X1,X3),hAPP_fun_a_bool_bool(X2,X3)) = hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X1,X2),X3),
c_0_1652,
[final] ).
cnf(c_0_2181,plain,
hAPP_bool_bool(hAPP_p393069232l_bool(X1,X3),hAPP_pname_bool(X2,X3)) = hAPP_pname_bool(cOMBS_568398431l_bool(X1,X2),X3),
c_0_1653,
[final] ).
cnf(c_0_2182,plain,
hAPP_bool_bool(hAPP_n1006566506l_bool(X1,X3),hAPP_nat_bool(X2,X3)) = hAPP_nat_bool(cOMBS_nat_bool_bool(X1,X2),X3),
c_0_1654,
[final] ).
cnf(c_0_2183,plain,
hAPP_bool_bool(hAPP_a_fun_bool_bool(X1,X3),hAPP_a_bool(X2,X3)) = hAPP_a_bool(cOMBS_a_bool_bool(X1,X2),X3),
c_0_1655,
[final] ).
cnf(c_0_2184,plain,
insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,insert_pname(X2,X3)),
c_0_1656,
[final] ).
cnf(c_0_2185,plain,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
c_0_1657,
[final] ).
cnf(c_0_2186,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
c_0_1658,
[final] ).
cnf(c_0_2187,plain,
hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1))) = hAPP_nat_nat(suc,X1),
c_0_1659,
[final] ).
cnf(c_0_2188,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
c_0_1660,
[final] ).
cnf(c_0_2189,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
c_0_1661,
[final] ).
cnf(c_0_2190,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
c_0_1662,
[final] ).
cnf(c_0_2191,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
c_0_1663,
[final] ).
cnf(c_0_2192,plain,
hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X1),X2),X3) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X1,X3),X2),
c_0_1664,
[final] ).
cnf(c_0_2193,plain,
hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X1),X2),X3) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X1,X3),X2),
c_0_1665,
[final] ).
cnf(c_0_2194,plain,
hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X1),X2),X3) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X1,X3),X2),
c_0_1666,
[final] ).
cnf(c_0_2195,plain,
hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X1,X3),X2),
c_0_1667,
[final] ).
cnf(c_0_2196,plain,
hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X1,X3),X2),
c_0_1668,
[final] ).
cnf(c_0_2197,plain,
hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X1,X3),X2),
c_0_1669,
[final] ).
cnf(c_0_2198,plain,
hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X1,X3),X2),
c_0_1670,
[final] ).
cnf(c_0_2199,plain,
hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X1,X3),X2),
c_0_1671,
[final] ).
cnf(c_0_2200,plain,
hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X1,X3),X2),
c_0_1672,
[final] ).
cnf(c_0_2201,plain,
hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X1,X3),X2),
c_0_1673,
[final] ).
cnf(c_0_2202,plain,
hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X1,X3),X2),
c_0_1674,
[final] ).
cnf(c_0_2203,plain,
hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X1,X3),X2),
c_0_1675,
[final] ).
cnf(c_0_2204,plain,
hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X1,X3),X2),
c_0_1676,
[final] ).
cnf(c_0_2205,plain,
hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1,X3),X2),
c_0_1677,
[final] ).
cnf(c_0_2206,plain,
hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X1,X3),X2),
c_0_1678,
[final] ).
cnf(c_0_2207,plain,
hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_p61793385e_bool(X1,X3),X2),
c_0_1679,
[final] ).
cnf(c_0_2208,plain,
hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X3),X2),
c_0_1680,
[final] ).
cnf(c_0_2209,plain,
hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_p1534023578a_bool(X1,X3),X2),
c_0_1681,
[final] ).
cnf(c_0_2210,plain,
hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_a_fun_a_bool(X1,X3),X2),
c_0_1682,
[final] ).
cnf(c_0_2211,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
c_0_1683,
[final] ).
cnf(c_0_2212,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| X1 != X3 ),
c_0_1684,
[final] ).
cnf(c_0_2213,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X2) ),
c_0_1685,
[final] ).
cnf(c_0_2214,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X2) ),
c_0_1686,
[final] ).
cnf(c_0_2215,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
c_0_1687,
[final] ).
cnf(c_0_2216,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| hBOOL(X1) ),
c_0_1688,
[final] ).
cnf(c_0_2217,plain,
hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
c_0_1689,
[final] ).
cnf(c_0_2218,plain,
hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f54304608l_bool(X2,X3)),
c_0_1690,
[final] ).
cnf(c_0_2219,plain,
hAPP_f198738859l_bool(cOMBB_338059395a_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
c_0_1691,
[final] ).
cnf(c_0_2220,plain,
hAPP_p393069232l_bool(cOMBB_675860798_pname(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_pname_bool(X2,X3)),
c_0_1692,
[final] ).
cnf(c_0_2221,plain,
hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
c_0_1693,
[final] ).
cnf(c_0_2222,plain,
hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_nat_bool(X2,X3)),
c_0_1694,
[final] ).
cnf(c_0_2223,plain,
hAPP_f54304608l_bool(cOMBB_238756964t_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f54304608l_bool(X2,X3)),
c_0_1695,
[final] ).
cnf(c_0_2224,plain,
hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_a_bool(X2,X3)),
c_0_1696,
[final] ).
cnf(c_0_2225,plain,
hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
c_0_1697,
[final] ).
cnf(c_0_2226,plain,
hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
c_0_1698,
[final] ).
cnf(c_0_2227,plain,
hAPP_bool_bool(X1,hAPP_pname_bool(X2,X3)) = hAPP_pname_bool(cOMBB_647938656_pname(X1,X2),X3),
c_0_1699,
[final] ).
cnf(c_0_2228,plain,
hAPP_nat_bool(cOMBB_bool_bool_nat(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_nat_bool(X2,X3)),
c_0_1700,
[final] ).
cnf(c_0_2229,plain,
hAPP_bool_bool(X1,hAPP_a_bool(X2,X3)) = hAPP_a_bool(cOMBB_bool_bool_a(X1,X2),X3),
c_0_1701,
[final] ).
cnf(c_0_2230,plain,
insert_a(X1,insert_a(X2,X3)) = insert_a(X2,insert_a(X1,X3)),
c_0_1702,
[final] ).
cnf(c_0_2231,plain,
insert_pname(X1,insert_pname(X2,X3)) = insert_pname(X2,insert_pname(X1,X3)),
c_0_1703,
[final] ).
cnf(c_0_2232,plain,
insert_nat(X1,insert_nat(X2,X3)) = insert_nat(X2,insert_nat(X1,X3)),
c_0_1704,
[final] ).
cnf(c_0_2233,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
c_0_1705,
[final] ).
cnf(c_0_2234,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
c_0_1706,
[final] ).
cnf(c_0_2235,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 != X2 ),
c_0_1707,
[final] ).
cnf(c_0_2236,plain,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
c_0_1708,
[final] ).
cnf(c_0_2237,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
c_0_1709,
[final] ).
cnf(c_0_2238,plain,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
c_0_1710,
[final] ).
cnf(c_0_2239,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
c_0_1711,
[final] ).
cnf(c_0_2240,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
c_0_1712,
[final] ).
cnf(c_0_2241,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
c_0_1713,
[final] ).
cnf(c_0_2242,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 != X2 ),
c_0_1714,
[final] ).
cnf(c_0_2243,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
c_0_1715,
[final] ).
cnf(c_0_2244,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
c_0_1716,
[final] ).
cnf(c_0_2245,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
c_0_1717,
[final] ).
cnf(c_0_2246,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
c_0_1718,
[final] ).
cnf(c_0_2247,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
c_0_1719,
[final] ).
cnf(c_0_2248,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
c_0_1720,
[final] ).
cnf(c_0_2249,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
c_0_1721,
[final] ).
cnf(c_0_2250,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
c_0_1722,
[final] ).
cnf(c_0_2251,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
c_0_1723,
[final] ).
cnf(c_0_2252,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
c_0_1724,
[final] ).
cnf(c_0_2253,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
c_0_1725,
[final] ).
cnf(c_0_2254,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
c_0_1726,
[final] ).
cnf(c_0_2255,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
c_0_1727,
[final] ).
cnf(c_0_2256,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
c_0_1728,
[final] ).
cnf(c_0_2257,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
c_0_1729,
[final] ).
cnf(c_0_2258,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
c_0_1730,
[final] ).
cnf(c_0_2259,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
c_0_1731,
[final] ).
cnf(c_0_2260,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
c_0_1732,
[final] ).
cnf(c_0_2261,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
c_0_1733,
[final] ).
cnf(c_0_2262,plain,
insert_a(X1,insert_a(X1,X2)) = insert_a(X1,X2),
c_0_1734,
[final] ).
cnf(c_0_2263,plain,
insert_pname(X1,insert_pname(X1,X2)) = insert_pname(X1,X2),
c_0_1735,
[final] ).
cnf(c_0_2264,plain,
insert_nat(X1,insert_nat(X1,X2)) = insert_nat(X1,X2),
c_0_1736,
[final] ).
cnf(c_0_2265,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(fNot,X1)) ),
c_0_1737,
[final] ).
cnf(c_0_2266,plain,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
c_0_1738,
[final] ).
cnf(c_0_2267,plain,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
c_0_1739,
[final] ).
cnf(c_0_2268,plain,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ),
c_0_1740,
[final] ).
cnf(c_0_2269,plain,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ),
c_0_1741,
[final] ).
cnf(c_0_2270,plain,
( is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun_pname_bool(X1) ),
c_0_1742,
[final] ).
cnf(c_0_2271,plain,
( is_fun949378684l_bool(insert_fun_a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun_a_bool(X1) ),
c_0_1743,
[final] ).
cnf(c_0_2272,plain,
( is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
c_0_1744,
[final] ).
cnf(c_0_2273,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
c_0_1745,
[final] ).
cnf(c_0_2274,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
c_0_1746,
[final] ).
cnf(c_0_2275,plain,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1747,
[final] ).
cnf(c_0_2276,plain,
( is_bool(hAPP_f1935102916l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1748,
[final] ).
cnf(c_0_2277,plain,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1749,
[final] ).
cnf(c_0_2278,plain,
( is_bool(hAPP_f621171935l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1750,
[final] ).
cnf(c_0_2279,plain,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1751,
[final] ).
cnf(c_0_2280,plain,
( is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1752,
[final] ).
cnf(c_0_2281,plain,
( is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_1753,
[final] ).
cnf(c_0_2282,plain,
( is_bool(hAPP_bool_bool(X1,X2))
| ~ is_bool(X2) ),
c_0_1754,
[final] ).
cnf(c_0_2283,plain,
( is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2))
| ~ is_pname(X2) ),
c_0_1755,
[final] ).
cnf(c_0_2284,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2))
| ~ is_pname(X2) ),
c_0_1756,
[final] ).
cnf(c_0_2285,plain,
( is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2))
| ~ is_a(X2) ),
c_0_1757,
[final] ).
cnf(c_0_2286,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2))
| ~ is_a(X2) ),
c_0_1758,
[final] ).
cnf(c_0_2287,plain,
( is_fun_pname_bool(image_1283814551_pname(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1759,
[final] ).
cnf(c_0_2288,plain,
( is_fun_a_bool(image_876012084bool_a(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1760,
[final] ).
cnf(c_0_2289,plain,
( is_fun_pname_bool(image_1854862208_pname(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1761,
[final] ).
cnf(c_0_2290,plain,
( is_fun_a_bool(image_fun_a_bool_a(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1762,
[final] ).
cnf(c_0_2291,plain,
( is_fun1661590463l_bool(image_47868345e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1763,
[final] ).
cnf(c_0_2292,plain,
( is_fun949378684l_bool(image_112932426a_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1764,
[final] ).
cnf(c_0_2293,plain,
( is_fun_pname_bool(image_pname_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1765,
[final] ).
cnf(c_0_2294,plain,
( is_fun_pname_bool(image_a_pname(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_1766,
[final] ).
cnf(c_0_2295,plain,
( is_fun_a_bool(image_a_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_1767,
[final] ).
cnf(c_0_2296,plain,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1768,
[final] ).
cnf(c_0_2297,plain,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1769,
[final] ).
cnf(c_0_2298,plain,
( is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1770,
[final] ).
cnf(c_0_2299,plain,
( is_fun_a_bool(cOMBS_a_bool_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_1771,
[final] ).
cnf(c_0_2300,plain,
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
c_0_1772,
[final] ).
cnf(c_0_2301,plain,
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
c_0_1773,
[final] ).
cnf(c_0_2302,plain,
( is_fun_pname_bool(cOMBB_647938656_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_1774,
[final] ).
cnf(c_0_2303,plain,
( is_fun_a_bool(cOMBB_bool_bool_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_1775,
[final] ).
cnf(c_0_2304,plain,
( hBOOL(hAPP_bool_bool(fNot,X1))
| hBOOL(X1) ),
c_0_1776,
[final] ).
cnf(c_0_2305,plain,
is_bool(hAPP_f1295398978l_bool(X1,X2)),
c_0_1777,
[final] ).
cnf(c_0_2306,plain,
is_bool(hAPP_f595608956l_bool(X1,X2)),
c_0_1778,
[final] ).
cnf(c_0_2307,plain,
is_bool(hAPP_f1363661463l_bool(X1,X2)),
c_0_1779,
[final] ).
cnf(c_0_2308,plain,
is_bool(hAPP_f937997336l_bool(X1,X2)),
c_0_1780,
[final] ).
cnf(c_0_2309,plain,
is_bool(hAPP_f389811538l_bool(X1,X2)),
c_0_1781,
[final] ).
cnf(c_0_2310,plain,
is_bool(hAPP_f292226953l_bool(X1,X2)),
c_0_1782,
[final] ).
cnf(c_0_2311,plain,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
c_0_1783,
[final] ).
cnf(c_0_2312,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
c_0_1784,
[final] ).
cnf(c_0_2313,plain,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
c_0_1785,
[final] ).
cnf(c_0_2314,plain,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
c_0_1786,
[final] ).
cnf(c_0_2315,plain,
is_fun_pname_bool(image_1604018183_pname(X1,X2)),
c_0_1787,
[final] ).
cnf(c_0_2316,plain,
is_fun_a_bool(image_526090948bool_a(X1,X2)),
c_0_1788,
[final] ).
cnf(c_0_2317,plain,
is_fun_pname_bool(image_1705983821_pname(X1,X2)),
c_0_1789,
[final] ).
cnf(c_0_2318,plain,
is_fun_a_bool(image_349102846bool_a(X1,X2)),
c_0_1790,
[final] ).
cnf(c_0_2319,plain,
is_fun_pname_bool(image_990671762_pname(X1,X2)),
c_0_1791,
[final] ).
cnf(c_0_2320,plain,
is_fun_a_bool(image_573985017bool_a(X1,X2)),
c_0_1792,
[final] ).
cnf(c_0_2321,plain,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
c_0_1793,
[final] ).
cnf(c_0_2322,plain,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
c_0_1794,
[final] ).
cnf(c_0_2323,plain,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
c_0_1795,
[final] ).
cnf(c_0_2324,plain,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
c_0_1796,
[final] ).
cnf(c_0_2325,plain,
is_fun_pname_bool(image_nat_pname(X1,X2)),
c_0_1797,
[final] ).
cnf(c_0_2326,plain,
is_fun_a_bool(image_nat_a(X1,X2)),
c_0_1798,
[final] ).
cnf(c_0_2327,plain,
( hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,X2)
| X1 != X2 ),
c_0_1799,
[final] ).
cnf(c_0_2328,plain,
hAPP_nat_nat(suc,X1) != X1,
c_0_1800,
[final] ).
cnf(c_0_2329,plain,
hAPP_nat_nat(suc,X1) != X1,
c_0_1801,
[final] ).
cnf(c_0_2330,plain,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
c_0_1802,
[final] ).
cnf(c_0_2331,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
c_0_1803,
[final] ).
cnf(c_0_2332,plain,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
c_0_1804,
[final] ).
cnf(c_0_2333,plain,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
c_0_1805,
[final] ).
cnf(c_0_2334,plain,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
c_0_1806,
[final] ).
cnf(c_0_2335,plain,
( collect_fun_a_bool(X1) = X1
| ~ is_fun949378684l_bool(X1) ),
c_0_1807,
[final] ).
cnf(c_0_2336,plain,
( collec1974731493e_bool(X1) = X1
| ~ is_fun1661590463l_bool(X1) ),
c_0_1808,
[final] ).
cnf(c_0_2337,plain,
( collect_pname(X1) = X1
| ~ is_fun_pname_bool(X1) ),
c_0_1809,
[final] ).
cnf(c_0_2338,plain,
is_pname(undefined_pname(pname)),
c_0_1810,
[final] ).
cnf(c_0_2339,plain,
is_a(undefined_a(x_a)),
c_0_1811,
[final] ).
cnf(c_0_2340,plain,
collect_nat(X1) = X1,
c_0_1812,
[final] ).
cnf(c_0_2341,plain,
collect_fun_nat_bool(X1) = X1,
c_0_1813,
[final] ).
cnf(c_0_2342,plain,
is_fun949378684l_bool(finite_finite_a),
c_0_1814,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1815_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,sk1_esk6_2(X2,X1))))))) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,sk1_esk6_2(X2,X1))))))) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,sk1_esk6_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,sk1_esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,sk1_esk5_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,sk1_esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,sk1_esk5_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,sk1_esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,sk1_esk5_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,sk1_esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,sk1_esk4_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,sk1_esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,sk1_esk4_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,sk1_esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,sk1_esk4_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,sk1_esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,sk1_esk3_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,sk1_esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,sk1_esk3_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,sk1_esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,sk1_esk3_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,sk1_esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,sk1_esk2_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,sk1_esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,sk1_esk2_3(X2,X3,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,sk1_esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,sk1_esk2_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,sk1_esk15_3(X1,X3,X2))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,sk1_esk15_3(X1,X3,X2))),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk1_3(X2,X3,X1)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk1_3(X2,X3,X1)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk1_3(X2,X3,X1)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk1_3(X2,X3,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk9_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk9_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk9_3(X1,X2,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk8_3(X1,X2,X3)),X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk8_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sk1_esk8_3(X1,X2,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk7_3(X1,X2,X3)),X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk7_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk7_3(X1,X2,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1826_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk15_3(X1,X3,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk15_3(X1,X3,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1827_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sk1_esk13_3(X3,X1,X2))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sk1_esk13_3(X3,X1,X2))))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sk1_esk13_3(X3,X1,X2))))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1836_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,sk1_esk13_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_1,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,sk1_esk13_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,sk1_esk13_3(X3,X1,X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| X1 = X2
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_4,axiom,
( ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| X1 = X2
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_5,axiom,
( ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_3,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| X1 = X2
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_4,axiom,
( ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| X1 = X2
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_5,axiom,
( ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_3,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| X1 = X2
| ~ is_fun949378684l_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_4,axiom,
( ~ is_fun949378684l_bool(X2)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| X1 = X2
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_5,axiom,
( ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X2)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_3,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| X1 = X2
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_4,axiom,
( ~ is_fun1661590463l_bool(X2)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| X1 = X2
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_5,axiom,
( ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X2)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_3,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| X1 = X2
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_3,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sk1_esk1_3(X2,X3,X1)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sk1_esk1_3(X2,X3,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sk1_esk1_3(X2,X3,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sk1_esk1_3(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1858_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X2))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1,X2))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X2))),hAPP_f98387925ol_nat(finite269641166l_bool,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_1,axiom,
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1,X2))),hAPP_f98387925ol_nat(finite269641166l_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X2))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_1,axiom,
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1,X2))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1870_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1887_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1894_0,axiom,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(minus_minus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1896_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1898_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1899_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1900_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1906_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1908_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( image_pname_a(X2,sk1_esk1_3(X2,X3,X1)) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ is_fun_a_bool(X1)
| image_pname_a(X2,sk1_esk1_3(X2,X3,X1)) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| image_pname_a(X2,sk1_esk1_3(X2,X3,X1)) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| image_pname_a(X2,sk1_esk1_3(X2,X3,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
( is_fun_pname_bool(sk1_esk1_3(X2,X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_1,axiom,
( ~ is_fun_a_bool(X1)
| is_fun_pname_bool(sk1_esk1_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| is_fun_pname_bool(sk1_esk1_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1)
| is_fun_pname_bool(sk1_esk1_3(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1917_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk12_2(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk12_2(X2,X1)),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sk1_esk11_2(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sk1_esk11_2(X2,X1)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk10_2(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk10_2(X2,X1)),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X2)),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1936_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X2)),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1937_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X2)),insert_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1940_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1941_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk6_2(X2,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk6_2(X2,X1)),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk6_2(X2,X1)),X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
( hAPP_pname_a(X2,sk1_esk9_3(X1,X2,X3)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_1,axiom,
( ~ is_a(X1)
| hAPP_pname_a(X2,sk1_esk9_3(X1,X2,X3)) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| hAPP_pname_a(X2,sk1_esk9_3(X1,X2,X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1943_0,axiom,
( image_pname_a(X2,sk1_esk8_3(X1,X2,X3)) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( ~ is_fun_a_bool(X1)
| image_pname_a(X2,sk1_esk8_3(X1,X2,X3)) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| image_pname_a(X2,sk1_esk8_3(X1,X2,X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( hAPP_pname_a(X2,sk1_esk7_3(X1,X2,X3)) = X1
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( ~ is_a(X1)
| hAPP_pname_a(X2,sk1_esk7_3(X1,X2,X3)) = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| hAPP_pname_a(X2,sk1_esk7_3(X1,X2,X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X3)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X3)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1947_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X3)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1948_0,axiom,
( is_pname(sk1_esk9_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_1,axiom,
( ~ is_a(X1)
| is_pname(sk1_esk9_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| is_pname(sk1_esk9_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1949_0,axiom,
( is_fun_pname_bool(sk1_esk8_3(X1,X2,X3))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( ~ is_fun_a_bool(X1)
| is_fun_pname_bool(sk1_esk8_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| is_fun_pname_bool(sk1_esk8_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( is_pname(sk1_esk7_3(X1,X2,X3))
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( ~ is_a(X1)
| is_pname(sk1_esk7_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| is_pname(sk1_esk7_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1951_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1955_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1956_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1957_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1958_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1963_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1967_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sk1_esk17_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sk1_esk17_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1968_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = X3
| hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_3,axiom,
( hAPP_nat_nat(minus_minus_nat(X2),X1) != hAPP_nat_nat(minus_minus_nat(X3),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
( hAPP_nat_nat(suc,sk1_esk14_2(X2,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1))
| hAPP_nat_nat(suc,sk1_esk14_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_1,axiom,
( X2 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_2,axiom,
( ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_3,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_4,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X2)
| ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_1,axiom,
( X2 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_2,axiom,
( ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_3,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_4,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1972_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ is_a(X3)
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( X1 = X3
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ is_a(X3)
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| X1 = X3
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_a(X3)
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_3,axiom,
( ~ is_a(X3)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| X1 = X3
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_4,axiom,
( ~ is_a(X1)
| ~ is_a(X3)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| X1 = X3
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ is_pname(X3)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( X1 = X3
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ is_pname(X3)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| X1 = X3
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_pname(X3)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_3,axiom,
( ~ is_pname(X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| X1 = X3
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_4,axiom,
( ~ is_pname(X1)
| ~ is_pname(X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| X1 = X3
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3))
| is_pname(sk1_esk15_3(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_1,axiom,
( is_pname(sk1_esk15_3(X1,X3,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1)
| X1 != image_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| ~ is_fun_pname_bool(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| X1 != image_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| ~ is_fun_pname_bool(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_2,axiom,
( X1 != image_pname_a(X2,X4)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| ~ is_fun_pname_bool(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_3,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| X1 != image_pname_a(X2,X4)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_pname_bool(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_4,axiom,
( ~ is_fun_pname_bool(X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X3))
| X1 != image_pname_a(X2,X4)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1)
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| ~ is_pname(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| ~ is_pname(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_2,axiom,
( X1 != hAPP_pname_a(X2,X4)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| ~ is_pname(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_3,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_pname(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_4,axiom,
( ~ is_pname(X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
( hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_3,axiom,
( X2 != X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X2),X1) = hAPP_nat_nat(minus_minus_nat(X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1990_0,axiom,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
( X1 = hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( X1 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2)))
| X1 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X1 = X3
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( X1 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2)))
| X1 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( X1 != hAPP_pname_a(X2,X4)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| X1 != hAPP_pname_a(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| X1 != hAPP_pname_a(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_2,axiom,
( X1 != hAPP_pname_a(X2,X4)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1998_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_2,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_2,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_3,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( X2 = X1
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ is_fun_a_bool(X1)
| X2 = X1
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_2,axiom,
( ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| X2 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_3,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| X2 = X1
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_4,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( X2 = X1
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ is_fun_pname_bool(X1)
| X2 = X1
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_2,axiom,
( ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| X2 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_3,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| X2 = X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_4,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 = X2
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_3,axiom,
( ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 = X2
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_4,axiom,
( ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 = X2
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_3,axiom,
( ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 = X2
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_4,axiom,
( ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk12_2(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sk1_esk12_2(X2,X1)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sk1_esk11_2(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sk1_esk11_2(X2,X1)),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk10_2(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk10_2(X2,X1)),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sk1_esk16_1(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sk1_esk16_1(X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),sk1_esk16_1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2026_0,axiom,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_fun_a_bool_nat(finite_card_a,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_fun_a_bool_nat(finite_card_a,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_fun_a_bool_nat(finite_card_a,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_f921600141ol_nat(finite_card_pname,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_f921600141ol_nat(finite_card_pname,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_f921600141ol_nat(finite_card_pname,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_f22106695ol_nat(finite_card_nat,X1)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_f22106695ol_nat(finite_card_nat,X1)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_f22106695ol_nat(finite_card_nat,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1)
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1)
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_2,axiom,
( X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_3,axiom,
( ~ is_fun_a_bool(X1)
| X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| ~ is_fun_a_bool(X2)
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_4,axiom,
( ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| insert_a(X3,X1) != insert_a(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_5,axiom,
( insert_a(X3,X1) != insert_a(X3,X2)
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_2,axiom,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_3,axiom,
( ~ is_fun_pname_bool(X1)
| X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ is_fun_pname_bool(X2)
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_4,axiom,
( ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| insert_pname(X3,X1) != insert_pname(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_5,axiom,
( insert_pname(X3,X1) != insert_pname(X3,X2)
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_0,axiom,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2037_0,axiom,
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
| hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2038_0,axiom,
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
| hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_0,axiom,
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_1,axiom,
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
| hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2040_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk17_2(X1,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sk1_esk17_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2044_0,axiom,
( insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2045_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| X2 = X3
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X2 = X3
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_2,axiom,
( X2 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_3,axiom,
( insert_nat(X1,X2) != insert_nat(X1,X3)
| X2 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2046_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| insert_a(X3,X1) = insert_a(X3,X2)
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| insert_a(X3,X1) = insert_a(X3,X2)
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_2,axiom,
( insert_a(X3,X1) = insert_a(X3,X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_3,axiom,
( ~ is_fun_a_bool(X1)
| insert_a(X3,X1) = insert_a(X3,X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| ~ is_fun_a_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_4,axiom,
( ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| insert_a(X3,X1) = insert_a(X3,X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_5,axiom,
( X1 != X2
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| insert_a(X3,X1) = insert_a(X3,X2)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2047_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| insert_pname(X3,X1) = insert_pname(X3,X2)
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| insert_pname(X3,X1) = insert_pname(X3,X2)
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_2,axiom,
( insert_pname(X3,X1) = insert_pname(X3,X2)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_3,axiom,
( ~ is_fun_pname_bool(X1)
| insert_pname(X3,X1) = insert_pname(X3,X2)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ is_fun_pname_bool(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_4,axiom,
( ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| insert_pname(X3,X1) = insert_pname(X3,X2)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_5,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| insert_pname(X3,X1) = insert_pname(X3,X2)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2048_0,axiom,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_0,axiom,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2050_0,axiom,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2051_0,axiom,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_1,axiom,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2052_0,axiom,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_0,axiom,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_0,axiom,
( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_1,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2055_0,axiom,
( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_1,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2056_0,axiom,
( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2061_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2066_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2067_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_2,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2068_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_2,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2069_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_2,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2070_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_2,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2072_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_2,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2073_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| insert_nat(X1,X2) = insert_nat(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| insert_nat(X1,X2) = insert_nat(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_2,axiom,
( insert_nat(X1,X2) = insert_nat(X1,X3)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_3,axiom,
( X2 != X3
| insert_nat(X1,X2) = insert_nat(X1,X3)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| is_pname(sk1_esk6_2(X2,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( is_pname(sk1_esk6_2(X2,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_2,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| is_pname(sk1_esk6_2(X2,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( hBOOL(hAPP_a_bool(X3,X1))
| X2 = X1
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( X2 = X1
| hBOOL(hAPP_a_bool(X3,X1))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_a_bool(X3,X1))
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_3,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_a_bool(X3,X1))
| ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_4,axiom,
( ~ hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X2)
| ~ is_a(X1)
| X2 = X1
| hBOOL(hAPP_a_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( hBOOL(hAPP_pname_bool(X3,X1))
| X2 = X1
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( X2 = X1
| hBOOL(hAPP_pname_bool(X3,X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_pname_bool(X3,X1))
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_3,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_pname_bool(X3,X1))
| ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_4,axiom,
( ~ hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X1
| hBOOL(hAPP_pname_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2079_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2080_0,axiom,
( hBOOL(hAPP_nat_bool(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( X3 = X2
| hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ~ hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2))
| X3 = X2
| hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2085_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2085_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2086_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2088_0,axiom,
( hBOOL(hAPP_pname_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_0,axiom,
( hBOOL(hAPP_a_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_0,axiom,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| ~ is_a(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_2,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3)))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_3,axiom,
( X2 != X1
| ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),insert_a(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2092_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_1,axiom,
( ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| ~ is_pname(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_2,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3)))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_3,axiom,
( X2 != X1
| ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),insert_pname(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2093_0,axiom,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_2,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ hBOOL(hAPP_a_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_3,axiom,
( ~ hBOOL(hAPP_a_bool(X3,X1))
| ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2094_0,axiom,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_1,axiom,
( ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_2,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ hBOOL(hAPP_pname_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_3,axiom,
( ~ hBOOL(hAPP_pname_bool(X3,X1))
| ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2095_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_1,axiom,
( X1 != hAPP_nat_nat(suc,X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2096_0,axiom,
( insert_a(X1,X2) = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| insert_a(X1,X2) = X2
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_2,axiom,
( ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| insert_a(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2097_0,axiom,
( insert_pname(X1,X2) = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| insert_pname(X1,X2) = X2
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_2,axiom,
( ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| insert_pname(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2098_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2098_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 = X2
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2098_2,axiom,
( ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 = X2
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2098_3,axiom,
( ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2099_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 = X2
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_2,axiom,
( ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 = X2
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_3,axiom,
( ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2100_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_1,axiom,
( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 = X2
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_2,axiom,
( ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 = X2
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_3,axiom,
( ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2101_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 = X2
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_2,axiom,
( ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 = X2
| ~ is_a(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_3,axiom,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2104_0,axiom,
( insert_nat(X1,X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| insert_nat(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( X1 != X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( X1 != X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_1,axiom,
( ~ hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_2,axiom,
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1))
| ~ hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( ~ hBOOL(hAPP_nat_bool(X2,X3))
| hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_2,axiom,
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2118_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_1,axiom,
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X2),X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_1,axiom,
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2120_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_1,axiom,
( ~ hBOOL(hAPP_pname_bool(X2,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2121_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_a_bool(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2121_1,axiom,
( ~ hBOOL(hAPP_a_bool(X2,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2122_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( ~ hBOOL(hAPP_nat_bool(X2,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2124_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2125_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2126_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2127_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2128_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2129_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2130_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2131_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2132_0,axiom,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_1,axiom,
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2133_0,axiom,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_1,axiom,
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2134_0,axiom,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_1,axiom,
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2135_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2136_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2137_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2138_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2144_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2145_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2147_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2148_0,axiom,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2149_0,axiom,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2153_0,axiom,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2155_0,axiom,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2156_0,axiom,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2157_0,axiom,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2159_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2160_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2162_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_1,axiom,
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2163_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_1,axiom,
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2164_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_1,axiom,
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2165_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_1,axiom,
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2166_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_1,axiom,
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_1,axiom,
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_1,axiom,
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2171_0,axiom,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_1,axiom,
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2172_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_1,axiom,
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2173_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2174_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2176_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| is_pname(sk1_esk12_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( is_pname(sk1_esk12_2(X2,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2177_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(sk1_esk11_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( is_a(sk1_esk11_2(X2,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2185_0,axiom,
( hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X1)
| ~ is_a(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_1,axiom,
( ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| ~ is_a(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_2,axiom,
( ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_3,axiom,
( X2 != X1
| ~ is_a(X2)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(insert_a(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2186_0,axiom,
( hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| ~ is_pname(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_2,axiom,
( ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_3,axiom,
( X2 != X1
| ~ is_pname(X2)
| ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(insert_pname(X2,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2188_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_2,axiom,
( ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_3,axiom,
( X2 != X1
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_fun_a_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_3,axiom,
( X2 != X1
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_1,axiom,
( ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_2,axiom,
( ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_3,axiom,
( X2 != X1
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_1,axiom,
( ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_fun_pname_bool(X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_2,axiom,
( ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_3,axiom,
( X2 != X1
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2211_0,axiom,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( X1 != X3
| hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2233_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( X1 != X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( X1 != X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( X1 != X2
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( X1 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( X1 != X2
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( X1 != X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( X1 != X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2241_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_1,axiom,
( X1 != X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( X1 != X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( X2 != X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( X2 != X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( X2 != X1
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( X1 != X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( X1 != X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( X1 != X2
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( X1 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2265_0,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( ~ hBOOL(hAPP_bool_bool(fNot,X1))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2268_0,axiom,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_pname(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( ~ is_pname(X2)
| is_bool(hAPP_pname_bool(X1,X2))
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_2,axiom,
( ~ is_fun_pname_bool(X1)
| ~ is_pname(X2)
| is_bool(hAPP_pname_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_a(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( ~ is_a(X2)
| is_bool(hAPP_a_bool(X1,X2))
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_2,axiom,
( ~ is_fun_a_bool(X1)
| ~ is_a(X2)
| is_bool(hAPP_a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_2,axiom,
( ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(insert1325755072e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( is_fun949378684l_bool(insert_fun_a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(insert_fun_a_bool(X1,X2))
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_2,axiom,
( ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(insert_fun_a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_pname(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_2,axiom,
( ~ is_pname(X1)
| ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(insert_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_0,axiom,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
( is_bool(hAPP_f1935102916l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_bool(hAPP_f1935102916l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_0,axiom,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2278_0,axiom,
( is_bool(hAPP_f621171935l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_bool(hAPP_f621171935l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( ~ is_fun_a_bool(X2)
| is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_0,axiom,
( is_bool(hAPP_bool_bool(X1,X2))
| ~ is_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_1,axiom,
( ~ is_bool(X2)
| is_bool(hAPP_bool_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2283_0,axiom,
( is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2))
| ~ is_pname(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( ~ is_pname(X2)
| is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2))
| ~ is_pname(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ is_pname(X2)
| is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2))
| ~ is_a(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( ~ is_a(X2)
| is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2))
| ~ is_a(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( ~ is_a(X2)
| is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( is_fun_pname_bool(image_1283814551_pname(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun_pname_bool(image_1283814551_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( is_fun_a_bool(image_876012084bool_a(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun_a_bool(image_876012084bool_a(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( is_fun_pname_bool(image_1854862208_pname(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun_pname_bool(image_1854862208_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( is_fun_a_bool(image_fun_a_bool_a(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun_a_bool(image_fun_a_bool_a(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
( is_fun1661590463l_bool(image_47868345e_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun1661590463l_bool(image_47868345e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_0,axiom,
( is_fun949378684l_bool(image_112932426a_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun949378684l_bool(image_112932426a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_0,axiom,
( is_fun_pname_bool(image_pname_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(image_pname_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2294_0,axiom,
( is_fun_pname_bool(image_a_pname(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( ~ is_fun_a_bool(X2)
| is_fun_pname_bool(image_a_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2295_0,axiom,
( is_fun_a_bool(image_a_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( ~ is_fun_a_bool(X2)
| is_fun_a_bool(image_a_a(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( is_fun_a_bool(cOMBS_a_bool_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ~ is_fun_a_bool(X2)
| is_fun_a_bool(cOMBS_a_bool_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2300_0,axiom,
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2))
| ~ is_fun1661590463l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ~ is_fun1661590463l_bool(X2)
| is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_0,axiom,
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2))
| ~ is_fun949378684l_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2301_1,axiom,
( ~ is_fun949378684l_bool(X2)
| is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2302_0,axiom,
( is_fun_pname_bool(cOMBB_647938656_pname(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ is_fun_pname_bool(X2)
| is_fun_pname_bool(cOMBB_647938656_pname(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( is_fun_a_bool(cOMBB_bool_bool_a(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ is_fun_a_bool(X2)
| is_fun_a_bool(cOMBB_bool_bool_a(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( hBOOL(hAPP_bool_bool(fNot,X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2327_0,axiom,
( hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( X1 != X2
| hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2330_0,axiom,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( ~ is_fun_a_bool(X1)
| is_fun949378684l_bool(p(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(collec1974731493e_bool(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_0,axiom,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(collect_fun_a_bool(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2333_0,axiom,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_1,axiom,
( ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(collect_pname(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2334_0,axiom,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_1,axiom,
( ~ is_fun_a_bool(X1)
| is_fun_a_bool(collect_a(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2335_0,axiom,
( collect_fun_a_bool(X1) = X1
| ~ is_fun949378684l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( ~ is_fun949378684l_bool(X1)
| collect_fun_a_bool(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2336_0,axiom,
( collec1974731493e_bool(X1) = X1
| ~ is_fun1661590463l_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( ~ is_fun1661590463l_bool(X1)
| collec1974731493e_bool(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2337_0,axiom,
( collect_pname(X1) = X1
| ~ is_fun_pname_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_1,axiom,
( ~ is_fun_pname_bool(X1)
| collect_pname(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_1997_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_2328_0,axiom,
hAPP_nat_nat(suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
hAPP_nat_nat(suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_1881_0,axiom,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))),X2)) = insert_fun_a_bool(X1,collect_fun_a_bool(X2)),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))),X2)) = insert1325755072e_bool(X1,collec1974731493e_bool(X2)),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X2)) = insert_fun_nat_bool(X1,collect_fun_nat_bool(X2)),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))),X2)) = insert_a(X1,collect_a(X2)),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),X2)) = insert_pname(X1,collect_pname(X2)),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)) = insert_nat(X1,collect_nat(X2)),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1893_0,axiom,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1978_0,axiom,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))) = insert_fun_a_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1979_0,axiom,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))) = insert1325755072e_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_0,axiom,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = insert_fun_nat_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))) = insert_a(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = insert_pname(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))) = insert_nat(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))) = insert_fun_a_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))) = insert1325755072e_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = insert_fun_nat_bool(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))) = insert_a(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))) = insert_pname(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))) = insert_nat(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_2025_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2060_0,axiom,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X3)),X2),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2078_0,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1)))),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2102_0,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2103_0,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2112_0,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X1))),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2113_0,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X1))),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X1))),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2115_0,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X1,X2))),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X1,X2))),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_0,axiom,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X1,X2))),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2175_0,axiom,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2178_0,axiom,
hAPP_bool_bool(hAPP_f1476298914l_bool(X1,X3),hAPP_f1664156314l_bool(X2,X3)) = hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
hAPP_bool_bool(hAPP_f1748468828l_bool(X1,X3),hAPP_f54304608l_bool(X2,X3)) = hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
hAPP_bool_bool(hAPP_f198738859l_bool(X1,X3),hAPP_fun_a_bool_bool(X2,X3)) = hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_0,axiom,
hAPP_bool_bool(hAPP_p393069232l_bool(X1,X3),hAPP_pname_bool(X2,X3)) = hAPP_pname_bool(cOMBS_568398431l_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2182_0,axiom,
hAPP_bool_bool(hAPP_n1006566506l_bool(X1,X3),hAPP_nat_bool(X2,X3)) = hAPP_nat_bool(cOMBS_nat_bool_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2183_0,axiom,
hAPP_bool_bool(hAPP_a_fun_bool_bool(X1,X3),hAPP_a_bool(X2,X3)) = hAPP_a_bool(cOMBS_a_bool_bool(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2184_0,axiom,
insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)) = image_pname_a(X1,insert_pname(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2187_0,axiom,
hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1))) = hAPP_nat_nat(suc,X1),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2192_0,axiom,
hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X1),X2),X3) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X1),X2),X3) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2194_0,axiom,
hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X1),X2),X3) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_0,axiom,
hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2202_0,axiom,
hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_p61793385e_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_0,axiom,
hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_p1534023578a_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_a_fun_a_bool(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2217_0,axiom,
hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
hAPP_f198738859l_bool(cOMBB_338059395a_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
hAPP_p393069232l_bool(cOMBB_675860798_pname(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_pname_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_nat_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
hAPP_f54304608l_bool(cOMBB_238756964t_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_a_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
hAPP_bool_bool(X1,hAPP_pname_bool(X2,X3)) = hAPP_pname_bool(cOMBB_647938656_pname(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
hAPP_nat_bool(cOMBB_bool_bool_nat(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_nat_bool(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
hAPP_bool_bool(X1,hAPP_a_bool(X2,X3)) = hAPP_a_bool(cOMBB_bool_bool_a(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
insert_a(X1,insert_a(X2,X3)) = insert_a(X2,insert_a(X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
insert_pname(X1,insert_pname(X2,X3)) = insert_pname(X2,insert_pname(X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
insert_nat(X1,insert_nat(X2,X3)) = insert_nat(X2,insert_nat(X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2254_0,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2262_0,axiom,
insert_a(X1,insert_a(X1,X2)) = insert_a(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
insert_pname(X1,insert_pname(X1,X2)) = insert_pname(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
insert_nat(X1,insert_nat(X1,X2)) = insert_nat(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2266_0,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2305_0,axiom,
is_bool(hAPP_f1295398978l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
is_bool(hAPP_f595608956l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
is_bool(hAPP_f1363661463l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2308_0,axiom,
is_bool(hAPP_f937997336l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2309_0,axiom,
is_bool(hAPP_f389811538l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
is_bool(hAPP_f292226953l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_0,axiom,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2313_0,axiom,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
is_fun_pname_bool(image_1604018183_pname(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
is_fun_a_bool(image_526090948bool_a(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
is_fun_pname_bool(image_1705983821_pname(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2318_0,axiom,
is_fun_a_bool(image_349102846bool_a(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
is_fun_pname_bool(image_990671762_pname(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_0,axiom,
is_fun_a_bool(image_573985017bool_a(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_0,axiom,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
is_fun_pname_bool(image_nat_pname(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
is_fun_a_bool(image_nat_a(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2338_0,axiom,
is_pname(undefined_pname(pname)),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
is_a(undefined_a(x_a)),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
collect_nat(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
collect_fun_nat_bool(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
is_fun949378684l_bool(finite_finite_a),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('<stdin>',conj_6) ).
fof(c_0_1_002,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
file('<stdin>',conj_2) ).
fof(c_0_2_003,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
file('<stdin>',conj_5) ).
fof(c_0_3_004,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
file('<stdin>',conj_3) ).
fof(c_0_4_005,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('<stdin>',conj_1) ).
fof(c_0_5_006,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('<stdin>',conj_4) ).
fof(c_0_6_007,hypothesis,
! [X1,X2] :
( ( is_fun1661590463l_bool(X1)
& is_fun_pname_bool(X2) )
=> is_bool(hAPP_f1664156314l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(c_0_7_008,hypothesis,
! [X1,X2] :
( ( is_fun949378684l_bool(X1)
& is_fun_a_bool(X2) )
=> is_bool(hAPP_fun_a_bool_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(c_0_8_009,hypothesis,
! [X1,X2] :
( ( is_a(X1)
& is_fun_a_bool(X2) )
=> is_fun_a_bool(insert_a(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oinsert_000t__a) ).
fof(c_0_9_010,hypothesis,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
fof(c_0_10_011,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(c_0_11_012,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_a(hAPP_pname_a(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
fof(c_0_12_013,hypothesis,
! [X1,X2] :
( is_a(X2)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2)) ),
file('<stdin>',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).
fof(c_0_13_014,hypothesis,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_a_bool(image_pname_a(X1,X2)) ),
file('<stdin>',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
fof(c_0_14_015,hypothesis,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(c_0_15_016,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('<stdin>',conj_0) ).
fof(c_0_16_017,hypothesis,
is_pname(pn),
file('<stdin>',gsy_v_pn) ).
fof(c_0_17_018,hypothesis,
is_fun_pname_bool(u),
file('<stdin>',gsy_v_U) ).
fof(c_0_18_019,hypothesis,
is_fun_a_bool(g),
file('<stdin>',gsy_v_G) ).
fof(c_0_19_020,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
file('<stdin>',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
fof(c_0_20_021,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_21_022,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
c_0_1 ).
fof(c_0_22_023,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_23_024,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
c_0_3 ).
fof(c_0_24_025,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
c_0_4 ).
fof(c_0_25_026,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
c_0_5 ).
fof(c_0_26_027,hypothesis,
! [X1,X2] :
( ( is_fun1661590463l_bool(X1)
& is_fun_pname_bool(X2) )
=> is_bool(hAPP_f1664156314l_bool(X1,X2)) ),
c_0_6 ).
fof(c_0_27_028,hypothesis,
! [X1,X2] :
( ( is_fun949378684l_bool(X1)
& is_fun_a_bool(X2) )
=> is_bool(hAPP_fun_a_bool_bool(X1,X2)) ),
c_0_7 ).
fof(c_0_28_029,hypothesis,
! [X1,X2] :
( ( is_a(X1)
& is_fun_a_bool(X2) )
=> is_fun_a_bool(insert_a(X1,X2)) ),
c_0_8 ).
fof(c_0_29_030,hypothesis,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2)) ),
c_0_9 ).
fof(c_0_30_031,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(X1,X2)) ),
c_0_10 ).
fof(c_0_31_032,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_a(hAPP_pname_a(X1,X2)) ),
c_0_11 ).
fof(c_0_32_033,hypothesis,
! [X1,X2] :
( is_a(X2)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2)) ),
c_0_12 ).
fof(c_0_33_034,hypothesis,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_a_bool(image_pname_a(X1,X2)) ),
c_0_13 ).
fof(c_0_34_035,hypothesis,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
c_0_14 ).
fof(c_0_35_036,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
c_0_15 ).
fof(c_0_36_037,hypothesis,
is_pname(pn),
c_0_16 ).
fof(c_0_37_038,hypothesis,
is_fun_pname_bool(u),
c_0_17 ).
fof(c_0_38_039,hypothesis,
is_fun_a_bool(g),
c_0_18 ).
fof(c_0_39_040,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
c_0_19 ).
fof(c_0_40_041,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
c_0_20 ).
fof(c_0_41_042,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
c_0_21 ).
fof(c_0_42_043,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
c_0_22 ).
fof(c_0_43_044,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
c_0_23 ).
fof(c_0_44_045,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
c_0_24 ).
fof(c_0_45_046,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
c_0_25 ).
fof(c_0_46_047,hypothesis,
! [X3,X4] :
( ~ is_fun1661590463l_bool(X3)
| ~ is_fun_pname_bool(X4)
| is_bool(hAPP_f1664156314l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_47_048,hypothesis,
! [X3,X4] :
( ~ is_fun949378684l_bool(X3)
| ~ is_fun_a_bool(X4)
| is_bool(hAPP_fun_a_bool_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_48_049,hypothesis,
! [X3,X4] :
( ~ is_a(X3)
| ~ is_fun_a_bool(X4)
| is_fun_a_bool(insert_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_49_050,hypothesis,
! [X3,X4] :
( ~ is_fun_a_bool(X4)
| is_fun949378684l_bool(hAPP_f1631501043l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
fof(c_0_50_051,hypothesis,
! [X3,X4] :
( ~ is_pname(X4)
| is_fun1661590463l_bool(hAPP_p338031245l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_51_052,hypothesis,
! [X3,X4] :
( ~ is_pname(X4)
| is_a(hAPP_pname_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
fof(c_0_52_053,hypothesis,
! [X3,X4] :
( ~ is_a(X4)
| is_fun949378684l_bool(hAPP_a85458249l_bool(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])]) ).
fof(c_0_53_054,hypothesis,
! [X3,X4] :
( ~ is_fun_pname_bool(X4)
| is_fun_a_bool(image_pname_a(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
fof(c_0_54_055,hypothesis,
! [X3,X4] : is_bool(hAPP_nat_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_55_056,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
c_0_35 ).
fof(c_0_56_057,hypothesis,
is_pname(pn),
c_0_36 ).
fof(c_0_57_058,hypothesis,
is_fun_pname_bool(u),
c_0_37 ).
fof(c_0_58_059,hypothesis,
is_fun_a_bool(g),
c_0_38 ).
fof(c_0_59_060,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
c_0_39 ).
cnf(c_0_60_061,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_61_062,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_62_063,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_63_064,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_64_065,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_65_066,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_66_067,hypothesis,
( is_bool(hAPP_f1664156314l_bool(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_67_068,hypothesis,
( is_bool(hAPP_fun_a_bool_bool(X1,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_68_069,hypothesis,
( is_fun_a_bool(insert_a(X1,X2))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_69_070,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_70_071,hypothesis,
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X1,X2))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_71_072,hypothesis,
( is_a(hAPP_pname_a(X1,X2))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_72_073,hypothesis,
( is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_73_074,hypothesis,
( is_fun_a_bool(image_pname_a(X1,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_74_075,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_75_076,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_76_077,hypothesis,
is_pname(pn),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_77_078,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_78_079,hypothesis,
is_fun_a_bool(g),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_79_080,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_80_081,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
c_0_60,
[final] ).
cnf(c_0_81_082,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
c_0_61,
[final] ).
cnf(c_0_82_083,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
c_0_62,
[final] ).
cnf(c_0_83_084,hypothesis,
hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) = hAPP_fun_a_bool_nat(finite_card_a,g),
c_0_63,
[final] ).
cnf(c_0_84_085,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
c_0_64,
[final] ).
cnf(c_0_85_086,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
c_0_65,
[final] ).
cnf(c_0_86_087,hypothesis,
( is_bool(hAPP_f1664156314l_bool(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ is_fun1661590463l_bool(X1) ),
c_0_66,
[final] ).
cnf(c_0_87_088,hypothesis,
( is_bool(hAPP_fun_a_bool_bool(X1,X2))
| ~ is_fun_a_bool(X2)
| ~ is_fun949378684l_bool(X1) ),
c_0_67,
[final] ).
cnf(c_0_88_089,hypothesis,
( is_fun_a_bool(insert_a(X1,X2))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ),
c_0_68,
[final] ).
cnf(c_0_89_090,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2))
| ~ is_fun_a_bool(X2) ),
c_0_69,
[final] ).
cnf(c_0_90_091,hypothesis,
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X1,X2))
| ~ is_pname(X2) ),
c_0_70,
[final] ).
cnf(c_0_91_092,hypothesis,
( is_a(hAPP_pname_a(X1,X2))
| ~ is_pname(X2) ),
c_0_71,
[final] ).
cnf(c_0_92_093,hypothesis,
( is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2))
| ~ is_a(X2) ),
c_0_72,
[final] ).
cnf(c_0_93_094,hypothesis,
( is_fun_a_bool(image_pname_a(X1,X2))
| ~ is_fun_pname_bool(X2) ),
c_0_73,
[final] ).
cnf(c_0_94_095,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
c_0_74,
[final] ).
cnf(c_0_95_096,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
c_0_75,
[final] ).
cnf(c_0_96_097,hypothesis,
is_pname(pn),
c_0_76,
[final] ).
cnf(c_0_97_098,hypothesis,
is_fun_pname_bool(u),
c_0_77,
[final] ).
cnf(c_0_98_099,hypothesis,
is_fun_a_bool(g),
c_0_78,
[final] ).
cnf(c_0_99_100,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
c_0_79,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_876,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p',c_0_1938_1) ).
cnf(c_2621,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(copy,[status(esa)],[c_876]) ).
cnf(c_89524,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,pn)),image_pname_a(X0,u))) ),
inference(instantiation,[status(thm)],[c_2621]) ).
cnf(c_124699,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
inference(instantiation,[status(thm)],[c_89524]) ).
cnf(c_988,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p',c_0_1889_2) ).
cnf(c_2733,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
inference(copy,[status(esa)],[c_988]) ).
cnf(c_89751,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
inference(instantiation,[status(thm)],[c_2733]) ).
cnf(c_1183,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p',c_0_84) ).
cnf(c_1184,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p',c_0_85) ).
cnf(c_1179,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p',c_0_80) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_124699,c_89751,c_1183,c_1184,c_1179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 02:08:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.19/0.48 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.48 % FOF problem with conjecture
% 0.19/0.48 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_cd01d4 | grep -v "SZS"
% 0.19/0.51
% 0.19/0.51 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.51
% 0.19/0.51 %
% 0.19/0.51 % ------ iProver source info
% 0.19/0.51
% 0.19/0.51 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.51 % git: non_committed_changes: true
% 0.19/0.51 % git: last_make_outside_of_git: true
% 0.19/0.51
% 0.19/0.51 %
% 0.19/0.51 % ------ Input Options
% 0.19/0.51
% 0.19/0.51 % --out_options all
% 0.19/0.51 % --tptp_safe_out true
% 0.19/0.51 % --problem_path ""
% 0.19/0.51 % --include_path ""
% 0.19/0.51 % --clausifier .//eprover
% 0.19/0.51 % --clausifier_options --tstp-format
% 0.19/0.51 % --stdin false
% 0.19/0.51 % --dbg_backtrace false
% 0.19/0.51 % --dbg_dump_prop_clauses false
% 0.19/0.51 % --dbg_dump_prop_clauses_file -
% 0.19/0.51 % --dbg_out_stat false
% 0.19/0.51
% 0.19/0.51 % ------ General Options
% 0.19/0.51
% 0.19/0.51 % --fof false
% 0.19/0.51 % --time_out_real 150.
% 0.19/0.51 % --time_out_prep_mult 0.2
% 0.19/0.51 % --time_out_virtual -1.
% 0.19/0.51 % --schedule none
% 0.19/0.51 % --ground_splitting input
% 0.19/0.51 % --splitting_nvd 16
% 0.19/0.51 % --non_eq_to_eq false
% 0.19/0.51 % --prep_gs_sim true
% 0.19/0.51 % --prep_unflatten false
% 0.19/0.51 % --prep_res_sim true
% 0.19/0.51 % --prep_upred true
% 0.19/0.51 % --res_sim_input true
% 0.19/0.51 % --clause_weak_htbl true
% 0.19/0.51 % --gc_record_bc_elim false
% 0.19/0.51 % --symbol_type_check false
% 0.19/0.51 % --clausify_out false
% 0.19/0.51 % --large_theory_mode false
% 0.19/0.51 % --prep_sem_filter none
% 0.19/0.51 % --prep_sem_filter_out false
% 0.19/0.51 % --preprocessed_out false
% 0.19/0.51 % --sub_typing false
% 0.19/0.51 % --brand_transform false
% 0.19/0.51 % --pure_diseq_elim true
% 0.19/0.51 % --min_unsat_core false
% 0.19/0.51 % --pred_elim true
% 0.19/0.51 % --add_important_lit false
% 0.19/0.51 % --soft_assumptions false
% 0.19/0.51 % --reset_solvers false
% 0.19/0.51 % --bc_imp_inh []
% 0.19/0.51 % --conj_cone_tolerance 1.5
% 0.19/0.51 % --prolific_symb_bound 500
% 0.19/0.51 % --lt_threshold 2000
% 0.19/0.51
% 0.19/0.51 % ------ SAT Options
% 0.19/0.51
% 0.19/0.51 % --sat_mode false
% 0.19/0.51 % --sat_fm_restart_options ""
% 0.19/0.51 % --sat_gr_def false
% 0.19/0.51 % --sat_epr_types true
% 0.19/0.51 % --sat_non_cyclic_types false
% 0.19/0.51 % --sat_finite_models false
% 0.19/0.51 % --sat_fm_lemmas false
% 0.19/0.51 % --sat_fm_prep false
% 0.19/0.51 % --sat_fm_uc_incr true
% 0.19/0.51 % --sat_out_model small
% 0.19/0.51 % --sat_out_clauses false
% 0.19/0.51
% 0.19/0.51 % ------ QBF Options
% 0.19/0.51
% 0.19/0.51 % --qbf_mode false
% 0.19/0.51 % --qbf_elim_univ true
% 0.19/0.51 % --qbf_sk_in true
% 0.19/0.51 % --qbf_pred_elim true
% 0.19/0.51 % --qbf_split 32
% 0.19/0.51
% 0.19/0.51 % ------ BMC1 Options
% 0.19/0.51
% 0.19/0.51 % --bmc1_incremental false
% 0.19/0.51 % --bmc1_axioms reachable_all
% 0.19/0.51 % --bmc1_min_bound 0
% 0.19/0.51 % --bmc1_max_bound -1
% 0.19/0.51 % --bmc1_max_bound_default -1
% 0.19/0.51 % --bmc1_symbol_reachability true
% 0.19/0.51 % --bmc1_property_lemmas false
% 0.19/0.51 % --bmc1_k_induction false
% 0.19/0.51 % --bmc1_non_equiv_states false
% 0.19/0.51 % --bmc1_deadlock false
% 0.19/0.51 % --bmc1_ucm false
% 0.19/0.51 % --bmc1_add_unsat_core none
% 0.19/0.51 % --bmc1_unsat_core_children false
% 0.19/0.51 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.51 % --bmc1_out_stat full
% 0.19/0.51 % --bmc1_ground_init false
% 0.19/0.51 % --bmc1_pre_inst_next_state false
% 0.19/0.51 % --bmc1_pre_inst_state false
% 0.19/0.51 % --bmc1_pre_inst_reach_state false
% 0.19/0.51 % --bmc1_out_unsat_core false
% 0.19/0.51 % --bmc1_aig_witness_out false
% 0.19/0.51 % --bmc1_verbose false
% 0.19/0.51 % --bmc1_dump_clauses_tptp false
% 1.31/1.54 % --bmc1_dump_unsat_core_tptp false
% 1.31/1.54 % --bmc1_dump_file -
% 1.31/1.54 % --bmc1_ucm_expand_uc_limit 128
% 1.31/1.54 % --bmc1_ucm_n_expand_iterations 6
% 1.31/1.54 % --bmc1_ucm_extend_mode 1
% 1.31/1.54 % --bmc1_ucm_init_mode 2
% 1.31/1.54 % --bmc1_ucm_cone_mode none
% 1.31/1.54 % --bmc1_ucm_reduced_relation_type 0
% 1.31/1.54 % --bmc1_ucm_relax_model 4
% 1.31/1.54 % --bmc1_ucm_full_tr_after_sat true
% 1.31/1.54 % --bmc1_ucm_expand_neg_assumptions false
% 1.31/1.54 % --bmc1_ucm_layered_model none
% 1.31/1.54 % --bmc1_ucm_max_lemma_size 10
% 1.31/1.54
% 1.31/1.54 % ------ AIG Options
% 1.31/1.54
% 1.31/1.54 % --aig_mode false
% 1.31/1.54
% 1.31/1.54 % ------ Instantiation Options
% 1.31/1.54
% 1.31/1.54 % --instantiation_flag true
% 1.31/1.54 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.31/1.54 % --inst_solver_per_active 750
% 1.31/1.54 % --inst_solver_calls_frac 0.5
% 1.31/1.54 % --inst_passive_queue_type priority_queues
% 1.31/1.54 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.31/1.54 % --inst_passive_queues_freq [25;2]
% 1.31/1.54 % --inst_dismatching true
% 1.31/1.54 % --inst_eager_unprocessed_to_passive true
% 1.31/1.54 % --inst_prop_sim_given true
% 1.31/1.54 % --inst_prop_sim_new false
% 1.31/1.54 % --inst_orphan_elimination true
% 1.31/1.54 % --inst_learning_loop_flag true
% 1.31/1.54 % --inst_learning_start 3000
% 1.31/1.54 % --inst_learning_factor 2
% 1.31/1.54 % --inst_start_prop_sim_after_learn 3
% 1.31/1.54 % --inst_sel_renew solver
% 1.31/1.54 % --inst_lit_activity_flag true
% 1.31/1.54 % --inst_out_proof true
% 1.31/1.54
% 1.31/1.54 % ------ Resolution Options
% 1.31/1.54
% 1.31/1.54 % --resolution_flag true
% 1.31/1.54 % --res_lit_sel kbo_max
% 1.31/1.54 % --res_to_prop_solver none
% 1.31/1.54 % --res_prop_simpl_new false
% 1.31/1.54 % --res_prop_simpl_given false
% 1.31/1.54 % --res_passive_queue_type priority_queues
% 1.31/1.54 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.31/1.54 % --res_passive_queues_freq [15;5]
% 1.31/1.54 % --res_forward_subs full
% 1.31/1.54 % --res_backward_subs full
% 1.31/1.54 % --res_forward_subs_resolution true
% 1.31/1.54 % --res_backward_subs_resolution true
% 1.31/1.54 % --res_orphan_elimination false
% 1.31/1.54 % --res_time_limit 1000.
% 1.31/1.54 % --res_out_proof true
% 1.31/1.54 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s
% 1.31/1.54 % --modulo true
% 1.31/1.54
% 1.31/1.54 % ------ Combination Options
% 1.31/1.54
% 1.31/1.54 % --comb_res_mult 1000
% 1.31/1.54 % --comb_inst_mult 300
% 1.31/1.54 % ------
% 1.31/1.54
% 1.31/1.54 % ------ Parsing...% successful
% 1.31/1.54
% 1.31/1.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e snvd_s sp: 0 0s snvd_e %
% 1.31/1.54
% 1.31/1.54 % ------ Proving...
% 1.31/1.54 % ------ Problem Properties
% 1.31/1.54
% 1.31/1.54 %
% 1.31/1.54 % EPR false
% 1.31/1.54 % Horn false
% 1.31/1.54 % Has equality true
% 1.31/1.54
% 1.31/1.54 % % ------ Input Options Time Limit: Unbounded
% 1.31/1.54
% 1.31/1.54
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 Compiling...
% 1.31/1.54 Loading plugin: done.
% 1.31/1.54 % % ------ Current options:
% 1.31/1.54
% 1.31/1.54 % ------ Input Options
% 1.31/1.54
% 1.31/1.54 % --out_options all
% 1.31/1.54 % --tptp_safe_out true
% 1.31/1.54 % --problem_path ""
% 1.31/1.54 % --include_path ""
% 1.31/1.54 % --clausifier .//eprover
% 1.31/1.54 % --clausifier_options --tstp-format
% 1.31/1.54 % --stdin false
% 1.31/1.54 % --dbg_backtrace false
% 1.31/1.54 % --dbg_dump_prop_clauses false
% 1.31/1.54 % --dbg_dump_prop_clauses_file -
% 1.31/1.54 % --dbg_out_stat false
% 1.31/1.54
% 1.31/1.54 % ------ General Options
% 1.31/1.54
% 1.31/1.54 % --fof false
% 1.31/1.54 % --time_out_real 150.
% 1.31/1.54 % --time_out_prep_mult 0.2
% 1.31/1.54 % --time_out_virtual -1.
% 1.31/1.54 % --schedule none
% 1.31/1.54 % --ground_splitting input
% 1.31/1.54 % --splitting_nvd 16
% 1.31/1.54 % --non_eq_to_eq false
% 1.31/1.54 % --prep_gs_sim true
% 1.31/1.54 % --prep_unflatten false
% 1.31/1.54 % --prep_res_sim true
% 1.31/1.54 % --prep_upred true
% 1.31/1.54 % --res_sim_input true
% 1.31/1.54 % --clause_weak_htbl true
% 1.31/1.54 % --gc_record_bc_elim false
% 1.31/1.54 % --symbol_type_check false
% 1.31/1.54 % --clausify_out false
% 1.31/1.54 % --large_theory_mode false
% 1.31/1.54 % --prep_sem_filter none
% 1.31/1.54 % --prep_sem_filter_out false
% 1.31/1.54 % --preprocessed_out false
% 1.31/1.54 % --sub_typing false
% 1.31/1.54 % --brand_transform false
% 1.31/1.54 % --pure_diseq_elim true
% 1.31/1.54 % --min_unsat_core false
% 1.31/1.54 % --pred_elim true
% 1.31/1.54 % --add_important_lit false
% 1.31/1.54 % --soft_assumptions false
% 1.31/1.54 % --reset_solvers false
% 1.31/1.54 % --bc_imp_inh []
% 1.31/1.54 % --conj_cone_tolerance 1.5
% 1.31/1.54 % --prolific_symb_bound 500
% 1.31/1.54 % --lt_threshold 2000
% 1.31/1.54
% 1.31/1.54 % ------ SAT Options
% 1.31/1.54
% 1.31/1.54 % --sat_mode false
% 1.31/1.54 % --sat_fm_restart_options ""
% 1.31/1.54 % --sat_gr_def false
% 1.31/1.54 % --sat_epr_types true
% 1.31/1.54 % --sat_non_cyclic_types false
% 1.31/1.54 % --sat_finite_models false
% 1.31/1.54 % --sat_fm_lemmas false
% 1.31/1.54 % --sat_fm_prep false
% 1.31/1.54 % --sat_fm_uc_incr true
% 1.31/1.54 % --sat_out_model small
% 1.31/1.54 % --sat_out_clauses false
% 1.31/1.54
% 1.31/1.54 % ------ QBF Options
% 1.31/1.54
% 1.31/1.54 % --qbf_mode false
% 1.31/1.54 % --qbf_elim_univ true
% 1.31/1.54 % --qbf_sk_in true
% 1.31/1.54 % --qbf_pred_elim true
% 1.31/1.54 % --qbf_split 32
% 1.31/1.54
% 1.31/1.54 % ------ BMC1 Options
% 1.31/1.54
% 1.31/1.54 % --bmc1_incremental false
% 1.31/1.54 % --bmc1_axioms reachable_all
% 1.31/1.54 % --bmc1_min_bound 0
% 1.31/1.54 % --bmc1_max_bound -1
% 1.31/1.54 % --bmc1_max_bound_default -1
% 1.31/1.54 % --bmc1_symbol_reachability true
% 1.31/1.54 % --bmc1_property_lemmas false
% 1.31/1.54 % --bmc1_k_induction false
% 1.31/1.54 % --bmc1_non_equiv_states false
% 1.31/1.54 % --bmc1_deadlock false
% 1.31/1.54 % --bmc1_ucm false
% 1.31/1.54 % --bmc1_add_unsat_core none
% 1.31/1.54 % --bmc1_unsat_core_children false
% 1.31/1.54 % --bmc1_unsat_core_extrapolate_axioms false
% 1.31/1.54 % --bmc1_out_stat full
% 1.31/1.54 % --bmc1_ground_init false
% 1.31/1.54 % --bmc1_pre_inst_next_state false
% 1.31/1.54 % --bmc1_pre_inst_state false
% 1.31/1.54 % --bmc1_pre_inst_reach_state false
% 1.31/1.54 % --bmc1_out_unsat_core false
% 1.31/1.54 % --bmc1_aig_witness_out false
% 1.31/1.54 % --bmc1_verbose false
% 1.31/1.54 % --bmc1_dump_clauses_tptp false
% 1.31/1.54 % --bmc1_dump_unsat_core_tptp false
% 1.31/1.54 % --bmc1_dump_file -
% 1.31/1.54 % --bmc1_ucm_expand_uc_limit 128
% 1.31/1.54 % --bmc1_ucm_n_expand_iterations 6
% 1.31/1.54 % --bmc1_ucm_extend_mode 1
% 1.31/1.54 % --bmc1_ucm_init_mode 2
% 1.31/1.54 % --bmc1_ucm_cone_mode none
% 1.31/1.54 % --bmc1_ucm_reduced_relation_type 0
% 1.31/1.54 % --bmc1_ucm_relax_model 4
% 1.31/1.54 % --bmc1_ucm_full_tr_after_sat true
% 1.31/1.54 % --bmc1_ucm_expand_neg_assumptions false
% 1.31/1.54 % --bmc1_ucm_layered_model none
% 1.31/1.54 % --bmc1_ucm_max_lemma_size 10
% 1.31/1.54
% 1.31/1.54 % ------ AIG Options
% 1.31/1.54
% 1.31/1.54 % --aig_mode false
% 1.31/1.54
% 1.31/1.54 % ------ Instantiation Options
% 1.31/1.54
% 1.31/1.54 % --instantiation_flag true
% 1.31/1.54 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.31/1.54 % --inst_solver_per_active 750
% 1.31/1.54 % --inst_solver_calls_frac 0.5
% 1.31/1.54 % --inst_passive_queue_type priority_queues
% 1.31/1.54 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.27/150.51 % --inst_passive_queues_freq [25;2]
% 150.27/150.51 % --inst_dismatching true
% 150.27/150.51 % --inst_eager_unprocessed_to_passive true
% 150.27/150.51 % --inst_prop_sim_given true
% 150.27/150.51 % --inst_prop_sim_new false
% 150.27/150.51 % --inst_orphan_elimination true
% 150.27/150.51 % --inst_learning_loop_flag true
% 150.27/150.51 % --inst_learning_start 3000
% 150.27/150.51 % --inst_learning_factor 2
% 150.27/150.51 % --inst_start_prop_sim_after_learn 3
% 150.27/150.51 % --inst_sel_renew solver
% 150.27/150.51 % --inst_lit_activity_flag true
% 150.27/150.51 % --inst_out_proof true
% 150.27/150.51
% 150.27/150.51 % ------ Resolution Options
% 150.27/150.51
% 150.27/150.51 % --resolution_flag true
% 150.27/150.51 % --res_lit_sel kbo_max
% 150.27/150.51 % --res_to_prop_solver none
% 150.27/150.51 % --res_prop_simpl_new false
% 150.27/150.51 % --res_prop_simpl_given false
% 150.27/150.51 % --res_passive_queue_type priority_queues
% 150.27/150.51 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.27/150.51 % --res_passive_queues_freq [15;5]
% 150.27/150.51 % --res_forward_subs full
% 150.27/150.51 % --res_backward_subs full
% 150.27/150.51 % --res_forward_subs_resolution true
% 150.27/150.51 % --res_backward_subs_resolution true
% 150.27/150.51 % --res_orphan_elimination false
% 150.27/150.51 % --res_time_limit 1000.
% 150.27/150.51 % --res_out_proof true
% 150.27/150.51 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s
% 150.27/150.51 % --modulo true
% 150.27/150.51
% 150.27/150.51 % ------ Combination Options
% 150.27/150.51
% 150.27/150.51 % --comb_res_mult 1000
% 150.27/150.51 % --comb_inst_mult 300
% 150.27/150.51 % ------
% 150.27/150.51
% 150.27/150.51
% 150.27/150.51
% 150.27/150.51 % ------ Proving...
% 150.27/150.51 %
% 150.27/150.51
% 150.27/150.51
% 150.27/150.51 % Time Out Real
% 150.27/150.51
% 150.27/150.51 % ------ Statistics
% 150.27/150.51
% 150.27/150.51 % ------ General
% 150.27/150.51
% 150.27/150.51 % num_of_input_clauses: 707
% 150.27/150.51 % num_of_input_neg_conjectures: 1
% 150.27/150.51 % num_of_splits: 0
% 150.27/150.51 % num_of_split_atoms: 0
% 150.27/150.51 % num_of_sem_filtered_clauses: 0
% 150.27/150.51 % num_of_subtypes: 0
% 150.27/150.51 % monotx_restored_types: 0
% 150.27/150.51 % sat_num_of_epr_types: 0
% 150.27/150.51 % sat_num_of_non_cyclic_types: 0
% 150.27/150.51 % sat_guarded_non_collapsed_types: 0
% 150.27/150.51 % is_epr: 0
% 150.27/150.51 % is_horn: 0
% 150.27/150.51 % has_eq: 1
% 150.27/150.51 % num_pure_diseq_elim: 0
% 150.27/150.51 % simp_replaced_by: 0
% 150.27/150.51 % res_preprocessed: 21
% 150.27/150.51 % prep_upred: 0
% 150.27/150.51 % prep_unflattend: 3
% 150.27/150.51 % pred_elim_cands: 7
% 150.27/150.51 % pred_elim: 6
% 150.27/150.51 % pred_elim_cl: 10
% 150.27/150.51 % pred_elim_cycles: 7
% 150.27/150.51 % forced_gc_time: 0
% 150.27/150.51 % gc_basic_clause_elim: 0
% 150.27/150.51 % parsing_time: 0.039
% 150.27/150.51 % sem_filter_time: 0.
% 150.27/150.51 % pred_elim_time: 0.
% 150.27/150.51 % out_proof_time: 0.
% 150.27/150.51 % monotx_time: 0.
% 150.27/150.51 % subtype_inf_time: 0.
% 150.27/150.51 % unif_index_cands_time: 0.746
% 150.27/150.51 % unif_index_add_time: 0.122
% 150.27/150.51 % total_time: 150.017
% 150.27/150.51 % num_of_symbols: 274
% 150.27/150.51 % num_of_terms: 889968
% 150.27/150.51
% 150.27/150.51 % ------ Propositional Solver
% 150.27/150.51
% 150.27/150.51 % prop_solver_calls: 28
% 150.27/150.51 % prop_fast_solver_calls: 67
% 150.27/150.51 % prop_num_of_clauses: 62104
% 150.27/150.51 % prop_preprocess_simplified: 63801
% 150.27/150.51 % prop_fo_subsumed: 0
% 150.27/150.51 % prop_solver_time: 0.028
% 150.27/150.51 % prop_fast_solver_time: 0.
% 150.27/150.51 % prop_unsat_core_time: 0.
% 150.27/150.51
% 150.27/150.51 % ------ QBF
% 150.27/150.51
% 150.27/150.51 % qbf_q_res: 0
% 150.27/150.51 % qbf_num_tautologies: 0
% 150.27/150.51 % qbf_prep_cycles: 0
% 150.27/150.51
% 150.27/150.51 % ------ BMC1
% 150.27/150.51
% 150.27/150.51 % bmc1_current_bound: -1
% 150.27/150.51 % bmc1_last_solved_bound: -1
% 150.27/150.51 % bmc1_unsat_core_size: -1
% 150.27/150.51 % bmc1_unsat_core_parents_size: -1
% 150.27/150.51 % bmc1_merge_next_fun: 0
% 150.27/150.51 % bmc1_unsat_core_clauses_time: 0.
% 150.27/150.52
% 150.27/150.52 % ------ Instantiation
% 150.27/150.52
% 150.27/150.52 % inst_num_of_clauses: 24695
% 150.27/150.52 % inst_num_in_passive: 17515
% 150.27/150.52 % inst_num_in_active: 3690
% 150.27/150.52 % inst_num_in_unprocessed: 3487
% 150.27/150.52 % inst_num_of_loops: 4499
% 150.27/150.52 % inst_num_of_learning_restarts: 1
% 150.27/150.52 % inst_num_moves_active_passive: 805
% 150.27/150.52 % inst_lit_activity: 4012
% 150.27/150.52 % inst_lit_activity_moves: 2
% 150.27/150.52 % inst_num_tautologies: 3
% 150.27/150.52 % inst_num_prop_implied: 0
% 150.27/150.52 % inst_num_existing_simplified: 0
% 150.27/150.52 % inst_num_eq_res_simplified: 0
% 150.27/150.52 % inst_num_child_elim: 0
% 150.27/150.52 % inst_num_of_dismatching_blockings: 89066
% 150.27/150.52 % inst_num_of_non_proper_insts: 22194
% 150.27/150.52 % inst_num_of_duplicates: 13168
% 150.27/150.52 % inst_inst_num_from_inst_to_res: 0
% 150.27/150.52 % inst_dismatching_checking_time: 1.837
% 150.27/150.52
% 150.27/150.52 % ------ Resolution
% 150.27/150.52
% 150.27/150.52 % res_num_of_clauses: 519623
% 150.27/150.52 % res_num_in_passive: 503466
% 150.27/150.52 % res_num_in_active: 15931
% 150.27/150.52 % res_num_of_loops: 25441
% 150.27/150.52 % res_forward_subset_subsumed: 381868
% 150.27/150.52 % res_backward_subset_subsumed: 249
% 150.27/150.52 % res_forward_subsumed: 9810
% 150.27/150.52 % res_backward_subsumed: 86
% 150.27/150.52 % res_forward_subsumption_resolution: 741
% 150.27/150.52 % res_backward_subsumption_resolution: 1
% 150.27/150.52 % res_clause_to_clause_subsumption: 702192
% 150.27/150.52 % res_orphan_elimination: 0
% 150.27/150.52 % res_tautology_del: 9813
% 150.27/150.52 % res_num_eq_res_simplified: 6523
% 150.27/150.52 % res_num_sel_changes: 0
% 150.27/150.52 % res_moves_from_active_to_pass: 0
% 150.27/150.52
% 150.27/150.52 % Status Unknown
% 150.33/150.65 % Orienting using strategy ClausalAll
% 150.33/150.65 % FOF problem with conjecture
% 150.33/150.65 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_abd8b5.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_6794a6 | grep -v "SZS"
% 150.33/150.66
% 150.33/150.66 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.33/150.66
% 150.33/150.66 %
% 150.33/150.66 % ------ iProver source info
% 150.33/150.66
% 150.33/150.66 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.33/150.66 % git: non_committed_changes: true
% 150.33/150.66 % git: last_make_outside_of_git: true
% 150.33/150.66
% 150.33/150.66 %
% 150.33/150.66 % ------ Input Options
% 150.33/150.66
% 150.33/150.66 % --out_options all
% 150.33/150.66 % --tptp_safe_out true
% 150.33/150.66 % --problem_path ""
% 150.33/150.66 % --include_path ""
% 150.33/150.66 % --clausifier .//eprover
% 150.33/150.66 % --clausifier_options --tstp-format
% 150.33/150.66 % --stdin false
% 150.33/150.66 % --dbg_backtrace false
% 150.33/150.66 % --dbg_dump_prop_clauses false
% 150.33/150.66 % --dbg_dump_prop_clauses_file -
% 150.33/150.66 % --dbg_out_stat false
% 150.33/150.66
% 150.33/150.66 % ------ General Options
% 150.33/150.66
% 150.33/150.66 % --fof false
% 150.33/150.66 % --time_out_real 150.
% 150.33/150.66 % --time_out_prep_mult 0.2
% 150.33/150.66 % --time_out_virtual -1.
% 150.33/150.66 % --schedule none
% 150.33/150.66 % --ground_splitting input
% 150.33/150.66 % --splitting_nvd 16
% 150.33/150.66 % --non_eq_to_eq false
% 150.33/150.66 % --prep_gs_sim true
% 150.33/150.66 % --prep_unflatten false
% 150.33/150.66 % --prep_res_sim true
% 150.33/150.66 % --prep_upred true
% 150.33/150.66 % --res_sim_input true
% 150.33/150.66 % --clause_weak_htbl true
% 150.33/150.66 % --gc_record_bc_elim false
% 150.33/150.66 % --symbol_type_check false
% 150.33/150.66 % --clausify_out false
% 150.33/150.66 % --large_theory_mode false
% 150.33/150.66 % --prep_sem_filter none
% 150.33/150.66 % --prep_sem_filter_out false
% 150.33/150.66 % --preprocessed_out false
% 150.33/150.66 % --sub_typing false
% 150.33/150.66 % --brand_transform false
% 150.33/150.66 % --pure_diseq_elim true
% 150.33/150.66 % --min_unsat_core false
% 150.33/150.66 % --pred_elim true
% 150.33/150.66 % --add_important_lit false
% 150.33/150.66 % --soft_assumptions false
% 150.33/150.66 % --reset_solvers false
% 150.33/150.66 % --bc_imp_inh []
% 150.33/150.66 % --conj_cone_tolerance 1.5
% 150.33/150.66 % --prolific_symb_bound 500
% 150.33/150.66 % --lt_threshold 2000
% 150.33/150.66
% 150.33/150.66 % ------ SAT Options
% 150.33/150.66
% 150.33/150.66 % --sat_mode false
% 150.33/150.66 % --sat_fm_restart_options ""
% 150.33/150.66 % --sat_gr_def false
% 150.33/150.66 % --sat_epr_types true
% 150.33/150.66 % --sat_non_cyclic_types false
% 150.33/150.66 % --sat_finite_models false
% 150.33/150.66 % --sat_fm_lemmas false
% 150.33/150.66 % --sat_fm_prep false
% 150.33/150.66 % --sat_fm_uc_incr true
% 150.33/150.66 % --sat_out_model small
% 150.33/150.66 % --sat_out_clauses false
% 150.33/150.66
% 150.33/150.66 % ------ QBF Options
% 150.33/150.66
% 150.33/150.66 % --qbf_mode false
% 150.33/150.66 % --qbf_elim_univ true
% 150.33/150.66 % --qbf_sk_in true
% 150.33/150.66 % --qbf_pred_elim true
% 150.33/150.66 % --qbf_split 32
% 150.33/150.66
% 150.33/150.66 % ------ BMC1 Options
% 150.33/150.66
% 150.33/150.66 % --bmc1_incremental false
% 150.33/150.66 % --bmc1_axioms reachable_all
% 150.33/150.66 % --bmc1_min_bound 0
% 150.33/150.66 % --bmc1_max_bound -1
% 150.33/150.66 % --bmc1_max_bound_default -1
% 150.33/150.66 % --bmc1_symbol_reachability true
% 150.33/150.66 % --bmc1_property_lemmas false
% 150.33/150.66 % --bmc1_k_induction false
% 150.33/150.66 % --bmc1_non_equiv_states false
% 150.33/150.66 % --bmc1_deadlock false
% 150.33/150.66 % --bmc1_ucm false
% 150.33/150.66 % --bmc1_add_unsat_core none
% 150.33/150.66 % --bmc1_unsat_core_children false
% 150.33/150.66 % --bmc1_unsat_core_extrapolate_axioms false
% 150.33/150.66 % --bmc1_out_stat full
% 150.33/150.66 % --bmc1_ground_init false
% 150.33/150.66 % --bmc1_pre_inst_next_state false
% 150.33/150.66 % --bmc1_pre_inst_state false
% 150.33/150.66 % --bmc1_pre_inst_reach_state false
% 150.33/150.66 % --bmc1_out_unsat_core false
% 150.33/150.66 % --bmc1_aig_witness_out false
% 150.33/150.66 % --bmc1_verbose false
% 150.33/150.66 % --bmc1_dump_clauses_tptp false
% 151.21/151.53 % --bmc1_dump_unsat_core_tptp false
% 151.21/151.53 % --bmc1_dump_file -
% 151.21/151.53 % --bmc1_ucm_expand_uc_limit 128
% 151.21/151.53 % --bmc1_ucm_n_expand_iterations 6
% 151.21/151.53 % --bmc1_ucm_extend_mode 1
% 151.21/151.53 % --bmc1_ucm_init_mode 2
% 151.21/151.53 % --bmc1_ucm_cone_mode none
% 151.21/151.53 % --bmc1_ucm_reduced_relation_type 0
% 151.21/151.53 % --bmc1_ucm_relax_model 4
% 151.21/151.53 % --bmc1_ucm_full_tr_after_sat true
% 151.21/151.53 % --bmc1_ucm_expand_neg_assumptions false
% 151.21/151.53 % --bmc1_ucm_layered_model none
% 151.21/151.53 % --bmc1_ucm_max_lemma_size 10
% 151.21/151.53
% 151.21/151.53 % ------ AIG Options
% 151.21/151.53
% 151.21/151.53 % --aig_mode false
% 151.21/151.53
% 151.21/151.53 % ------ Instantiation Options
% 151.21/151.53
% 151.21/151.53 % --instantiation_flag true
% 151.21/151.53 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.21/151.53 % --inst_solver_per_active 750
% 151.21/151.53 % --inst_solver_calls_frac 0.5
% 151.21/151.53 % --inst_passive_queue_type priority_queues
% 151.21/151.53 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.21/151.53 % --inst_passive_queues_freq [25;2]
% 151.21/151.53 % --inst_dismatching true
% 151.21/151.53 % --inst_eager_unprocessed_to_passive true
% 151.21/151.53 % --inst_prop_sim_given true
% 151.21/151.53 % --inst_prop_sim_new false
% 151.21/151.53 % --inst_orphan_elimination true
% 151.21/151.53 % --inst_learning_loop_flag true
% 151.21/151.53 % --inst_learning_start 3000
% 151.21/151.53 % --inst_learning_factor 2
% 151.21/151.53 % --inst_start_prop_sim_after_learn 3
% 151.21/151.53 % --inst_sel_renew solver
% 151.21/151.53 % --inst_lit_activity_flag true
% 151.21/151.53 % --inst_out_proof true
% 151.21/151.53
% 151.21/151.53 % ------ Resolution Options
% 151.21/151.53
% 151.21/151.53 % --resolution_flag true
% 151.21/151.53 % --res_lit_sel kbo_max
% 151.21/151.53 % --res_to_prop_solver none
% 151.21/151.53 % --res_prop_simpl_new false
% 151.21/151.53 % --res_prop_simpl_given false
% 151.21/151.53 % --res_passive_queue_type priority_queues
% 151.21/151.53 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.21/151.53 % --res_passive_queues_freq [15;5]
% 151.21/151.53 % --res_forward_subs full
% 151.21/151.53 % --res_backward_subs full
% 151.21/151.53 % --res_forward_subs_resolution true
% 151.21/151.53 % --res_backward_subs_resolution true
% 151.21/151.53 % --res_orphan_elimination false
% 151.21/151.53 % --res_time_limit 1000.
% 151.21/151.53 % --res_out_proof true
% 151.21/151.53 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s
% 151.21/151.53 % --modulo true
% 151.21/151.53
% 151.21/151.53 % ------ Combination Options
% 151.21/151.53
% 151.21/151.53 % --comb_res_mult 1000
% 151.21/151.53 % --comb_inst_mult 300
% 151.21/151.53 % ------
% 151.21/151.53
% 151.21/151.53 % ------ Parsing...% successful
% 151.21/151.53
% 151.21/151.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e snvd_s sp: 0 0s snvd_e %
% 151.21/151.53
% 151.21/151.53 % ------ Proving...
% 151.21/151.53 % ------ Problem Properties
% 151.21/151.53
% 151.21/151.53 %
% 151.21/151.53 % EPR false
% 151.21/151.53 % Horn false
% 151.21/151.53 % Has equality true
% 151.21/151.53
% 151.21/151.53 % % ------ Input Options Time Limit: Unbounded
% 151.21/151.53
% 151.21/151.53
% 151.21/151.53 Compiling...
% 151.21/151.53 Loading plugin: done.
% 151.21/151.53 Compiling...
% 151.21/151.53 Loading plugin: done.
% 151.21/151.53 Compiling...
% 151.21/151.53 Loading plugin: done.
% 151.21/151.53 Compiling...
% 151.21/151.53 Loading plugin: done.
% 151.21/151.53 % % ------ Current options:
% 151.21/151.53
% 151.21/151.53 % ------ Input Options
% 151.21/151.53
% 151.21/151.53 % --out_options all
% 151.21/151.53 % --tptp_safe_out true
% 151.21/151.53 % --problem_path ""
% 151.21/151.53 % --include_path ""
% 151.21/151.53 % --clausifier .//eprover
% 151.21/151.53 % --clausifier_options --tstp-format
% 151.21/151.53 % --stdin false
% 151.21/151.53 % --dbg_backtrace false
% 151.21/151.53 % --dbg_dump_prop_clauses false
% 151.21/151.53 % --dbg_dump_prop_clauses_file -
% 151.21/151.53 % --dbg_out_stat false
% 151.21/151.53
% 151.21/151.53 % ------ General Options
% 151.21/151.53
% 151.21/151.53 % --fof false
% 151.21/151.53 % --time_out_real 150.
% 151.21/151.53 % --time_out_prep_mult 0.2
% 151.21/151.53 % --time_out_virtual -1.
% 151.21/151.53 % --schedule none
% 151.21/151.53 % --ground_splitting input
% 151.21/151.53 % --splitting_nvd 16
% 151.21/151.53 % --non_eq_to_eq false
% 151.21/151.53 % --prep_gs_sim true
% 151.21/151.53 % --prep_unflatten false
% 151.21/151.53 % --prep_res_sim true
% 151.21/151.53 % --prep_upred true
% 151.21/151.53 % --res_sim_input true
% 151.21/151.53 % --clause_weak_htbl true
% 151.21/151.53 % --gc_record_bc_elim false
% 151.21/151.53 % --symbol_type_check false
% 151.21/151.53 % --clausify_out false
% 151.21/151.53 % --large_theory_mode false
% 151.21/151.53 % --prep_sem_filter none
% 151.21/151.53 % --prep_sem_filter_out false
% 151.21/151.53 % --preprocessed_out false
% 151.21/151.53 % --sub_typing false
% 151.21/151.53 % --brand_transform false
% 151.21/151.53 % --pure_diseq_elim true
% 151.21/151.53 % --min_unsat_core false
% 151.21/151.53 % --pred_elim true
% 151.21/151.53 % --add_important_lit false
% 151.21/151.53 % --soft_assumptions false
% 151.21/151.53 % --reset_solvers false
% 151.21/151.53 % --bc_imp_inh []
% 151.21/151.53 % --conj_cone_tolerance 1.5
% 151.21/151.53 % --prolific_symb_bound 500
% 151.21/151.53 % --lt_threshold 2000
% 151.21/151.53
% 151.21/151.53 % ------ SAT Options
% 151.21/151.53
% 151.21/151.53 % --sat_mode false
% 151.21/151.53 % --sat_fm_restart_options ""
% 151.21/151.53 % --sat_gr_def false
% 151.21/151.53 % --sat_epr_types true
% 151.21/151.53 % --sat_non_cyclic_types false
% 151.21/151.53 % --sat_finite_models false
% 151.21/151.53 % --sat_fm_lemmas false
% 151.21/151.53 % --sat_fm_prep false
% 151.21/151.53 % --sat_fm_uc_incr true
% 151.21/151.53 % --sat_out_model small
% 151.21/151.53 % --sat_out_clauses false
% 151.21/151.53
% 151.21/151.53 % ------ QBF Options
% 151.21/151.53
% 151.21/151.53 % --qbf_mode false
% 151.21/151.53 % --qbf_elim_univ true
% 151.21/151.53 % --qbf_sk_in true
% 151.21/151.53 % --qbf_pred_elim true
% 151.21/151.53 % --qbf_split 32
% 151.21/151.53
% 151.21/151.53 % ------ BMC1 Options
% 151.21/151.53
% 151.21/151.53 % --bmc1_incremental false
% 151.21/151.53 % --bmc1_axioms reachable_all
% 151.21/151.53 % --bmc1_min_bound 0
% 151.21/151.53 % --bmc1_max_bound -1
% 151.21/151.53 % --bmc1_max_bound_default -1
% 151.21/151.53 % --bmc1_symbol_reachability true
% 151.21/151.53 % --bmc1_property_lemmas false
% 151.21/151.53 % --bmc1_k_induction false
% 151.21/151.53 % --bmc1_non_equiv_states false
% 151.21/151.53 % --bmc1_deadlock false
% 151.21/151.53 % --bmc1_ucm false
% 151.21/151.53 % --bmc1_add_unsat_core none
% 151.21/151.53 % --bmc1_unsat_core_children false
% 151.21/151.53 % --bmc1_unsat_core_extrapolate_axioms false
% 151.21/151.53 % --bmc1_out_stat full
% 151.21/151.53 % --bmc1_ground_init false
% 151.21/151.53 % --bmc1_pre_inst_next_state false
% 151.21/151.53 % --bmc1_pre_inst_state false
% 151.21/151.53 % --bmc1_pre_inst_reach_state false
% 151.21/151.53 % --bmc1_out_unsat_core false
% 151.21/151.53 % --bmc1_aig_witness_out false
% 151.21/151.53 % --bmc1_verbose false
% 151.21/151.53 % --bmc1_dump_clauses_tptp false
% 151.21/151.53 % --bmc1_dump_unsat_core_tptp false
% 151.21/151.53 % --bmc1_dump_file -
% 151.21/151.53 % --bmc1_ucm_expand_uc_limit 128
% 151.21/151.53 % --bmc1_ucm_n_expand_iterations 6
% 151.21/151.53 % --bmc1_ucm_extend_mode 1
% 151.21/151.53 % --bmc1_ucm_init_mode 2
% 151.21/151.53 % --bmc1_ucm_cone_mode none
% 151.21/151.53 % --bmc1_ucm_reduced_relation_type 0
% 151.21/151.53 % --bmc1_ucm_relax_model 4
% 151.21/151.53 % --bmc1_ucm_full_tr_after_sat true
% 151.21/151.53 % --bmc1_ucm_expand_neg_assumptions false
% 151.21/151.53 % --bmc1_ucm_layered_model none
% 151.21/151.53 % --bmc1_ucm_max_lemma_size 10
% 151.21/151.53
% 151.21/151.53 % ------ AIG Options
% 151.21/151.53
% 151.21/151.53 % --aig_mode false
% 151.21/151.53
% 151.21/151.53 % ------ Instantiation Options
% 151.21/151.53
% 151.21/151.53 % --instantiation_flag true
% 151.21/151.53 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.21/151.53 % --inst_solver_per_active 750
% 151.21/151.53 % --inst_solver_calls_frac 0.5
% 151.21/151.53 % --inst_passive_queue_type priority_queues
% 151.21/151.53 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 154.93/155.25 % --inst_passive_queues_freq [25;2]
% 154.93/155.25 % --inst_dismatching true
% 154.93/155.25 % --inst_eager_unprocessed_to_passive true
% 154.93/155.25 % --inst_prop_sim_given true
% 154.93/155.25 % --inst_prop_sim_new false
% 154.93/155.25 % --inst_orphan_elimination true
% 154.93/155.25 % --inst_learning_loop_flag true
% 154.93/155.25 % --inst_learning_start 3000
% 154.93/155.25 % --inst_learning_factor 2
% 154.93/155.25 % --inst_start_prop_sim_after_learn 3
% 154.93/155.25 % --inst_sel_renew solver
% 154.93/155.25 % --inst_lit_activity_flag true
% 154.93/155.25 % --inst_out_proof true
% 154.93/155.25
% 154.93/155.25 % ------ Resolution Options
% 154.93/155.25
% 154.93/155.25 % --resolution_flag true
% 154.93/155.25 % --res_lit_sel kbo_max
% 154.93/155.25 % --res_to_prop_solver none
% 154.93/155.25 % --res_prop_simpl_new false
% 154.93/155.25 % --res_prop_simpl_given false
% 154.93/155.25 % --res_passive_queue_type priority_queues
% 154.93/155.25 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 154.93/155.25 % --res_passive_queues_freq [15;5]
% 154.93/155.25 % --res_forward_subs full
% 154.93/155.25 % --res_backward_subs full
% 154.93/155.25 % --res_forward_subs_resolution true
% 154.93/155.25 % --res_backward_subs_resolution true
% 154.93/155.25 % --res_orphan_elimination false
% 154.93/155.25 % --res_time_limit 1000.
% 154.93/155.25 % --res_out_proof true
% 154.93/155.25 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_22e8cb.s
% 154.93/155.25 % --modulo true
% 154.93/155.25
% 154.93/155.25 % ------ Combination Options
% 154.93/155.25
% 154.93/155.25 % --comb_res_mult 1000
% 154.93/155.25 % --comb_inst_mult 300
% 154.93/155.25 % ------
% 154.93/155.25
% 154.93/155.25
% 154.93/155.25
% 154.93/155.25 % ------ Proving...
% 154.93/155.25 %
% 154.93/155.25
% 154.93/155.25
% 154.93/155.25 % ------ Statistics
% 154.93/155.25
% 154.93/155.25 % ------ General
% 154.93/155.25
% 154.93/155.25 % num_of_input_clauses: 1191
% 154.93/155.25 % num_of_input_neg_conjectures: 1
% 154.93/155.25 % num_of_splits: 0
% 154.93/155.25 % num_of_split_atoms: 0
% 154.93/155.25 % num_of_sem_filtered_clauses: 0
% 154.93/155.25 % num_of_subtypes: 0
% 154.93/155.25 % monotx_restored_types: 0
% 154.93/155.25 % sat_num_of_epr_types: 0
% 154.93/155.25 % sat_num_of_non_cyclic_types: 0
% 154.93/155.25 % sat_guarded_non_collapsed_types: 0
% 154.93/155.25 % is_epr: 0
% 154.93/155.25 % is_horn: 0
% 154.93/155.25 % has_eq: 1
% 154.93/155.25 % num_pure_diseq_elim: 0
% 154.93/155.25 % simp_replaced_by: 0
% 154.93/155.25 % res_preprocessed: 21
% 154.93/155.25 % prep_upred: 0
% 154.93/155.25 % prep_unflattend: 3
% 154.93/155.25 % pred_elim_cands: 7
% 154.93/155.25 % pred_elim: 6
% 154.93/155.25 % pred_elim_cl: 10
% 154.93/155.25 % pred_elim_cycles: 7
% 154.93/155.25 % forced_gc_time: 0
% 154.93/155.25 % gc_basic_clause_elim: 0
% 154.93/155.25 % parsing_time: 0.028
% 154.93/155.25 % sem_filter_time: 0.
% 154.93/155.25 % pred_elim_time: 0.
% 154.93/155.25 % out_proof_time: 0.001
% 154.93/155.25 % monotx_time: 0.
% 154.93/155.25 % subtype_inf_time: 0.
% 154.93/155.25 % unif_index_cands_time: 0.026
% 154.93/155.25 % unif_index_add_time: 0.015
% 154.93/155.25 % total_time: 4.593
% 154.93/155.25 % num_of_symbols: 274
% 154.93/155.25 % num_of_terms: 81641
% 154.93/155.25
% 154.93/155.25 % ------ Propositional Solver
% 154.93/155.25
% 154.93/155.25 % prop_solver_calls: 4
% 154.93/155.25 % prop_fast_solver_calls: 67
% 154.93/155.25 % prop_num_of_clauses: 3463
% 154.93/155.25 % prop_preprocess_simplified: 8675
% 154.93/155.25 % prop_fo_subsumed: 0
% 154.93/155.25 % prop_solver_time: 0.001
% 154.93/155.25 % prop_fast_solver_time: 0.
% 154.93/155.25 % prop_unsat_core_time: 0.
% 154.93/155.25
% 154.93/155.25 % ------ QBF
% 154.93/155.25
% 154.93/155.25 % qbf_q_res: 0
% 154.93/155.25 % qbf_num_tautologies: 0
% 154.93/155.25 % qbf_prep_cycles: 0
% 154.93/155.25
% 154.93/155.25 % ------ BMC1
% 154.93/155.25
% 154.93/155.25 % bmc1_current_bound: -1
% 154.93/155.25 % bmc1_last_solved_bound: -1
% 154.93/155.25 % bmc1_unsat_core_size: -1
% 154.93/155.25 % bmc1_unsat_core_parents_size: -1
% 154.93/155.25 % bmc1_merge_next_fun: 0
% 154.93/155.25 % bmc1_unsat_core_clauses_time: 0.
% 154.93/155.25
% 154.93/155.25 % ------ Instantiation
% 154.93/155.25
% 154.93/155.25 % inst_num_of_clauses: 2342
% 154.93/155.25 % inst_num_in_passive: 1628
% 154.93/155.25 % inst_num_in_active: 712
% 154.93/155.25 % inst_num_in_unprocessed: 0
% 154.93/155.25 % inst_num_of_loops: 1019
% 154.93/155.25 % inst_num_of_learning_restarts: 0
% 154.93/155.25 % inst_num_moves_active_passive: 305
% 154.93/155.25 % inst_lit_activity: 106
% 154.93/155.25 % inst_lit_activity_moves: 0
% 154.93/155.25 % inst_num_tautologies: 0
% 154.93/155.25 % inst_num_prop_implied: 0
% 154.93/155.25 % inst_num_existing_simplified: 0
% 154.93/155.25 % inst_num_eq_res_simplified: 0
% 154.93/155.25 % inst_num_child_elim: 0
% 154.93/155.25 % inst_num_of_dismatching_blockings: 1784
% 154.93/155.25 % inst_num_of_non_proper_insts: 2677
% 154.93/155.25 % inst_num_of_duplicates: 2036
% 154.93/155.25 % inst_inst_num_from_inst_to_res: 0
% 154.93/155.25 % inst_dismatching_checking_time: 0.003
% 154.93/155.25
% 154.93/155.25 % ------ Resolution
% 154.93/155.25
% 154.93/155.25 % res_num_of_clauses: 29173
% 154.93/155.25 % res_num_in_passive: 25380
% 154.93/155.25 % res_num_in_active: 3158
% 154.93/155.25 % res_num_of_loops: 4000
% 154.93/155.25 % res_forward_subset_subsumed: 20845
% 154.93/155.25 % res_backward_subset_subsumed: 142
% 154.93/155.25 % res_forward_subsumed: 1308
% 154.93/155.25 % res_backward_subsumed: 2
% 154.93/155.25 % res_forward_subsumption_resolution: 15
% 154.93/155.25 % res_backward_subsumption_resolution: 0
% 154.93/155.25 % res_clause_to_clause_subsumption: 15246
% 154.93/155.25 % res_orphan_elimination: 0
% 154.93/155.25 % res_tautology_del: 671
% 154.93/155.25 % res_num_eq_res_simplified: 0
% 154.93/155.25 % res_num_sel_changes: 0
% 154.93/155.25 % res_moves_from_active_to_pass: 0
% 154.93/155.25
% 154.93/155.25 % Status Unsatisfiable
% 154.93/155.25 % SZS status Theorem
% 154.93/155.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------