TPTP Problem File: SWW472+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW472+3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 327, 1000 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_1000_fofmg_l327 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 1270 ( 359 unt; 0 def)
% Number of atoms : 3129 ( 888 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 2243 ( 384 ~; 81 |; 125 &)
% ( 266 <=>;1387 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 179 ( 179 usr; 70 con; 0-3 aty)
% Number of variables : 3352 (3278 !; 74 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 17:49:26
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (27)
fof(gsy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____uwgpyvfjxg__,axiom,
! [B_1_1,B_2_1] : is_bool(big_se1212619424_state(B_1_1,B_2_1)) ).
fof(gsy_c_Big__Operators_Osemilattice__big_000tc__Int__Oint,axiom,
! [B_1_1,B_2_1] : is_bool(big_se913005884ig_int(B_1_1,B_2_1)) ).
fof(gsy_c_Big__Operators_Osemilattice__big_000tc__Nat__Onat,axiom,
! [B_1_1,B_2_1] : is_bool(big_se275732192ig_nat(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [B_1_1] : is_bool(finite1720675051_state(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Int__Oint_000tc__Int__Oint,axiom,
! [B_1_1] : is_bool(finite1973466193nt_int(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Nat__Onat_000tc__Nat__Onat,axiom,
! [B_1_1] : is_bool(finite2130160977at_nat(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri,axiom,
! [B_1_1] : is_bool(finite2036162504e_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mt,axiom,
! [B_1_1] : is_bool(finite58652534t_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mt,axiom,
! [B_1_1] : is_bool(finite1956789438t_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple,axiom,
! [B_1_1,B_2_1] : is_bool(finite683959609_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint,axiom,
! [B_1_1,B_2_1] : is_bool(finite1626084323ne_int(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,axiom,
! [B_1_1,B_2_1] : is_bool(finite988810631ne_nat(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [B_1_1,B_2_1] : is_bool(finite416071164_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint,axiom,
! [B_1_1,B_2_1] : is_bool(finite1432773856em_int(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,axiom,
! [B_1_1,B_2_1] : is_bool(finite795500164em_nat(B_1_1,B_2_1)) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_state_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_H242767318e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_int_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1410040974l_bool(B_1_1,B_2_1)) ).
%----Relevant facts (1200)
fof(fact_0_empty,axiom,
! [G_1] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),bot_bo784226126e_bool)) ).
fof(fact_1_triple_Oinject,axiom,
! [Fun1_2,Com_1,Fun2_2,Fun1_1,Com,Fun2_1] :
( hoare_1191504582_state(Fun1_2,Com_1,Fun2_2) = hoare_1191504582_state(Fun1_1,Com,Fun2_1)
<=> ( Fun1_2 = Fun1_1
& Com_1 = Com
& Fun2_2 = Fun2_1 ) ) ).
fof(fact_2_hoare__sound,axiom,
! [G_1,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))
=> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_1),Ts)) ) ).
fof(fact_3_cut,axiom,
! [G_1,G_2,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),G_2))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) ) ) ).
fof(fact_4_hoare__derivs_Oinsert,axiom,
! [Ts,G_1,T_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts))) ) ) ).
fof(fact_5_derivs__insertD,axiom,
! [G_1,T_1,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool)))
& hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) ) ) ).
fof(fact_6_conseq2,axiom,
! [Qa,G_1,Pa,Ca,Q_4] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Q_4)),bot_bo784226126e_bool)))
=> ( ! [Z_13,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_4,Z_13),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_7_conseq1,axiom,
! [Pa,G_1,P_1,Ca,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_1,Ca,Qa)),bot_bo784226126e_bool)))
=> ( ! [Z_13,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_13),S_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_8_insertE,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2)))
=> ( A_1 != B_2
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) ) ) ).
fof(fact_9_insertE,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2)))
=> ( A_1 != B_2
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) ) ) ).
fof(fact_10_insertE,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),A_2)))
=> ( A_1 != B_2
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) ) ) ).
fof(fact_11_insertCI,axiom,
! [B_2,A_1,B_29] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29))
=> A_1 = B_2 )
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))) ) ).
fof(fact_12_insertCI,axiom,
! [B_2,A_1,B_29] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29))
=> A_1 = B_2 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))) ) ).
fof(fact_13_insertCI,axiom,
! [B_2,A_1,B_29] :
( ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29))
=> A_1 = B_2 )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))) ) ).
fof(fact_14_conseq12,axiom,
! [Qa,Pa,G_1,P_1,Ca,Q_4] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_1,Ca,Q_4)),bot_bo784226126e_bool)))
=> ( ! [Z_13,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1))
=> ! [S_2] :
( ! [Z_14] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_14),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_4,Z_14),S_2)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_2)) ) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_15_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),bot_bot_fun_int_bool)) ).
fof(fact_16_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),bot_bot_fun_nat_bool)) ).
fof(fact_17_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),bot_bo784226126e_bool)) ).
fof(fact_18_empty__not__insert,axiom,
! [A_1,A_2] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) ).
fof(fact_19_empty__not__insert,axiom,
! [A_1,A_2] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) ).
fof(fact_20_empty__not__insert,axiom,
! [A_1,A_2] : bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) ).
fof(fact_21_insert__not__empty,axiom,
! [A_1,A_2] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) != bot_bot_fun_int_bool ).
fof(fact_22_insert__not__empty,axiom,
! [A_1,A_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) != bot_bot_fun_nat_bool ).
fof(fact_23_insert__not__empty,axiom,
! [A_1,A_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) != bot_bo784226126e_bool ).
fof(fact_24_singleton__iff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)))
<=> B_2 = A_1 ) ).
fof(fact_25_singleton__iff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)))
<=> B_2 = A_1 ) ).
fof(fact_26_singleton__iff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)))
<=> B_2 = A_1 ) ).
fof(fact_27_doubleton__eq__iff,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool))
<=> ( ( A_1 = Ca
& B_2 = D_1 )
| ( A_1 = D_1
& B_2 = Ca ) ) ) ).
fof(fact_28_doubleton__eq__iff,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool))
<=> ( ( A_1 = Ca
& B_2 = D_1 )
| ( A_1 = D_1
& B_2 = Ca ) ) ) ).
fof(fact_29_doubleton__eq__iff,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Ca),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D_1),bot_bo784226126e_bool))
<=> ( ( A_1 = Ca
& B_2 = D_1 )
| ( A_1 = D_1
& B_2 = Ca ) ) ) ).
fof(fact_30_equals0D,axiom,
! [A_1,A_2] :
( A_2 = bot_bot_fun_int_bool
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) ) ).
fof(fact_31_equals0D,axiom,
! [A_1,A_2] :
( A_2 = bot_bot_fun_nat_bool
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) ) ).
fof(fact_32_equals0D,axiom,
! [A_1,A_2] :
( A_2 = bot_bo784226126e_bool
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) ) ).
fof(fact_33_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f1805168059t_bool(collect_int,Pa) = bot_bot_fun_int_bool
<=> ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2)) ) ).
fof(fact_34_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f800510211t_bool(collect_nat,Pa) = bot_bot_fun_nat_bool
<=> ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2)) ) ).
fof(fact_35_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f806699093e_bool(collec637225377_state,Pa) = bot_bo784226126e_bool
<=> ! [X_2] : ~ hBOOL(hAPP_H242767318e_bool(Pa,X_2)) ) ).
fof(fact_36_empty__iff,axiom,
! [Ca] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),bot_bot_fun_int_bool)) ).
fof(fact_37_empty__iff,axiom,
! [Ca] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),bot_bot_fun_nat_bool)) ).
fof(fact_38_empty__iff,axiom,
! [Ca] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),bot_bo784226126e_bool)) ).
fof(fact_39_empty__Collect__eq,axiom,
! [Pa] :
( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(collect_int,Pa)
<=> ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2)) ) ).
fof(fact_40_empty__Collect__eq,axiom,
! [Pa] :
( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,Pa)
<=> ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2)) ) ).
fof(fact_41_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,Pa)
<=> ! [X_2] : ~ hBOOL(hAPP_H242767318e_bool(Pa,X_2)) ) ).
fof(fact_42_ex__in__conv,axiom,
! [A_2] :
( ? [X_2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2))
<=> A_2 != bot_bot_fun_int_bool ) ).
fof(fact_43_ex__in__conv,axiom,
! [A_2] :
( ? [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
<=> A_2 != bot_bot_fun_nat_bool ) ).
fof(fact_44_ex__in__conv,axiom,
! [A_2] :
( ? [X_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2))
<=> A_2 != bot_bo784226126e_bool ) ).
fof(fact_45_all__not__in__conv,axiom,
! [A_2] :
( ! [X_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2))
<=> A_2 = bot_bot_fun_int_bool ) ).
fof(fact_46_all__not__in__conv,axiom,
! [A_2] :
( ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
<=> A_2 = bot_bot_fun_nat_bool ) ).
fof(fact_47_all__not__in__conv,axiom,
! [A_2] :
( ! [X_2] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2))
<=> A_2 = bot_bo784226126e_bool ) ).
fof(fact_48_empty__def,axiom,
bot_bot_fun_int_bool = hAPP_f1805168059t_bool(collect_int,cOMBK_bool_int(fFalse)) ).
fof(fact_49_empty__def,axiom,
bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,cOMBK_bool_nat(fFalse)) ).
fof(fact_50_empty__def,axiom,
bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,cOMBK_988866959_state(fFalse)) ).
fof(fact_51_insert__absorb,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) = A_2 ) ).
fof(fact_52_insert__absorb,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) = A_2 ) ).
fof(fact_53_insert__absorb,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) = A_2 ) ).
fof(fact_54_insertI2,axiom,
! [B_2,A_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))) ) ).
fof(fact_55_insertI2,axiom,
! [B_2,A_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))) ) ).
fof(fact_56_insertI2,axiom,
! [B_2,A_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))) ) ).
fof(fact_57_insert__ident,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29)
<=> A_2 = B_29 ) ) ) ).
fof(fact_58_insert__ident,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29)
<=> A_2 = B_29 ) ) ) ).
fof(fact_59_insert__ident,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> ( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29)
<=> A_2 = B_29 ) ) ) ).
fof(fact_60_insert__code,axiom,
! [Y_1,A_2,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A_2),X_1))
<=> ( Y_1 = X_1
| hBOOL(hAPP_int_bool(A_2,X_1)) ) ) ).
fof(fact_61_insert__code,axiom,
! [Y_1,A_2,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_2),X_1))
<=> ( Y_1 = X_1
| hBOOL(hAPP_nat_bool(A_2,X_1)) ) ) ).
fof(fact_62_insert__code,axiom,
! [Y_1,A_2,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_2),X_1))
<=> ( Y_1 = X_1
| hBOOL(hAPP_H242767318e_bool(A_2,X_1)) ) ) ).
fof(fact_63_insert__iff,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2)))
<=> ( A_1 = B_2
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) ) ) ).
fof(fact_64_insert__iff,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2)))
<=> ( A_1 = B_2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) ) ) ).
fof(fact_65_insert__iff,axiom,
! [A_1,B_2,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),A_2)))
<=> ( A_1 = B_2
| hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) ) ) ).
fof(fact_66_insert__commute,axiom,
! [X_1,Y_1,A_2] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) ).
fof(fact_67_insert__commute,axiom,
! [X_1,Y_1,A_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) ).
fof(fact_68_insert__commute,axiom,
! [X_1,Y_1,A_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) ).
fof(fact_69_insert__absorb2,axiom,
! [X_1,A_2] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2) ).
fof(fact_70_insert__absorb2,axiom,
! [X_1,A_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2) ).
fof(fact_71_insert__absorb2,axiom,
! [X_1,A_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2) ).
fof(fact_72_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(collect_int,Pa)) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fimplies),hAPP_f1805168059t_bool(cOMBB_bool_bool_int(fNot),hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_1)))),Pa)) ).
fof(fact_73_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(collect_nat,Pa)) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fimplies),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)))),Pa)) ).
fof(fact_74_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(collec637225377_state,Pa)) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fimplies),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_H216526335e_bool(cOMBC_1967329268e_bool(fequal1440809015_state),A_1)))),Pa)) ).
fof(fact_75_insert__compr,axiom,
! [A_1,B_29] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fdisj),hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_1))),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B_29))) ).
fof(fact_76_insert__compr,axiom,
! [A_1,B_29] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_29))) ).
fof(fact_77_insert__compr,axiom,
! [A_1,B_29] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(cOMBC_1967329268e_bool(fequal1440809015_state),A_1))),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),B_29))) ).
fof(fact_78_insertI1,axiom,
! [A_1,B_29] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29))) ).
fof(fact_79_insertI1,axiom,
! [A_1,B_29] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29))) ).
fof(fact_80_insertI1,axiom,
! [A_1,B_29] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29))) ).
fof(fact_81_singleton__inject,axiom,
! [A_1,B_2] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),bot_bot_fun_int_bool)
=> A_1 = B_2 ) ).
fof(fact_82_singleton__inject,axiom,
! [A_1,B_2] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),bot_bot_fun_nat_bool)
=> A_1 = B_2 ) ).
fof(fact_83_singleton__inject,axiom,
! [A_1,B_2] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),bot_bo784226126e_bool)
=> A_1 = B_2 ) ).
fof(fact_84_singletonE,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)))
=> B_2 = A_1 ) ).
fof(fact_85_singletonE,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)))
=> B_2 = A_1 ) ).
fof(fact_86_singletonE,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)))
=> B_2 = A_1 ) ).
fof(fact_87_the__elem__eq,axiom,
! [X_1] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1 ).
fof(fact_88_the__elem__eq,axiom,
! [X_1] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1 ).
fof(fact_89_the__elem__eq,axiom,
! [X_1] : hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1 ).
fof(fact_90_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_91_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_92_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_93_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_94_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_95_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_96_hoare__derivs_OSkip,axiom,
! [G_1,Pa] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,skip,Pa)),bot_bo784226126e_bool))) ).
fof(fact_97_Comp,axiom,
! [D_1,R_3,G_1,Pa,Ca,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Qa,D_1,R_3)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,semi(Ca,D_1),R_3)),bot_bo784226126e_bool))) ) ) ).
fof(fact_98_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1,Com_2,Fun2] : Y_1 != hoare_1191504582_state(Fun1,Com_2,Fun2) ).
fof(fact_99_Set_Oset__insert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ~ ! [B_46] :
( A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_46)
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_46)) ) ) ).
fof(fact_100_Set_Oset__insert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ~ ! [B_46] :
( A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_46)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_46)) ) ) ).
fof(fact_101_Set_Oset__insert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ~ ! [B_46] :
( A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_46)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_46)) ) ) ).
fof(fact_102_mk__disjoint__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> ? [B_46] :
( A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_46)
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_46)) ) ) ).
fof(fact_103_mk__disjoint__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> ? [B_46] :
( A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_46)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_46)) ) ) ).
fof(fact_104_mk__disjoint__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> ? [B_46] :
( A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_46)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_46)) ) ) ).
fof(fact_105_equals0I,axiom,
! [A_2] :
( ! [Y_5] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_5),A_2))
=> A_2 = bot_bot_fun_int_bool ) ).
fof(fact_106_equals0I,axiom,
! [A_2] :
( ! [Y_5] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_5),A_2))
=> A_2 = bot_bot_fun_nat_bool ) ).
fof(fact_107_equals0I,axiom,
! [A_2] :
( ! [Y_5] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_5),A_2))
=> A_2 = bot_bo784226126e_bool ) ).
fof(fact_108_conseq,axiom,
! [Qa,G_1,Ca,Pa] :
( ! [Z_13,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1))
=> ? [P_2,Q_3] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_2,Ca,Q_3)),bot_bo784226126e_bool)))
& ! [S_2] :
( ! [Z_14] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_14),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_14),S_2)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_2)) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))) ) ).
fof(fact_109_nonempty__iff,axiom,
! [A_2] :
( A_2 != bot_bot_fun_int_bool
<=> ? [X_2,B_46] :
( A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_46)
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_46)) ) ) ).
fof(fact_110_nonempty__iff,axiom,
! [A_2] :
( A_2 != bot_bot_fun_nat_bool
<=> ? [X_2,B_46] :
( A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_46)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_46)) ) ) ).
fof(fact_111_nonempty__iff,axiom,
! [A_2] :
( A_2 != bot_bo784226126e_bool
<=> ? [X_2,B_46] :
( A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_46)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_46)) ) ) ).
fof(fact_112_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),bot_bot_fun_int_bool)) ) ).
fof(fact_113_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),bot_bot_fun_nat_bool)) ) ).
fof(fact_114_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),bot_bo784226126e_bool)) ) ).
fof(fact_115_com_Osimps_I13_J,axiom,
! [Com1_3,Com2_3] : semi(Com1_3,Com2_3) != skip ).
fof(fact_116_com_Osimps_I12_J,axiom,
! [Com1_3,Com2_3] : skip != semi(Com1_3,Com2_3) ).
fof(fact_117_com_Osimps_I3_J,axiom,
! [Com1,Com2,Com1_1,Com2_1] :
( semi(Com1,Com2) = semi(Com1_1,Com2_1)
<=> ( Com1 = Com1_1
& Com2 = Com2_1 ) ) ).
fof(fact_118_fold1Set__sing,axiom,
! [F,A_1,B_2] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)),B_2))
<=> A_1 = B_2 ) ).
fof(fact_119_fold1Set__sing,axiom,
! [F,A_1,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)),B_2))
<=> A_1 = B_2 ) ).
fof(fact_120_fold1Set__sing,axiom,
! [F,A_1,B_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)),B_2))
<=> A_1 = B_2 ) ).
fof(fact_121_folding__one_Osingleton,axiom,
! [X_1,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1 ) ).
fof(fact_122_folding__one_Osingleton,axiom,
! [X_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1 ) ).
fof(fact_123_folding__one_Osingleton,axiom,
! [X_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1 ) ).
fof(fact_124_fold1__singleton,axiom,
! [F,A_1] : hAPP_f1594865479ol_int(finite_fold1_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)) = A_1 ).
fof(fact_125_fold1__singleton,axiom,
! [F,A_1] : hAPP_f22106695ol_nat(finite_fold1_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1 ).
fof(fact_126_fold1__singleton,axiom,
! [F,A_1] : hAPP_f718417177_state(finite1255650454_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)) = A_1 ).
fof(fact_127_fold1__singleton__def,axiom,
! [A_1,G,F] :
( G = finite_fold1_int(F)
=> hAPP_f1594865479ol_int(G,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)) = A_1 ) ).
fof(fact_128_fold1__singleton__def,axiom,
! [A_1,G,F] :
( G = finite_fold1_nat(F)
=> hAPP_f22106695ol_nat(G,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1 ) ).
fof(fact_129_fold1__singleton__def,axiom,
! [A_1,G,F] :
( G = finite1255650454_state(F)
=> hAPP_f718417177_state(G,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)) = A_1 ) ).
fof(fact_130_empty__fold1SetE,axiom,
! [F,X_1] : ~ hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),bot_bot_fun_int_bool),X_1)) ).
fof(fact_131_empty__fold1SetE,axiom,
! [F,X_1] : ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),bot_bot_fun_nat_bool),X_1)) ).
fof(fact_132_empty__fold1SetE,axiom,
! [F,X_1] : ~ hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),bot_bo784226126e_bool),X_1)) ).
fof(fact_133_fold1Set__nonempty,axiom,
! [F,A_2,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A_2),X_1))
=> A_2 != bot_bot_fun_int_bool ) ).
fof(fact_134_fold1Set__nonempty,axiom,
! [F,A_2,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A_2),X_1))
=> A_2 != bot_bot_fun_nat_bool ) ).
fof(fact_135_fold1Set__nonempty,axiom,
! [F,A_2,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A_2),X_1))
=> A_2 != bot_bo784226126e_bool ) ).
fof(fact_136_subset__singletonD,axiom,
! [A_2,X_1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))
=> ( A_2 = bot_bot_fun_int_bool
| A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool) ) ) ).
fof(fact_137_subset__singletonD,axiom,
! [A_2,X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))
=> ( A_2 = bot_bot_fun_nat_bool
| A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool) ) ) ).
fof(fact_138_subset__singletonD,axiom,
! [A_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))
=> ( A_2 = bot_bo784226126e_bool
| A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool) ) ) ).
fof(fact_139_order__refl,axiom,
! [X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),X_1)) ).
fof(fact_140_order__refl,axiom,
! [X_36] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_36),X_36)) ).
fof(fact_141_order__refl,axiom,
! [X_36] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_36),X_36)) ).
fof(fact_142_equalityI,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2))
=> A_2 = B_29 ) ) ).
fof(fact_143_subsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) ) ) ).
fof(fact_144_subsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) ) ) ).
fof(fact_145_subsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) ) ) ).
fof(fact_146_empty__subsetI,axiom,
! [A_2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_2)) ).
fof(fact_147_empty__subsetI,axiom,
! [A_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_2)) ).
fof(fact_148_empty__subsetI,axiom,
! [A_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_2)) ).
fof(fact_149_linorder__le__cases,axiom,
! [X_35,Y_34] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_35),Y_34))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_34),X_35)) ) ).
fof(fact_150_linorder__le__cases,axiom,
! [X_35,Y_34] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_35),Y_34))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_34),X_35)) ) ).
fof(fact_151_le__funE,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))) ) ).
fof(fact_152_xt1_I6_J,axiom,
! [Z_1,Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),Y_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),X_1)) ) ) ).
fof(fact_153_xt1_I6_J,axiom,
! [Z_12,Y_33,X_34] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_33),X_34))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_12),Y_33))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_12),X_34)) ) ) ).
fof(fact_154_xt1_I6_J,axiom,
! [Z_12,Y_33,X_34] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_33),X_34))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_12),Y_33))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_12),X_34)) ) ) ).
fof(fact_155_xt1_I5_J,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
=> X_1 = Y_1 ) ) ).
fof(fact_156_xt1_I5_J,axiom,
! [Y_32,X_33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_32),X_33))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_33),Y_32))
=> X_33 = Y_32 ) ) ).
fof(fact_157_xt1_I5_J,axiom,
! [Y_32,X_33] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_32),X_33))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_33),Y_32))
=> X_33 = Y_32 ) ) ).
fof(fact_158_order__trans,axiom,
! [Z_1,X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),Z_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z_1)) ) ) ).
fof(fact_159_order__trans,axiom,
! [Z_11,X_32,Y_31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Y_31))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_31),Z_11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Z_11)) ) ) ).
fof(fact_160_order__trans,axiom,
! [Z_11,X_32,Y_31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Y_31))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_31),Z_11))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Z_11)) ) ) ).
fof(fact_161_order__antisym,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1))
=> X_1 = Y_1 ) ) ).
fof(fact_162_order__antisym,axiom,
! [X_31,Y_30] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_31),Y_30))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_30),X_31))
=> X_31 = Y_30 ) ) ).
fof(fact_163_order__antisym,axiom,
! [X_31,Y_30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_31),Y_30))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_30),X_31))
=> X_31 = Y_30 ) ) ).
fof(fact_164_xt1_I4_J,axiom,
! [Ca,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> ( B_2 = Ca
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),A_1)) ) ) ).
fof(fact_165_xt1_I4_J,axiom,
! [C_35,B_45,A_61] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_45),A_61))
=> ( B_45 = C_35
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_35),A_61)) ) ) ).
fof(fact_166_xt1_I4_J,axiom,
! [C_35,B_45,A_61] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_45),A_61))
=> ( B_45 = C_35
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_35),A_61)) ) ) ).
fof(fact_167_ord__le__eq__trans,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( B_2 = Ca
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),Ca)) ) ) ).
fof(fact_168_ord__le__eq__trans,axiom,
! [C_34,A_60,B_44] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_60),B_44))
=> ( B_44 = C_34
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_60),C_34)) ) ) ).
fof(fact_169_ord__le__eq__trans,axiom,
! [C_34,A_60,B_44] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_60),B_44))
=> ( B_44 = C_34
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_60),C_34)) ) ) ).
fof(fact_170_xt1_I3_J,axiom,
! [Ca,A_1,B_2] :
( A_1 = B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),A_1)) ) ) ).
fof(fact_171_xt1_I3_J,axiom,
! [C_33,A_59,B_43] :
( A_59 = B_43
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_33),B_43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_33),A_59)) ) ) ).
fof(fact_172_xt1_I3_J,axiom,
! [C_33,A_59,B_43] :
( A_59 = B_43
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_33),B_43))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_33),A_59)) ) ) ).
fof(fact_173_ord__eq__le__trans,axiom,
! [Ca,A_1,B_2] :
( A_1 = B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),Ca)) ) ) ).
fof(fact_174_ord__eq__le__trans,axiom,
! [C_32,A_58,B_42] :
( A_58 = B_42
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_42),C_32))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_58),C_32)) ) ) ).
fof(fact_175_ord__eq__le__trans,axiom,
! [C_32,A_58,B_42] :
( A_58 = B_42
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_42),C_32))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_58),C_32)) ) ) ).
fof(fact_176_predicate1D,axiom,
! [X_1,Pa,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa))
=> ( hBOOL(hAPP_H242767318e_bool(Pa,X_1))
=> hBOOL(hAPP_H242767318e_bool(Qa,X_1)) ) ) ).
fof(fact_177_mem__def,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
<=> hBOOL(hAPP_H242767318e_bool(A_2,X_1)) ) ).
fof(fact_178_mem__def,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
<=> hBOOL(hAPP_int_bool(A_2,X_1)) ) ).
fof(fact_179_mem__def,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
<=> hBOOL(hAPP_nat_bool(A_2,X_1)) ) ).
fof(fact_180_Collect__def,axiom,
! [Pa] : hAPP_f806699093e_bool(collec637225377_state,Pa) = Pa ).
fof(fact_181_order__antisym__conv,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_182_order__antisym__conv,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_183_order__antisym__conv,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_184_le__funD,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))) ) ).
fof(fact_185_order__eq__refl,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) ) ).
fof(fact_186_order__eq__refl,axiom,
! [X_30,Y_29] :
( X_30 = Y_29
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Y_29)) ) ).
fof(fact_187_order__eq__refl,axiom,
! [X_30,Y_29] :
( X_30 = Y_29
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_30),Y_29)) ) ).
fof(fact_188_rev__predicate1D,axiom,
! [Qa,Pa,X_1] :
( hBOOL(hAPP_H242767318e_bool(Pa,X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa))
=> hBOOL(hAPP_H242767318e_bool(Qa,X_1)) ) ) ).
fof(fact_189_order__eq__iff,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) ) ) ).
fof(fact_190_order__eq__iff,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ) ) ).
fof(fact_191_order__eq__iff,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) ) ) ).
fof(fact_192_linorder__linear,axiom,
! [X_29,Y_28] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_29),Y_28))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_28),X_29)) ) ).
fof(fact_193_linorder__linear,axiom,
! [X_29,Y_28] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_28))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_28),X_29)) ) ).
fof(fact_194_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
<=> ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2))) ) ).
fof(fact_195_equalityE,axiom,
! [A_2,B_29] :
( A_2 = B_29
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) ) ) ).
fof(fact_196_subset__trans,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),C_26)) ) ) ).
fof(fact_197_set__mp,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) ) ) ).
fof(fact_198_set__mp,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) ) ) ).
fof(fact_199_set__mp,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) ) ) ).
fof(fact_200_set__rev__mp,axiom,
! [B_29,X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) ) ) ).
fof(fact_201_set__rev__mp,axiom,
! [B_29,X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) ) ) ).
fof(fact_202_set__rev__mp,axiom,
! [B_29,X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) ) ) ).
fof(fact_203_in__mono,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) ) ) ).
fof(fact_204_in__mono,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) ) ) ).
fof(fact_205_in__mono,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) ) ) ).
fof(fact_206_equalityD2,axiom,
! [A_2,B_29] :
( A_2 = B_29
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) ) ).
fof(fact_207_equalityD1,axiom,
! [A_2,B_29] :
( A_2 = B_29
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ).
fof(fact_208_set__eq__subset,axiom,
! [A_2,B_29] :
( A_2 = B_29
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) ) ) ).
fof(fact_209_subset__refl,axiom,
! [A_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),A_2)) ).
fof(fact_210_le__bot,axiom,
! [A_1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_1),bot_bot_fun_int_bool))
=> A_1 = bot_bot_fun_int_bool ) ).
fof(fact_211_le__bot,axiom,
! [A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool))
=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_212_le__bot,axiom,
! [A_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_1),bot_bot_bool))
=> ( hBOOL(A_1)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_213_le__bot,axiom,
! [A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),bot_bo784226126e_bool))
=> A_1 = bot_bo784226126e_bool ) ).
fof(fact_214_le__bot,axiom,
! [A_57] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_57),bot_bot_nat))
=> A_57 = bot_bot_nat ) ).
fof(fact_215_bot__unique,axiom,
! [A_1] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_1),bot_bot_fun_int_bool))
<=> A_1 = bot_bot_fun_int_bool ) ).
fof(fact_216_bot__unique,axiom,
! [A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool))
<=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_217_bot__unique,axiom,
! [A_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_1),bot_bot_bool))
<=> ( hBOOL(A_1)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_218_bot__unique,axiom,
! [A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),bot_bo784226126e_bool))
<=> A_1 = bot_bo784226126e_bool ) ).
fof(fact_219_bot__unique,axiom,
! [A_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),bot_bot_nat))
<=> A_1 = bot_bot_nat ) ).
fof(fact_220_bot__least,axiom,
! [A_1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_1)) ).
fof(fact_221_bot__least,axiom,
! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1)) ).
fof(fact_222_bot__least,axiom,
! [A_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_1)) ).
fof(fact_223_bot__least,axiom,
! [A_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_1)) ).
fof(fact_224_bot__least,axiom,
! [A_56] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_56)) ).
fof(fact_225_subset__empty,axiom,
! [A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool))
<=> A_2 = bot_bot_fun_int_bool ) ).
fof(fact_226_subset__empty,axiom,
! [A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool))
<=> A_2 = bot_bot_fun_nat_bool ) ).
fof(fact_227_subset__empty,axiom,
! [A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),bot_bo784226126e_bool))
<=> A_2 = bot_bo784226126e_bool ) ).
fof(fact_228_insert__mono,axiom,
! [A_1,C_26,D_10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_26),D_10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),C_26)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),D_10))) ) ).
fof(fact_229_insert__mono,axiom,
! [A_1,C_26,D_10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_26),D_10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),C_26)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),D_10))) ) ).
fof(fact_230_insert__mono,axiom,
! [A_1,C_26,D_10] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_26),D_10))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),C_26)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),D_10))) ) ).
fof(fact_231_subset__insertI2,axiom,
! [B_2,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))) ) ).
fof(fact_232_subset__insertI2,axiom,
! [B_2,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))) ) ).
fof(fact_233_subset__insertI2,axiom,
! [B_2,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))) ) ).
fof(fact_234_subset__insert,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) ) ) ).
fof(fact_235_subset__insert,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) ) ) ).
fof(fact_236_subset__insert,axiom,
! [B_29,X_1,A_2] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29)))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ) ).
fof(fact_237_insert__subset,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) ) ) ).
fof(fact_238_insert__subset,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) ) ) ).
fof(fact_239_insert__subset,axiom,
! [X_1,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ) ).
fof(fact_240_subset__insertI,axiom,
! [B_29,A_1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29))) ).
fof(fact_241_subset__insertI,axiom,
! [B_29,A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29))) ).
fof(fact_242_subset__insertI,axiom,
! [B_29,A_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29))) ).
fof(fact_243_thin,axiom,
! [G_1,G_2,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G_2),G_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) ) ) ).
fof(fact_244_weaken,axiom,
! [Ts,G_1,Ts_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),Ts_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) ) ) ).
fof(fact_245_asm,axiom,
! [Ts,G_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),G_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) ) ).
fof(fact_246_subsetI,axiom,
! [B_29,A_2] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_29)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ).
fof(fact_247_subsetI,axiom,
! [B_29,A_2] :
( ! [X_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_29)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) ) ).
fof(fact_248_subsetI,axiom,
! [B_29,A_2] :
( ! [X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_29)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) ) ).
fof(fact_249_le__funI,axiom,
! [F,G] :
( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) ) ).
fof(fact_250_predicate1I,axiom,
! [Qa,Pa] :
( ! [X_2] :
( hBOOL(hAPP_H242767318e_bool(Pa,X_2))
=> hBOOL(hAPP_H242767318e_bool(Qa,X_2)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa)) ) ).
fof(fact_251_Collect__mono,axiom,
! [Qa,Pa] :
( ! [X_2] :
( hBOOL(hAPP_H242767318e_bool(Pa,X_2))
=> hBOOL(hAPP_H242767318e_bool(Qa,X_2)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(collec637225377_state,Pa)),hAPP_f806699093e_bool(collec637225377_state,Qa))) ) ).
fof(fact_252_xt2,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,B_2)),A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Y_5)),hAPP_f1676271015ol_nat(F,X_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Ca)),A_1)) ) ) ) ).
fof(fact_253_xt2,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,B_2)),A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Y_5)),hAPP_f166061059ol_int(F,X_2))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Ca)),A_1)) ) ) ) ).
fof(fact_254_xt2,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,B_2)),A_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Y_5)),hAPP_n1497837059e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Ca)),A_1)) ) ) ) ).
fof(fact_255_xt2,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,B_2)),A_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Y_5)),hAPP_i468480167e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Ca)),A_1)) ) ) ) ).
fof(fact_256_xt1_I15_J,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_f806699093e_bool(F,B_2)
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_5)),hAPP_f806699093e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Ca)),A_1)) ) ) ) ).
fof(fact_257_xt1_I15_J,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_nat_nat(F,B_2)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_5)),hAPP_nat_nat(F,X_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Ca)),A_1)) ) ) ) ).
fof(fact_258_xt1_I15_J,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_int_int(F,B_2)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),B_2))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Y_5)),hAPP_int_int(F,X_2))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Ca)),A_1)) ) ) ) ).
fof(fact_259_order__subst1,axiom,
! [Ca,A_1,F,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,B_2)))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,Ca))) ) ) ) ).
fof(fact_260_order__subst1,axiom,
! [Ca,A_1,F,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,B_2)))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,Ca))) ) ) ) ).
fof(fact_261_order__subst1,axiom,
! [Ca,A_1,F,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,B_2)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,Ca))) ) ) ) ).
fof(fact_262_order__subst1,axiom,
! [Ca,A_1,F,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,B_2)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,Ca))) ) ) ) ).
fof(fact_263_ord__eq__le__subst,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_n1497837059e_bool(F,B_2)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,Ca))) ) ) ) ).
fof(fact_264_ord__eq__le__subst,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_i468480167e_bool(F,B_2)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,Ca))) ) ) ) ).
fof(fact_265_ord__eq__le__subst,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_f1676271015ol_nat(F,B_2)
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,Ca))) ) ) ) ).
fof(fact_266_ord__eq__le__subst,axiom,
! [Ca,A_1,F,B_2] :
( A_1 = hAPP_f166061059ol_int(F,B_2)
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,Ca))) ) ) ) ).
fof(fact_267_order__subst2,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,B_2)),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,A_1)),Ca)) ) ) ) ).
fof(fact_268_order__subst2,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,B_2)),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,A_1)),Ca)) ) ) ) ).
fof(fact_269_order__subst2,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,B_2)),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,A_1)),Ca)) ) ) ) ).
fof(fact_270_order__subst2,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,B_2)),Ca))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,A_1)),Ca)) ) ) ) ).
fof(fact_271_ord__le__eq__subst,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2))
=> ( hAPP_n1497837059e_bool(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,A_1)),Ca)) ) ) ) ).
fof(fact_272_ord__le__eq__subst,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2))
=> ( hAPP_i468480167e_bool(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,A_1)),Ca)) ) ) ) ).
fof(fact_273_ord__le__eq__subst,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( hAPP_f1676271015ol_nat(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,A_1)),Ca)) ) ) ) ).
fof(fact_274_ord__le__eq__subst,axiom,
! [F,Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( hAPP_f166061059ol_int(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,A_1)),Ca)) ) ) ) ).
fof(fact_275_xt3,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_n1497837059e_bool(F,B_2)))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Y_5)),hAPP_n1497837059e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_n1497837059e_bool(F,A_1))) ) ) ) ).
fof(fact_276_xt3,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_i468480167e_bool(F,B_2)))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Y_5)),hAPP_i468480167e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_i468480167e_bool(F,A_1))) ) ) ) ).
fof(fact_277_xt3,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f1676271015ol_nat(F,B_2)))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Y_5)),hAPP_f1676271015ol_nat(F,X_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f1676271015ol_nat(F,A_1))) ) ) ) ).
fof(fact_278_xt3,axiom,
! [Ca,F,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_f166061059ol_int(F,B_2)))
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Y_5)),hAPP_f166061059ol_int(F,X_2))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_f166061059ol_int(F,A_1))) ) ) ) ).
fof(fact_279_xt1_I16_J,axiom,
! [F,Ca,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> ( hAPP_f806699093e_bool(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_5)),hAPP_f806699093e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_f806699093e_bool(F,A_1))) ) ) ) ).
fof(fact_280_xt1_I16_J,axiom,
! [F,Ca,B_2,A_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),A_1))
=> ( hAPP_nat_nat(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_5)),hAPP_nat_nat(F,X_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_nat_nat(F,A_1))) ) ) ) ).
fof(fact_281_xt1_I16_J,axiom,
! [F,Ca,B_2,A_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_1))
=> ( hAPP_int_int(F,B_2) = Ca
=> ( ! [X_2,Y_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Y_5)),hAPP_int_int(F,X_2))) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_int_int(F,A_1))) ) ) ) ).
fof(fact_282_fold1Set_Ointros,axiom,
! [F,A_1,A_2,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_1),A_2),X_1))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)),X_1)) ) ) ).
fof(fact_283_fold1Set_Ointros,axiom,
! [F,A_1,A_2,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_1),A_2),X_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)),X_1)) ) ) ).
fof(fact_284_fold1Set_Ointros,axiom,
! [F,A_1,A_2,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_1),A_2),X_1))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)),X_1)) ) ) ).
fof(fact_285_folding__one_Oinsert,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( A_2 != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2)) ) ) ) ) ).
fof(fact_286_folding__one_Oinsert,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( A_2 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2)) ) ) ) ) ).
fof(fact_287_folding__one_Oinsert,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( A_2 != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2)) ) ) ) ) ).
fof(fact_288_Powp__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,powp_H1405539888_state(A_2)),powp_H1405539888_state(B_29))) ) ).
fof(fact_289_subset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) ) ) ) ).
fof(fact_290_subset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) ) ) ) ).
fof(fact_291_subset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ) ) ).
fof(fact_292_diff__single__insert,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29))) ) ) ).
fof(fact_293_diff__single__insert,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29))) ) ) ).
fof(fact_294_diff__single__insert,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29))) ) ) ).
fof(fact_295_folding__one_Oeq__fold,axiom,
! [A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_f1594865479ol_int(finite_fold1_int(F),A_2) ) ) ).
fof(fact_296_folding__one_Oeq__fold,axiom,
! [A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A_2) ) ) ).
fof(fact_297_folding__one_Oeq__fold,axiom,
! [A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hAPP_f718417177_state(F_1,A_2) = hAPP_f718417177_state(finite1255650454_state(F),A_2) ) ) ).
fof(fact_298_folding__one_Oclosed,axiom,
! [A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( A_2 != bot_bot_fun_int_bool
=> ( ! [X_2,Y_5] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_5),bot_bot_fun_int_bool))))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A_2)),A_2)) ) ) ) ) ).
fof(fact_299_folding__one_Oclosed,axiom,
! [A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( A_2 != bot_bot_fun_nat_bool
=> ( ! [X_2,Y_5] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_5),bot_bot_fun_nat_bool))))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A_2)),A_2)) ) ) ) ) ).
fof(fact_300_folding__one_Oclosed,axiom,
! [A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( A_2 != bot_bo784226126e_bool
=> ( ! [X_2,Y_5] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_5)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_5),bot_bo784226126e_bool))))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(F_1,A_2)),A_2)) ) ) ) ) ).
fof(fact_301_DiffE,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) ) ) ).
fof(fact_302_DiffE,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))
=> ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) ) ) ).
fof(fact_303_DiffE,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) ) ) ).
fof(fact_304_DiffI,axiom,
! [B_29,Ca,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) ) ) ).
fof(fact_305_DiffI,axiom,
! [B_29,Ca,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) ) ) ).
fof(fact_306_DiffI,axiom,
! [B_29,Ca,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) ) ) ).
fof(fact_307_finite_OemptyI,axiom,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)) ).
fof(fact_308_finite_OemptyI,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)) ).
fof(fact_309_finite_OemptyI,axiom,
hBOOL(hAPP_f1378282496l_bool(finite694102371_state,bot_bo784226126e_bool)) ).
fof(fact_310_finite_OinsertI,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2))) ) ).
fof(fact_311_finite_OinsertI,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2))) ) ).
fof(fact_312_finite_OinsertI,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2))) ) ).
fof(fact_313_finite__Diff,axiom,
! [B_29,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) ) ).
fof(fact_314_finite__Diff,axiom,
! [B_29,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) ) ).
fof(fact_315_finite__Diff,axiom,
! [B_29,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) ) ).
fof(fact_316_finite__Diff__insert,axiom,
! [A_2,A_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29))))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) ) ).
fof(fact_317_finite__Diff__insert,axiom,
! [A_2,A_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29))))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) ) ).
fof(fact_318_finite__Diff__insert,axiom,
! [A_2,A_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29))))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) ) ).
fof(fact_319_finite__Diff2,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) ) ) ).
fof(fact_320_finite__Diff2,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) ) ) ).
fof(fact_321_finite__Diff2,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) ) ) ).
fof(fact_322_DiffD2,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) ) ).
fof(fact_323_DiffD2,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) ) ).
fof(fact_324_DiffD2,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) ) ).
fof(fact_325_DiffD1,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) ) ).
fof(fact_326_DiffD1,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) ) ).
fof(fact_327_DiffD1,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) ) ).
fof(fact_328_Diff__idemp,axiom,
! [A_2,B_29] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29) ).
fof(fact_329_Diff__idemp,axiom,
! [A_2,B_29] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29) ).
fof(fact_330_Diff__idemp,axiom,
! [A_2,B_29] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29) ).
fof(fact_331_Diff__iff,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) ) ) ).
fof(fact_332_Diff__iff,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) ) ) ).
fof(fact_333_Diff__iff,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) ) ) ).
fof(fact_334_set__diff__eq,axiom,
! [A_2,B_29] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),A_2))),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),B_29)))) ).
fof(fact_335_set__diff__eq,axiom,
! [A_2,B_29] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fconj),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A_2))),hAPP_f1805168059t_bool(cOMBB_bool_bool_int(fNot),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B_29)))) ).
fof(fact_336_set__diff__eq,axiom,
! [A_2,B_29] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_2))),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_29)))) ).
fof(fact_337_Diff__cancel,axiom,
! [A_2] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),A_2) = bot_bot_fun_int_bool ).
fof(fact_338_Diff__cancel,axiom,
! [A_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),A_2) = bot_bot_fun_nat_bool ).
fof(fact_339_Diff__cancel,axiom,
! [A_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),A_2) = bot_bo784226126e_bool ).
fof(fact_340_Diff__empty,axiom,
! [A_2] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),bot_bot_fun_int_bool) = A_2 ).
fof(fact_341_Diff__empty,axiom,
! [A_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),bot_bot_fun_nat_bool) = A_2 ).
fof(fact_342_Diff__empty,axiom,
! [A_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),bot_bo784226126e_bool) = A_2 ).
fof(fact_343_empty__Diff,axiom,
! [A_2] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A_2) = bot_bot_fun_int_bool ).
fof(fact_344_empty__Diff,axiom,
! [A_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A_2) = bot_bot_fun_nat_bool ).
fof(fact_345_empty__Diff,axiom,
! [A_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,bot_bo784226126e_bool),A_2) = bot_bo784226126e_bool ).
fof(fact_346_insert__Diff1,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29) ) ).
fof(fact_347_insert__Diff1,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29) ) ).
fof(fact_348_insert__Diff1,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29) ) ).
fof(fact_349_insert__Diff__if,axiom,
! [A_2,X_1,B_29] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)) ) ) ).
fof(fact_350_insert__Diff__if,axiom,
! [A_2,X_1,B_29] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)) ) ) ).
fof(fact_351_insert__Diff__if,axiom,
! [A_2,X_1,B_29] :
( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)) ) ) ).
fof(fact_352_double__diff,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B_29),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_26),A_2)) = A_2 ) ) ).
fof(fact_353_double__diff,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),C_26))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B_29),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_26),A_2)) = A_2 ) ) ).
fof(fact_354_double__diff,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),C_26))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B_29),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_26),A_2)) = A_2 ) ) ).
fof(fact_355_Diff__mono,axiom,
! [D_10,B_29,A_2,C_26] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),C_26))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,D_10),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_26),D_10))) ) ) ).
fof(fact_356_Diff__mono,axiom,
! [D_10,B_29,A_2,C_26] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_26))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_10),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_26),D_10))) ) ) ).
fof(fact_357_Diff__mono,axiom,
! [D_10,B_29,A_2,C_26] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_26))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_10),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_26),D_10))) ) ) ).
fof(fact_358_Diff__subset,axiom,
! [A_2,B_29] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),A_2)) ).
fof(fact_359_Diff__subset,axiom,
! [A_2,B_29] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),A_2)) ).
fof(fact_360_Diff__subset,axiom,
! [A_2,B_29] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),A_2)) ).
fof(fact_361_finite__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) ) ).
fof(fact_362_finite__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) ) ).
fof(fact_363_finite__insert,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) ) ).
fof(fact_364_finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) ) ) ).
fof(fact_365_finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) ) ) ).
fof(fact_366_finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) ) ) ).
fof(fact_367_rev__finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) ) ) ).
fof(fact_368_rev__finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) ) ) ).
fof(fact_369_rev__finite__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) ) ) ).
fof(fact_370_empty__fold__graphE,axiom,
! [F,Z_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),bot_bot_fun_int_bool),X_1))
=> X_1 = Z_1 ) ).
fof(fact_371_empty__fold__graphE,axiom,
! [F,Z_1,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),bot_bot_fun_nat_bool),X_1))
=> X_1 = Z_1 ) ).
fof(fact_372_empty__fold__graphE,axiom,
! [F,Z_1,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),bot_bo784226126e_bool),X_1))
=> X_1 = Z_1 ) ).
fof(fact_373_fold__graph_OemptyI,axiom,
! [F,Z_1] : hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),bot_bot_fun_int_bool),Z_1)) ).
fof(fact_374_fold__graph_OemptyI,axiom,
! [F,Z_1] : hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),bot_bot_fun_nat_bool),Z_1)) ).
fof(fact_375_fold__graph_OemptyI,axiom,
! [F,Z_1] : hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),bot_bo784226126e_bool),Z_1)) ).
fof(fact_376_fold__graph_OinsertI,axiom,
! [F,Z_1,Y_1,X_1,A_2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1))
=> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_1))) ) ) ).
fof(fact_377_fold__graph_OinsertI,axiom,
! [F,Z_1,Y_1,X_1,A_2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_1))) ) ) ).
fof(fact_378_fold__graph_OinsertI,axiom,
! [F,Z_1,Y_1,X_1,A_2] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),Y_1))) ) ) ).
fof(fact_379_folding__one_Oremove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,A_2) = X_1 )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ) ) ) ) ).
fof(fact_380_folding__one_Oremove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,A_2) = X_1 )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ) ) ) ) ).
fof(fact_381_folding__one_Oremove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,A_2) = X_1 )
& ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,A_2) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ) ) ) ) ).
fof(fact_382_folding__one_Oinsert__remove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = X_1 )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ) ) ) ).
fof(fact_383_folding__one_Oinsert__remove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = X_1 )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ) ) ) ).
fof(fact_384_folding__one_Oinsert__remove,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = X_1 )
& ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ) ) ) ).
fof(fact_385_insert__Diff,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) = A_2 ) ).
fof(fact_386_insert__Diff,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) = A_2 ) ).
fof(fact_387_insert__Diff,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) = A_2 ) ).
fof(fact_388_Diff__insert__absorb,axiom,
! [X_1,A_2] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A_2 ) ).
fof(fact_389_Diff__insert__absorb,axiom,
! [X_1,A_2] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A_2 ) ).
fof(fact_390_Diff__insert__absorb,axiom,
! [X_1,A_2] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = A_2 ) ).
fof(fact_391_insert__Diff__single,axiom,
! [A_1,A_2] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) ).
fof(fact_392_insert__Diff__single,axiom,
! [A_1,A_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) ).
fof(fact_393_insert__Diff__single,axiom,
! [A_1,A_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) ).
fof(fact_394_Diff__insert2,axiom,
! [A_2,A_1,B_29] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))),B_29) ).
fof(fact_395_Diff__insert2,axiom,
! [A_2,A_1,B_29] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))),B_29) ).
fof(fact_396_Diff__insert2,axiom,
! [A_2,A_1,B_29] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))),B_29) ).
fof(fact_397_Diff__insert,axiom,
! [A_2,A_1,B_29] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)) ).
fof(fact_398_Diff__insert,axiom,
! [A_2,A_1,B_29] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) ).
fof(fact_399_Diff__insert,axiom,
! [A_2,A_1,B_29] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)) ).
fof(fact_400_finite__empty__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,A_2))
=> ( ! [A_55,A_42] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,A_42))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_42),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),bot_bot_fun_int_bool)))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) ) ) ) ).
fof(fact_401_finite__empty__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,A_2))
=> ( ! [A_55,A_42] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,A_42))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_42),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),bot_bot_fun_nat_bool)))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) ) ) ) ).
fof(fact_402_finite__empty__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,A_2))
=> ( ! [A_55,A_42] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_42))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,A_42))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_42),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),bot_bo784226126e_bool)))) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool)) ) ) ) ).
fof(fact_403_finite__subset__induct,axiom,
! [Pa,A_2,F_1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F_1),A_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
=> ( ! [A_55,F_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),F_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),F_2))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_404_finite__subset__induct,axiom,
! [Pa,A_2,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
=> ( ! [A_55,F_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),F_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),F_2))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_405_finite__subset__induct,axiom,
! [Pa,A_2,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F_1),A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool))
=> ( ! [A_55,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,F_2))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),F_2))) ) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_406_insert__fold1SetE,axiom,
! [F,A_1,X_28,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),X_28)),X_1))
=> ~ ! [A_55,A_42] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),X_28) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42)
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_55),A_42),X_1))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42)) ) ) ) ).
fof(fact_407_insert__fold1SetE,axiom,
! [F,A_1,X_28,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_28)),X_1))
=> ~ ! [A_55,A_42] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_28) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42)
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_55),A_42),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42)) ) ) ) ).
fof(fact_408_insert__fold1SetE,axiom,
! [F,A_1,X_28,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),X_28)),X_1))
=> ~ ! [A_55,A_42] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),X_28) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42)
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_55),A_42),X_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42)) ) ) ) ).
fof(fact_409_finite__nonempty__imp__fold1Set,axiom,
! [F,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( A_2 != bot_bot_fun_int_bool
=> ? [X1] : hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A_2),X1)) ) ) ).
fof(fact_410_finite__nonempty__imp__fold1Set,axiom,
! [F,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( A_2 != bot_bot_fun_nat_bool
=> ? [X1] : hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A_2),X1)) ) ) ).
fof(fact_411_finite__nonempty__imp__fold1Set,axiom,
! [F,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( A_2 != bot_bo784226126e_bool
=> ? [X1] : hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A_2),X1)) ) ) ).
fof(fact_412_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ) ).
fof(fact_413_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ).
fof(fact_414_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,F_2))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)) ) ) ) ).
fof(fact_415_finite_Osimps,axiom,
! [A_1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_1))
<=> ( A_1 = bot_bot_fun_int_bool
| ? [A_42,A_55] :
( A_1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42)
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42)) ) ) ) ).
fof(fact_416_finite_Osimps,axiom,
! [A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
<=> ( A_1 = bot_bot_fun_nat_bool
| ? [A_42,A_55] :
( A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42)
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42)) ) ) ) ).
fof(fact_417_finite_Osimps,axiom,
! [A_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
<=> ( A_1 = bot_bo784226126e_bool
| ? [A_42,A_55] :
( A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42)
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_42)) ) ) ) ).
fof(fact_418_finite__imp__fold__graph,axiom,
! [F,Z_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ? [X1] : hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),X1)) ) ).
fof(fact_419_finite__imp__fold__graph,axiom,
! [F,Z_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ? [X1] : hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),X1)) ) ).
fof(fact_420_finite__imp__fold__graph,axiom,
! [F,Z_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ? [X1] : hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),X1)) ) ).
fof(fact_421_fold1Set_Osimps,axiom,
! [F,A1,A2] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A1),A2))
<=> ? [A_55,A_42,X_2] :
( A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42)
& A2 = X_2
& hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_55),A_42),X_2))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42)) ) ) ).
fof(fact_422_fold1Set_Osimps,axiom,
! [F,A1,A2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A1),A2))
<=> ? [A_55,A_42,X_2] :
( A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42)
& A2 = X_2
& hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_55),A_42),X_2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42)) ) ) ).
fof(fact_423_fold1Set_Osimps,axiom,
! [F,A1,A2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A1),A2))
<=> ? [A_55,A_42,X_2] :
( A1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42)
& A2 = X_2
& hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_55),A_42),X_2))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42)) ) ) ).
fof(fact_424_minus__apply,axiom,
! [A_2,B_29,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H242767318e_bool(A_2,X_1)),hAPP_H242767318e_bool(B_29,X_1))) ) ).
fof(fact_425_minus__apply,axiom,
! [A_2,B_29,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A_2,X_1)),hAPP_int_bool(B_29,X_1))) ) ).
fof(fact_426_minus__apply,axiom,
! [A_2,B_29,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_2,X_1)),hAPP_nat_bool(B_29,X_1))) ) ).
fof(fact_427_fun__diff__def,axiom,
! [A_2,B_29,X_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H242767318e_bool(A_2,X_2)),hAPP_H242767318e_bool(B_29,X_2))) ) ).
fof(fact_428_fun__diff__def,axiom,
! [A_2,B_29,X_2] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A_2,X_2)),hAPP_int_bool(B_29,X_2))) ) ).
fof(fact_429_fun__diff__def,axiom,
! [A_2,B_29,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_2,X_2)),hAPP_nat_bool(B_29,X_2))) ) ).
fof(fact_430_diff__eq__diff__less__eq,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),D_1)) ) ) ).
fof(fact_431_fold__graph_Osimps,axiom,
! [F,Z_1,A1,A2] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A1),A2))
<=> ( ( A1 = bot_bot_fun_int_bool
& A2 = Z_1 )
| ? [X_2,A_42,Y_5] :
( A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),A_42)
& A2 = hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_5)
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42))
& hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_42),Y_5)) ) ) ) ).
fof(fact_432_fold__graph_Osimps,axiom,
! [F,Z_1,A1,A2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A1),A2))
<=> ( ( A1 = bot_bot_fun_nat_bool
& A2 = Z_1 )
| ? [X_2,A_42,Y_5] :
( A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_42)
& A2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_5)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42))
& hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_42),Y_5)) ) ) ) ).
fof(fact_433_fold__graph_Osimps,axiom,
! [F,Z_1,A1,A2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A1),A2))
<=> ( ( A1 = bot_bo784226126e_bool
& A2 = Z_1 )
| ? [X_2,A_42,Y_5] :
( A1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_42)
& A2 = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_5)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_42))
& hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_42),Y_5)) ) ) ) ).
fof(fact_434_folding__one__idem_Osubset__idem,axiom,
! [B_29,A_2,F,F_1] :
( hBOOL(finite1432773856em_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( B_29 != bot_bot_fun_int_bool
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),A_2))
=> hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B_29)),hAPP_f1594865479ol_int(F_1,A_2)) = hAPP_f1594865479ol_int(F_1,A_2) ) ) ) ) ).
fof(fact_435_folding__one__idem_Osubset__idem,axiom,
! [B_29,A_2,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( B_29 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),A_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B_29)),hAPP_f22106695ol_nat(F_1,A_2)) = hAPP_f22106695ol_nat(F_1,A_2) ) ) ) ) ).
fof(fact_436_folding__one__idem_Osubset__idem,axiom,
! [B_29,A_2,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( B_29 != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,B_29)),hAPP_f718417177_state(F_1,A_2)) = hAPP_f718417177_state(F_1,A_2) ) ) ) ) ).
fof(fact_437_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1432773856em_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( A_2 != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2)) ) ) ) ).
fof(fact_438_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( A_2 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2)) ) ) ) ).
fof(fact_439_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( A_2 != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2)) ) ) ) ).
fof(fact_440_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
=> ( F_1 != bot_bot_fun_int_bool
=> ( ! [X_2] : hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),bot_bot_fun_int_bool)))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
=> ( F_2 != bot_bot_fun_int_bool
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_441_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( F_1 != bot_bot_fun_nat_bool
=> ( ! [X_2] : hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
=> ( F_2 != bot_bot_fun_nat_bool
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_442_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( F_1 != bot_bo784226126e_bool
=> ( ! [X_2] : hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( F_2 != bot_bo784226126e_bool
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,F_2))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_443_folding__one__idem_Oidem,axiom,
! [X_1,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),X_1) = X_1 ) ).
fof(fact_444_folding__one__idem_Oin__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2)) = hAPP_f718417177_state(F_1,A_2) ) ) ) ).
fof(fact_445_folding__one__idem_Oin__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1432773856em_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2)) = hAPP_f1594865479ol_int(F_1,A_2) ) ) ) ).
fof(fact_446_folding__one__idem_Oin__idem,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2)) = hAPP_f22106695ol_nat(F_1,A_2) ) ) ) ).
fof(fact_447_diff__eq__diff__eq,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1)
=> ( A_1 = B_2
<=> Ca = D_1 ) ) ).
fof(fact_448_comp__fun__commute_Ofold__graph__insertE__aux,axiom,
! [A_1,Z_1,A_2,Y_1,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> ? [Y_27] :
( Y_1 = hAPP_int_int(hAPP_int_fun_int_int(F,A_1),Y_27)
& hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))),Y_27)) ) ) ) ) ).
fof(fact_449_comp__fun__commute_Ofold__graph__insertE__aux,axiom,
! [A_1,Z_1,A_2,Y_1,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> ? [Y_27] :
( Y_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,A_1),Y_27)
& hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))),Y_27)) ) ) ) ) ).
fof(fact_450_comp__fun__commute_Ofold__graph__insertE__aux,axiom,
! [A_1,Z_1,A_2,Y_1,F] :
( hBOOL(finite1720675051_state(F))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> ? [Y_27] :
( Y_1 = hAPP_H574424047_state(hAPP_H280516760_state(F,A_1),Y_27)
& hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))),Y_27)) ) ) ) ) ).
fof(fact_451_semilattice__big_OF__eq,axiom,
! [A_2,F,F_1] :
( hBOOL(big_se913005884ig_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_f1594865479ol_int(finite_fold1_int(F),A_2) ) ) ).
fof(fact_452_semilattice__big_OF__eq,axiom,
! [A_2,F,F_1] :
( hBOOL(big_se275732192ig_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A_2) ) ) ).
fof(fact_453_semilattice__big_OF__eq,axiom,
! [A_2,F,F_1] :
( hBOOL(big_se1212619424_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hAPP_f718417177_state(F_1,A_2) = hAPP_f718417177_state(finite1255650454_state(F),A_2) ) ) ).
fof(fact_454_fold__graph__permute__diff,axiom,
! [A_1,B_2,A_2,X_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,B_2),A_2),X_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)))),X_1)) ) ) ) ).
fof(fact_455_fold__graph__permute__diff,axiom,
! [A_1,B_2,A_2,X_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,B_2),A_2),X_1))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),A_2))
=> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)))),X_1)) ) ) ) ).
fof(fact_456_fold1__insert,axiom,
! [X_1,A_2] :
( A_2 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A_2)) ) ) ) ).
fof(fact_457_fold1__insert,axiom,
! [X_1,A_2] :
( A_2 != bot_bot_fun_int_bool
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A_2)) ) ) ) ).
fof(fact_458_psubset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) ) ) ) ) ) ).
fof(fact_459_psubset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) ) ) ) ) ) ).
fof(fact_460_psubset__insert__iff,axiom,
! [A_2,X_1,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29)))
<=> ( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))
=> ( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ) ) ) ) ).
fof(fact_461_card__Diff1__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2))) ) ).
fof(fact_462_card__Diff1__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2))) ) ).
fof(fact_463_card__Diff1__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))) ) ).
fof(fact_464_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [A_54,B_41,C_31] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_54),B_41)),C_31) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_54),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_41),C_31)) ).
fof(fact_465_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [A_54,B_41,C_31] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_54),B_41)),C_31) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_54),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_41),C_31)) ).
fof(fact_466_psubsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) ) ) ).
fof(fact_467_psubsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) ) ) ).
fof(fact_468_psubsetD,axiom,
! [Ca,A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) ) ) ).
fof(fact_469_psubset__trans,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_29),C_26))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26)) ) ) ).
fof(fact_470_comp__fun__commute,axiom,
hBOOL(finite2130160977at_nat(times_times_nat)) ).
fof(fact_471_comp__fun__commute,axiom,
hBOOL(finite1973466193nt_int(times_times_int)) ).
fof(fact_472_order__less__irrefl,axiom,
! [X_1] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),X_1)) ).
fof(fact_473_order__less__irrefl,axiom,
! [X_27] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),X_27)) ).
fof(fact_474_order__less__irrefl,axiom,
! [X_27] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_27),X_27)) ).
fof(fact_475_linorder__neq__iff,axiom,
! [X_1,Y_1] :
( X_1 != Y_1
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) ) ) ).
fof(fact_476_linorder__neq__iff,axiom,
! [X_1,Y_1] :
( X_1 != Y_1
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) ) ) ).
fof(fact_477_not__less__iff__gr__or__eq,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
| X_1 = Y_1 ) ) ).
fof(fact_478_not__less__iff__gr__or__eq,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1))
| X_1 = Y_1 ) ) ).
fof(fact_479_linorder__less__linear,axiom,
! [X_26,Y_26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_26))
| X_26 = Y_26
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_26),X_26)) ) ).
fof(fact_480_linorder__less__linear,axiom,
! [X_26,Y_26] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_26),Y_26))
| X_26 = Y_26
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_26),X_26)) ) ).
fof(fact_481_comp__fun__commute_Ofun__left__comm,axiom,
! [X_1,Y_1,Z_1,F] :
( hBOOL(finite1973466193nt_int(F))
=> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_int_int(hAPP_int_fun_int_int(F,Y_1),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(F,Y_1),hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)) ) ).
fof(fact_482_comp__fun__commute_Ofun__left__comm,axiom,
! [X_1,Y_1,Z_1,F] :
( hBOOL(finite2130160977at_nat(F))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Y_1),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Y_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)) ) ).
fof(fact_483_linorder__antisym__conv3,axiom,
! [Y_1,X_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_484_linorder__antisym__conv3,axiom,
! [Y_1,X_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_485_linorder__neqE,axiom,
! [X_25,Y_25] :
( X_25 != Y_25
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_25))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_25),X_25)) ) ) ).
fof(fact_486_linorder__neqE,axiom,
! [X_25,Y_25] :
( X_25 != Y_25
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_25),Y_25))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_25),X_25)) ) ) ).
fof(fact_487_less__imp__neq,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> X_1 != Y_1 ) ).
fof(fact_488_less__imp__neq,axiom,
! [X_24,Y_24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_24))
=> X_24 != Y_24 ) ).
fof(fact_489_less__imp__neq,axiom,
! [X_24,Y_24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_24),Y_24))
=> X_24 != Y_24 ) ).
fof(fact_490_order__less__not__sym,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) ) ).
fof(fact_491_order__less__not__sym,axiom,
! [X_23,Y_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_23))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_23)) ) ).
fof(fact_492_order__less__not__sym,axiom,
! [X_23,Y_23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_23),Y_23))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_23),X_23)) ) ).
fof(fact_493_order__less__imp__not__less,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) ) ).
fof(fact_494_order__less__imp__not__less,axiom,
! [X_22,Y_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_22))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_22),X_22)) ) ).
fof(fact_495_order__less__imp__not__less,axiom,
! [X_22,Y_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_22),Y_22))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_22),X_22)) ) ).
fof(fact_496_order__less__imp__not__eq,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> X_1 != Y_1 ) ).
fof(fact_497_order__less__imp__not__eq,axiom,
! [X_21,Y_21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),Y_21))
=> X_21 != Y_21 ) ).
fof(fact_498_order__less__imp__not__eq,axiom,
! [X_21,Y_21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_21),Y_21))
=> X_21 != Y_21 ) ).
fof(fact_499_order__less__imp__not__eq2,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> Y_1 != X_1 ) ).
fof(fact_500_order__less__imp__not__eq2,axiom,
! [X_20,Y_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_20),Y_20))
=> Y_20 != X_20 ) ).
fof(fact_501_order__less__imp__not__eq2,axiom,
! [X_20,Y_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_20))
=> Y_20 != X_20 ) ).
fof(fact_502_order__less__imp__triv,axiom,
! [Pa,X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1))
=> hBOOL(Pa) ) ) ).
fof(fact_503_order__less__imp__triv,axiom,
! [Pa,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(Pa) ) ) ).
fof(fact_504_order__less__imp__triv,axiom,
! [Pa,X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1))
=> hBOOL(Pa) ) ) ).
fof(fact_505_order__less__asym_H,axiom,
! [A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)) ) ).
fof(fact_506_order__less__asym_H,axiom,
! [A_53,B_40] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_53),B_40))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_40),A_53)) ) ).
fof(fact_507_order__less__asym_H,axiom,
! [A_53,B_40] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_53),B_40))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_40),A_53)) ) ).
fof(fact_508_xt1_I9_J,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)) ) ).
fof(fact_509_xt1_I9_J,axiom,
! [B_39,A_52] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_39),A_52))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_52),B_39)) ) ).
fof(fact_510_xt1_I9_J,axiom,
! [B_39,A_52] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_39),A_52))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_52),B_39)) ) ).
fof(fact_511_ord__eq__less__trans,axiom,
! [Ca,A_1,B_2] :
( A_1 = B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),Ca))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),Ca)) ) ) ).
fof(fact_512_ord__eq__less__trans,axiom,
! [C_30,A_51,B_38] :
( A_51 = B_38
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_38),C_30))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_51),C_30)) ) ) ).
fof(fact_513_ord__eq__less__trans,axiom,
! [C_30,A_51,B_38] :
( A_51 = B_38
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_38),C_30))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_51),C_30)) ) ) ).
fof(fact_514_xt1_I1_J,axiom,
! [Ca,A_1,B_2] :
( A_1 = B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),A_1)) ) ) ).
fof(fact_515_xt1_I1_J,axiom,
! [C_29,A_50,B_37] :
( A_50 = B_37
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_29),B_37))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_29),A_50)) ) ) ).
fof(fact_516_xt1_I1_J,axiom,
! [C_29,A_50,B_37] :
( A_50 = B_37
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_29),B_37))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_29),A_50)) ) ) ).
fof(fact_517_ord__less__eq__trans,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2))
=> ( B_2 = Ca
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),Ca)) ) ) ).
fof(fact_518_ord__less__eq__trans,axiom,
! [C_28,A_49,B_36] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_49),B_36))
=> ( B_36 = C_28
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_49),C_28)) ) ) ).
fof(fact_519_ord__less__eq__trans,axiom,
! [C_28,A_49,B_36] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_49),B_36))
=> ( B_36 = C_28
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_49),C_28)) ) ) ).
fof(fact_520_xt1_I2_J,axiom,
! [Ca,B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1))
=> ( B_2 = Ca
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),A_1)) ) ) ).
fof(fact_521_xt1_I2_J,axiom,
! [C_27,B_35,A_48] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_35),A_48))
=> ( B_35 = C_27
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_27),A_48)) ) ) ).
fof(fact_522_xt1_I2_J,axiom,
! [C_27,B_35,A_48] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_35),A_48))
=> ( B_35 = C_27
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_27),A_48)) ) ) ).
fof(fact_523_order__less__trans,axiom,
! [Z_1,X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),Z_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1)) ) ) ).
fof(fact_524_order__less__trans,axiom,
! [Z_10,X_19,Y_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Y_19))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_19),Z_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Z_10)) ) ) ).
fof(fact_525_order__less__trans,axiom,
! [Z_10,X_19,Y_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Y_19))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_19),Z_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Z_10)) ) ) ).
fof(fact_526_xt1_I10_J,axiom,
! [Z_1,Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),Y_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1)) ) ) ).
fof(fact_527_xt1_I10_J,axiom,
! [Z_9,Y_18,X_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_18),X_18))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_18)) ) ) ).
fof(fact_528_xt1_I10_J,axiom,
! [Z_9,Y_18,X_18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_18),X_18))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_9),Y_18))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_9),X_18)) ) ) ).
fof(fact_529_order__less__asym,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) ) ).
fof(fact_530_order__less__asym,axiom,
! [X_17,Y_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_17),Y_17))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_17),X_17)) ) ).
fof(fact_531_order__less__asym,axiom,
! [X_17,Y_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_17),Y_17))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_17),X_17)) ) ).
fof(fact_532_linorder__cases,axiom,
! [X_16,Y_16] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_16),Y_16))
=> ( X_16 != Y_16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_16),X_16)) ) ) ).
fof(fact_533_linorder__cases,axiom,
! [X_16,Y_16] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_16),Y_16))
=> ( X_16 != Y_16
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_16),X_16)) ) ) ).
fof(fact_534_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,F),G))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G),F)) ) ) ).
fof(fact_535_linorder__not__less,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ) ).
fof(fact_536_linorder__not__less,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) ) ).
fof(fact_537_linorder__not__le,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) ) ).
fof(fact_538_linorder__not__le,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) ) ).
fof(fact_539_linorder__le__less__linear,axiom,
! [X_15,Y_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_15),X_15)) ) ).
fof(fact_540_linorder__le__less__linear,axiom,
! [X_15,Y_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_15),Y_15))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_15),X_15)) ) ).
fof(fact_541_order__less__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
& X_1 != Y_1 ) ) ).
fof(fact_542_order__less__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
& X_1 != Y_1 ) ) ).
fof(fact_543_order__less__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
& X_1 != Y_1 ) ) ).
fof(fact_544_less__le__not__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) ) ) ).
fof(fact_545_less__le__not__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ) ) ).
fof(fact_546_less__le__not__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) ) ) ).
fof(fact_547_order__le__less,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
| X_1 = Y_1 ) ) ).
fof(fact_548_order__le__less,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
| X_1 = Y_1 ) ) ).
fof(fact_549_order__le__less,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
| X_1 = Y_1 ) ) ).
fof(fact_550_leI,axiom,
! [X_14,Y_14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_14),X_14)) ) ).
fof(fact_551_leI,axiom,
! [X_14,Y_14] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_14),Y_14))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_14),X_14)) ) ).
fof(fact_552_not__leE,axiom,
! [Y_13,X_13] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_13)) ) ).
fof(fact_553_not__leE,axiom,
! [Y_13,X_13] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_13),X_13))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_13)) ) ).
fof(fact_554_linorder__antisym__conv1,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_555_linorder__antisym__conv1,axiom,
! [X_1,Y_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_556_order__neq__le__trans,axiom,
! [A_1,B_2] :
( A_1 != B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)) ) ) ).
fof(fact_557_order__neq__le__trans,axiom,
! [A_47,B_34] :
( A_47 != B_34
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_47),B_34))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_47),B_34)) ) ) ).
fof(fact_558_order__neq__le__trans,axiom,
! [A_47,B_34] :
( A_47 != B_34
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_47),B_34))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_47),B_34)) ) ) ).
fof(fact_559_xt1_I12_J,axiom,
! [A_1,B_2] :
( A_1 != B_2
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)) ) ) ).
fof(fact_560_xt1_I12_J,axiom,
! [A_46,B_33] :
( A_46 != B_33
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_33),A_46))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_33),A_46)) ) ) ).
fof(fact_561_xt1_I12_J,axiom,
! [A_46,B_33] :
( A_46 != B_33
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_33),A_46))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_33),A_46)) ) ) ).
fof(fact_562_leD,axiom,
! [Y_12,X_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_12),X_12))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_12),Y_12)) ) ).
fof(fact_563_leD,axiom,
! [Y_12,X_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_12),X_12))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_12),Y_12)) ) ).
fof(fact_564_order__less__imp__le,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) ) ).
fof(fact_565_order__less__imp__le,axiom,
! [X_11,Y_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),Y_11)) ) ).
fof(fact_566_order__less__imp__le,axiom,
! [X_11,Y_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_11),Y_11))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),Y_11)) ) ).
fof(fact_567_linorder__antisym__conv2,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_568_linorder__antisym__conv2,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_569_order__le__imp__less__or__eq,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
| X_1 = Y_1 ) ) ).
fof(fact_570_order__le__imp__less__or__eq,axiom,
! [X_10,Y_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10))
| X_10 = Y_10 ) ) ).
fof(fact_571_order__le__imp__less__or__eq,axiom,
! [X_10,Y_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_10))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_10),Y_10))
| X_10 = Y_10 ) ) ).
fof(fact_572_order__le__neq__trans,axiom,
! [A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2))
=> ( A_1 != B_2
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)) ) ) ).
fof(fact_573_order__le__neq__trans,axiom,
! [A_45,B_32] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_45),B_32))
=> ( A_45 != B_32
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_45),B_32)) ) ) ).
fof(fact_574_order__le__neq__trans,axiom,
! [A_45,B_32] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_45),B_32))
=> ( A_45 != B_32
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_45),B_32)) ) ) ).
fof(fact_575_xt1_I11_J,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1))
=> ( A_1 != B_2
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)) ) ) ).
fof(fact_576_xt1_I11_J,axiom,
! [B_31,A_44] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_31),A_44))
=> ( A_44 != B_31
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_44)) ) ) ).
fof(fact_577_xt1_I11_J,axiom,
! [B_31,A_44] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_31),A_44))
=> ( A_44 != B_31
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_31),A_44)) ) ) ).
fof(fact_578_order__less__le__trans,axiom,
! [Z_1,X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),Z_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1)) ) ) ).
fof(fact_579_order__less__le__trans,axiom,
! [Z_8,X_9,Y_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),Z_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Z_8)) ) ) ).
fof(fact_580_order__less__le__trans,axiom,
! [Z_8,X_9,Y_9] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),Z_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Z_8)) ) ) ).
fof(fact_581_xt1_I7_J,axiom,
! [Z_1,Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),Y_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1)) ) ) ).
fof(fact_582_xt1_I7_J,axiom,
! [Z_7,Y_8,X_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_8),X_8))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_7),X_8)) ) ) ).
fof(fact_583_xt1_I7_J,axiom,
! [Z_7,Y_8,X_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_8),X_8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_7),Y_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_7),X_8)) ) ) ).
fof(fact_584_order__le__less__trans,axiom,
! [Z_1,X_1,Y_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),Z_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1)) ) ) ).
fof(fact_585_order__le__less__trans,axiom,
! [Z_6,X_7,Y_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),Z_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Z_6)) ) ) ).
fof(fact_586_order__le__less__trans,axiom,
! [Z_6,X_7,Y_7] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Y_7))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_7),Z_6))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_7),Z_6)) ) ) ).
fof(fact_587_xt1_I8_J,axiom,
! [Z_1,Y_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),Y_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1)) ) ) ).
fof(fact_588_xt1_I8_J,axiom,
! [Z_5,Y_6,X_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_6))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_5),Y_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_5),X_6)) ) ) ).
fof(fact_589_xt1_I8_J,axiom,
! [Z_5,Y_6,X_6] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),X_6))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_5),Y_6))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_5),X_6)) ) ) ).
fof(fact_590_not__less__bot,axiom,
! [A_1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_1),bot_bot_fun_int_bool)) ).
fof(fact_591_not__less__bot,axiom,
! [A_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_1),bot_bot_fun_nat_bool)) ).
fof(fact_592_not__less__bot,axiom,
! [A_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,A_1),bot_bot_bool)) ).
fof(fact_593_not__less__bot,axiom,
! [A_1] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),bot_bo784226126e_bool)) ).
fof(fact_594_not__less__bot,axiom,
! [A_43] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_43),bot_bot_nat)) ).
fof(fact_595_bot__less,axiom,
! [A_1] :
( A_1 != bot_bot_fun_int_bool
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,bot_bot_fun_int_bool),A_1)) ) ).
fof(fact_596_bot__less,axiom,
! [A_1] :
( A_1 != bot_bot_fun_nat_bool
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,bot_bot_fun_nat_bool),A_1)) ) ).
fof(fact_597_bot__less,axiom,
! [A_1] :
( ~ ( hBOOL(A_1)
<=> hBOOL(bot_bot_bool) )
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,bot_bot_bool),A_1)) ) ).
fof(fact_598_bot__less,axiom,
! [A_1] :
( A_1 != bot_bo784226126e_bool
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,bot_bo784226126e_bool),A_1)) ) ).
fof(fact_599_bot__less,axiom,
! [A_1] :
( A_1 != bot_bot_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,bot_bot_nat),A_1)) ) ).
fof(fact_600_not__psubset__empty,axiom,
! [A_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),bot_bot_fun_int_bool)) ).
fof(fact_601_not__psubset__empty,axiom,
! [A_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),bot_bot_fun_nat_bool)) ).
fof(fact_602_not__psubset__empty,axiom,
! [A_2] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),bot_bo784226126e_bool)) ).
fof(fact_603_diff__eq__diff__less,axiom,
! [A_1,B_2,Ca,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ca),D_1)) ) ) ).
fof(fact_604_psubset__eq,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
& A_2 != B_29 ) ) ).
fof(fact_605_subset__iff__psubset__eq,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
| A_2 = B_29 ) ) ).
fof(fact_606_psubset__imp__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) ) ).
fof(fact_607_psubset__subset__trans,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26)) ) ) ).
fof(fact_608_subset__psubset__trans,axiom,
! [C_26,A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_29),C_26))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26)) ) ) ).
fof(fact_609_card__insert__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)))) ) ).
fof(fact_610_card__insert__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)))) ) ).
fof(fact_611_card__insert__le,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)))) ) ).
fof(fact_612_card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))) ) ) ).
fof(fact_613_card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))) ) ) ).
fof(fact_614_card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))) ) ) ).
fof(fact_615_card__seteq,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,B_29)),hAPP_f1676271015ol_nat(finite1401757860_state,A_2)))
=> A_2 = B_29 ) ) ) ).
fof(fact_616_card__seteq,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,B_29)),hAPP_f957591787ol_nat(finite_card_int,A_2)))
=> A_2 = B_29 ) ) ) ).
fof(fact_617_card__seteq,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_29)),hAPP_f22106695ol_nat(finite_card_nat,A_2)))
=> A_2 = B_29 ) ) ) ).
fof(fact_618_diff__card__le__card__Diff,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))) ) ).
fof(fact_619_diff__card__le__card__Diff,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))) ) ).
fof(fact_620_diff__card__le__card__Diff,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))) ) ).
fof(fact_621_comp__fun__commute_Ofold__graph__determ,axiom,
! [Y_1,Z_1,A_2,X_1,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1))
=> Y_1 = X_1 ) ) ) ).
fof(fact_622_comp__fun__commute_Ofold__graph__determ,axiom,
! [Y_1,Z_1,A_2,X_1,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),X_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1))
=> Y_1 = X_1 ) ) ) ).
fof(fact_623_comp__fun__commute_Ofold__graph__determ,axiom,
! [Y_1,Z_1,A_2,X_1,F] :
( hBOOL(finite1720675051_state(F))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),X_1))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1))
=> Y_1 = X_1 ) ) ) ).
fof(fact_624_fold__graph__insert__swap,axiom,
! [Z_1,B_2,A_2,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,B_2),A_2),Y_1))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),A_2))
=> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),Y_1))) ) ) ).
fof(fact_625_fold__graph__insert__swap,axiom,
! [Z_1,B_2,A_2,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,B_2),A_2),Y_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Z_1),Y_1))) ) ) ).
fof(fact_626_card__Diff__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29)) ) ) ).
fof(fact_627_card__Diff__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29)) ) ) ).
fof(fact_628_card__Diff__subset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29)) ) ) ).
fof(fact_629_fold1__in,axiom,
! [A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( A_2 != bot_bot_fun_int_bool
=> ( ! [X_2,Y_5] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_2),Y_5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_5),bot_bot_fun_int_bool))))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A_2)),A_2)) ) ) ) ).
fof(fact_630_fold1__in,axiom,
! [A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( A_2 != bot_bot_fun_nat_bool
=> ( ! [X_2,Y_5] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_2),Y_5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_5),bot_bot_fun_nat_bool))))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A_2)),A_2)) ) ) ) ).
fof(fact_631_comp__fun__commute_Ofold__graph__insertE,axiom,
! [Z_1,X_1,A_2,V_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),V_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ~ ! [Y_5] :
( V_2 = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_5)
=> ~ hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_5)) ) ) ) ) ).
fof(fact_632_comp__fun__commute_Ofold__graph__insertE,axiom,
! [Z_1,X_1,A_2,V_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),V_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ~ ! [Y_5] :
( V_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_5)
=> ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_5)) ) ) ) ) ).
fof(fact_633_comp__fun__commute_Ofold__graph__insertE,axiom,
! [Z_1,X_1,A_2,V_2,F] :
( hBOOL(finite1720675051_state(F))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),V_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ~ ! [Y_5] :
( V_2 = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),Y_5)
=> ~ hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_5)) ) ) ) ) ).
fof(fact_634_psubset__imp__ex__mem,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> ? [B_30] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_30),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B_29),A_2))) ) ).
fof(fact_635_psubset__imp__ex__mem,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29))
=> ? [B_30] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_30),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B_29),A_2))) ) ).
fof(fact_636_psubset__imp__ex__mem,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29))
=> ? [B_30] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_30),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B_29),A_2))) ) ).
fof(fact_637_psubset__card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))) ) ) ).
fof(fact_638_psubset__card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))) ) ) ).
fof(fact_639_psubset__card__mono,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))) ) ) ).
fof(fact_640_card__psubset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) ) ) ) ).
fof(fact_641_card__psubset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)) ) ) ) ).
fof(fact_642_card__psubset,axiom,
! [A_2,B_29] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)) ) ) ) ).
fof(fact_643_card__Diff1__less,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2))) ) ) ).
fof(fact_644_card__Diff1__less,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2))) ) ) ).
fof(fact_645_card__Diff1__less,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))) ) ) ).
fof(fact_646_card__Diff2__less,axiom,
! [Y_1,X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2))) ) ) ) ).
fof(fact_647_card__Diff2__less,axiom,
! [Y_1,X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2))) ) ) ) ).
fof(fact_648_card__Diff2__less,axiom,
! [Y_1,X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_1),A_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))) ) ) ) ).
fof(fact_649_finite__linorder__max__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
=> ( ! [B_30,A_42] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42))
=> ( ! [X_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),B_30)) )
=> ( hBOOL(hAPP_f448129468l_bool(Pa,A_42))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_30),A_42))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,A_2)) ) ) ) ).
fof(fact_650_finite__linorder__max__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
=> ( ! [B_30,A_42] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42))
=> ( ! [X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),B_30)) )
=> ( hBOOL(hAPP_f54304608l_bool(Pa,A_42))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_30),A_42))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,A_2)) ) ) ) ).
fof(fact_651_diff__less__mono,axiom,
! [C_25,A,B_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_25),A))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A),C_25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_1),C_25))) ) ) ).
fof(fact_652_less__diff__iff,axiom,
! [N,K,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ) ).
fof(fact_653_finite__linorder__min__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
=> ( ! [B_30,A_42] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42))
=> ( ! [X_2] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_30),X_2)) )
=> ( hBOOL(hAPP_f448129468l_bool(Pa,A_42))
=> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_30),A_42))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(Pa,A_2)) ) ) ) ).
fof(fact_654_finite__linorder__min__induct,axiom,
! [Pa,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
=> ( ! [B_30,A_42] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42))
=> ( ! [X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_30),X_2)) )
=> ( hBOOL(hAPP_f54304608l_bool(Pa,A_42))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_30),A_42))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,A_2)) ) ) ) ).
fof(fact_655_le__diff__iff,axiom,
! [N,K,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ) ) ).
fof(fact_656_Nat_Odiff__diff__eq,axiom,
! [N_1,K_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) ) ) ).
fof(fact_657_eq__diff__iff,axiom,
! [N,K,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K)
<=> M = N ) ) ) ).
fof(fact_658_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_659_nat__neq__iff,axiom,
! [M,N] :
( M != N
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ) ) ).
fof(fact_660_linorder__neqE__nat,axiom,
! [X,Y] :
( X != Y
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).
fof(fact_661_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_662_less__not__refl2,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
=> M_1 != N_1 ) ).
fof(fact_663_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_664_nat__less__cases,axiom,
! [Pa,M,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> ( ( M = N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) ) ) ) ).
fof(fact_665_mult__le__mono,axiom,
! [K_1,L_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1))) ) ) ).
fof(fact_666_le__antisym,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> M_1 = N_1 ) ) ).
fof(fact_667_le__trans,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1)) ) ) ).
fof(fact_668_mult__le__mono2,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))) ) ).
fof(fact_669_mult__le__mono1,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))) ) ).
fof(fact_670_eq__imp__le,axiom,
! [M_1,N_1] :
( M_1 = N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_671_nat__le__linear,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) ) ).
fof(fact_672_le__cube,axiom,
! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))) ).
fof(fact_673_le__square,axiom,
! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))) ).
fof(fact_674_le__refl,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).
fof(fact_675_diff__mult__distrib,axiom,
! [M_1,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1)) ).
fof(fact_676_diff__mult__distrib2,axiom,
! [K_1,M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)) ).
fof(fact_677_diff__commute,axiom,
! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),K_1)),J) ).
fof(fact_678_nat__less__le,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
& M != N ) ) ).
fof(fact_679_le__eq__less__or__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| M = N ) ) ).
fof(fact_680_less__imp__le__nat,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_681_le__neq__implies__less,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> ( M_1 != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ) ).
fof(fact_682_less__or__eq__imp__le,axiom,
! [M_1,N_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
| M_1 = N_1 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_683_diff__less__mono2,axiom,
! [L_1,M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))) ) ) ).
fof(fact_684_less__imp__diff__less,axiom,
! [N_1,J,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N_1)),K_1)) ) ).
fof(fact_685_diff__le__self,axiom,
! [M_1,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1)) ).
fof(fact_686_diff__le__mono2,axiom,
! [L_1,M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))) ) ).
fof(fact_687_diff__le__mono,axiom,
! [L_1,M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),L_1))) ) ).
fof(fact_688_diff__diff__cancel,axiom,
! [I_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I_1)) = I_1 ) ).
fof(fact_689_less__mono__imp__le__mono,axiom,
! [I_2,J_2,F] :
( ! [I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_1))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_2))) ) ) ).
fof(fact_690_termination__basic__simps_I5_J,axiom,
! [X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).
fof(fact_691_card__Diff__singleton__if,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),one_one_nat) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,A_2) ) ) ) ).
fof(fact_692_card__Diff__singleton__if,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),one_one_nat) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,A_2) ) ) ) ).
fof(fact_693_card__Diff__singleton__if,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),one_one_nat) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_f1676271015ol_nat(finite1401757860_state,A_2) ) ) ) ).
fof(fact_694_card__Diff__singleton,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),one_one_nat) ) ) ).
fof(fact_695_card__Diff__singleton,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),one_one_nat) ) ) ).
fof(fact_696_card__Diff__singleton,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),one_one_nat) ) ) ).
fof(fact_697_card__Diff__insert,axiom,
! [B_29,A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))),one_one_nat) ) ) ) ).
fof(fact_698_card__Diff__insert,axiom,
! [B_29,A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))),one_one_nat) ) ) ) ).
fof(fact_699_card__Diff__insert,axiom,
! [B_29,A_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))),one_one_nat) ) ) ) ).
fof(fact_700_comp__fun__commute_Ofold__insert__remove,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ) ).
fof(fact_701_comp__fun__commute_Ofold__insert__remove,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ) ).
fof(fact_702_nat__mult__assoc,axiom,
! [M_1,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1)) ).
fof(fact_703_nat__mult__eq__1__iff,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = one_one_nat
<=> ( M = one_one_nat
& N = one_one_nat ) ) ).
fof(fact_704_nat__mult__commute,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1) ).
fof(fact_705_nat__mult__1__right,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),one_one_nat) = N_1 ).
fof(fact_706_nat__1__eq__mult__iff,axiom,
! [M,N] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)
<=> ( M = one_one_nat
& N = one_one_nat ) ) ).
fof(fact_707_nat__mult__1,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N_1) = N_1 ).
fof(fact_708_one__reorient,axiom,
! [X_1] :
( one_one_int = X_1
<=> X_1 = one_one_int ) ).
fof(fact_709_one__reorient,axiom,
! [X_1] :
( one_one_nat = X_1
<=> X_1 = one_one_nat ) ).
fof(fact_710_mult__1__left,axiom,
! [A_41] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_41) = A_41 ).
fof(fact_711_mult__1__left,axiom,
! [A_41] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_41) = A_41 ).
fof(fact_712_mult__1,axiom,
! [A_40] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_40) = A_40 ).
fof(fact_713_mult__1,axiom,
! [A_40] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_40) = A_40 ).
fof(fact_714_mult__1__right,axiom,
! [A_39] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_39),one_one_int) = A_39 ).
fof(fact_715_mult__1__right,axiom,
! [A_39] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_39),one_one_nat) = A_39 ).
fof(fact_716_mult_Ocomm__neutral,axiom,
! [A_38] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_38),one_one_int) = A_38 ).
fof(fact_717_mult_Ocomm__neutral,axiom,
! [A_38] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_38),one_one_nat) = A_38 ).
fof(fact_718_comp__fun__commute_Ofold__fun__comm,axiom,
! [X_1,Z_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A_2) ) ) ).
fof(fact_719_comp__fun__commute_Ofold__fun__comm,axiom,
! [X_1,Z_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A_2) ) ) ).
fof(fact_720_comp__fun__commute_Ofold__equality,axiom,
! [Z_1,A_2,Y_1,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1))
=> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2) = Y_1 ) ) ).
fof(fact_721_comp__fun__commute_Ofold__equality,axiom,
! [Z_1,A_2,Y_1,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1))
=> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2) = Y_1 ) ) ).
fof(fact_722_comp__fun__commute_Ofold__equality,axiom,
! [Z_1,A_2,Y_1,F] :
( hBOOL(finite1720675051_state(F))
=> ( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1))
=> hAPP_f718417177_state(finite212984546_state(F,Z_1),A_2) = Y_1 ) ) ).
fof(fact_723_comp__fun__commute_Ofold__insert2,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A_2) ) ) ) ).
fof(fact_724_comp__fun__commute_Ofold__insert2,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A_2) ) ) ) ).
fof(fact_725_comp__fun__commute_Ofold__insert,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2)) ) ) ) ).
fof(fact_726_comp__fun__commute_Ofold__insert,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2)) ) ) ) ).
fof(fact_727_folding__one_Oeq__fold_H,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite1626084323ne_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,X_1),A_2) ) ) ) ).
fof(fact_728_folding__one_Oeq__fold_H,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,X_1),A_2) ) ) ) ).
fof(fact_729_folding__one_Oeq__fold_H,axiom,
! [X_1,A_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_f718417177_state(finite212984546_state(F,X_1),A_2) ) ) ) ).
fof(fact_730_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_1,A_2,F,F_1] :
( hBOOL(finite1432773856em_int(F,F_1))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,A_1),A_2) ) ) ).
fof(fact_731_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_1,A_2,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,A_1),A_2) ) ) ).
fof(fact_732_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_1,A_2,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)) = hAPP_f718417177_state(finite212984546_state(F,A_1),A_2) ) ) ).
fof(fact_733_comp__fun__commute_Ofold__graph__fold,axiom,
! [Z_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2))) ) ) ).
fof(fact_734_comp__fun__commute_Ofold__graph__fold,axiom,
! [Z_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2))) ) ) ).
fof(fact_735_comp__fun__commute_Ofold__graph__fold,axiom,
! [Z_1,A_2,F] :
( hBOOL(finite1720675051_state(F))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),hAPP_f718417177_state(finite212984546_state(F,Z_1),A_2))) ) ) ).
fof(fact_736_fold1__eq__fold,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))
=> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(times_times_int,A_1),A_2) ) ) ).
fof(fact_737_fold1__eq__fold,axiom,
! [A_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))
=> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(times_times_nat,A_1),A_2) ) ) ).
fof(fact_738_comp__fun__commute_Ofold__rec,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite1973466193nt_int(F))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ) ) ).
fof(fact_739_comp__fun__commute_Ofold__rec,axiom,
! [Z_1,X_1,A_2,F] :
( hBOOL(finite2130160977at_nat(F))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ) ) ).
fof(fact_740_less__1__mult,axiom,
! [N_3,M_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),N_3))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_8),N_3))) ) ) ).
fof(fact_741_less__1__mult,axiom,
! [N_3,M_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),M_8))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_8),N_3))) ) ) ).
fof(fact_742_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_37] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_37) = A_37 ).
fof(fact_743_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_37] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_37) = A_37 ).
fof(fact_744_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_36] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_36),one_one_int) = A_36 ).
fof(fact_745_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_36] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_36),one_one_nat) = A_36 ).
fof(fact_746_card_Oremove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ) ).
fof(fact_747_card_Oremove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ) ).
fof(fact_748_card_Oremove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ) ).
fof(fact_749_card_Oinsert__remove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ).
fof(fact_750_card_Oinsert__remove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ).
fof(fact_751_card_Oinsert__remove,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ).
fof(fact_752_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_5,Y_4,Z_4] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_4),Z_4)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),Y_4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),Z_4)) ).
fof(fact_753_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_5,Y_4,Z_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_4),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),Y_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),Z_4)) ).
fof(fact_754_crossproduct__noteq,axiom,
! [Ca,D_1,A_1,B_2] :
( ( A_1 != B_2
& Ca != D_1 )
<=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),D_1)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),D_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Ca)) ) ).
fof(fact_755_crossproduct__noteq,axiom,
! [Ca,D_1,A_1,B_2] :
( ( A_1 != B_2
& Ca != D_1 )
<=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_2),D_1)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_1),D_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_2),Ca)) ) ).
fof(fact_756_comm__semiring__class_Odistrib,axiom,
! [A_35,B_28,C_24] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_35),B_28)),C_24) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_35),C_24)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_28),C_24)) ).
fof(fact_757_comm__semiring__class_Odistrib,axiom,
! [A_35,B_28,C_24] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_35),B_28)),C_24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_35),C_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_28),C_24)) ).
fof(fact_758_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_34,B_27,C_23] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_34),B_27)),C_23) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_34),C_23)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_27),C_23)) ).
fof(fact_759_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_34,B_27,C_23] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_34),B_27)),C_23) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_34),C_23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_27),C_23)) ).
fof(fact_760_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_33,M_7,B_26] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_33),M_7)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_26),M_7)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_33),B_26)),M_7) ).
fof(fact_761_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_33,M_7,B_26] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_33),M_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_26),M_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_33),B_26)),M_7) ).
fof(fact_762_combine__common__factor,axiom,
! [A_32,E_1,B_25,C_22] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_32),E_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_25),E_1)),C_22)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_32),B_25)),E_1)),C_22) ).
fof(fact_763_combine__common__factor,axiom,
! [A_32,E_1,B_25,C_22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_32),E_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_25),E_1)),C_22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_32),B_25)),E_1)),C_22) ).
fof(fact_764_crossproduct__eq,axiom,
! [W,Y_1,X_1,Z_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Y_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_1))
<=> ( W = X_1
| Y_1 = Z_1 ) ) ).
fof(fact_765_crossproduct__eq,axiom,
! [W,Y_1,X_1,Z_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W),Y_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W),Z_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Y_1))
<=> ( W = X_1
| Y_1 = Z_1 ) ) ).
fof(fact_766_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_31,C_21] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_31),C_21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_21),A_31) ).
fof(fact_767_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_31,C_21] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_31),C_21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_21),A_31) ).
fof(fact_768_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_30,C_20,D_9] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_20),D_9)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_20),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),D_9)) ).
fof(fact_769_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_30,C_20,D_9] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_20),D_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),D_9)) ).
fof(fact_770_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_29,C_19,D_8] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_19),D_8)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),C_19)),D_8) ).
fof(fact_771_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_29,C_19,D_8] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_19),D_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),C_19)),D_8) ).
fof(fact_772_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_28,B_24,C_18] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),B_24)),C_18) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_24),C_18)) ).
fof(fact_773_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_28,B_24,C_18] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),B_24)),C_18) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_24),C_18)) ).
fof(fact_774_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_27,B_23,C_17] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_27),B_23)),C_17) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_27),C_17)),B_23) ).
fof(fact_775_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_27,B_23,C_17] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),B_23)),C_17) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),C_17)),B_23) ).
fof(fact_776_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_26,B_22,C_16,D_7] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),B_22)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_16),D_7)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),C_16)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_22),D_7)) ).
fof(fact_777_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_26,B_22,C_16,D_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),B_22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_16),D_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_22),D_7)) ).
fof(fact_778_add__right__imp__eq,axiom,
! [B_21,A_25,C_15] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_21),A_25) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_15),A_25)
=> B_21 = C_15 ) ).
fof(fact_779_add__right__imp__eq,axiom,
! [B_21,A_25,C_15] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_21),A_25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_15),A_25)
=> B_21 = C_15 ) ).
fof(fact_780_add__imp__eq,axiom,
! [A_24,B_20,C_14] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_24),B_20) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_24),C_14)
=> B_20 = C_14 ) ).
fof(fact_781_add__imp__eq,axiom,
! [A_24,B_20,C_14] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_24),B_20) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_24),C_14)
=> B_20 = C_14 ) ).
fof(fact_782_add__left__imp__eq,axiom,
! [A_23,B_19,C_13] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_23),B_19) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_23),C_13)
=> B_19 = C_13 ) ).
fof(fact_783_add__left__imp__eq,axiom,
! [A_23,B_19,C_13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_23),B_19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_23),C_13)
=> B_19 = C_13 ) ).
fof(fact_784_add__right__cancel,axiom,
! [B_2,A_1,Ca] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),A_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1)
<=> B_2 = Ca ) ).
fof(fact_785_add__right__cancel,axiom,
! [B_2,A_1,Ca] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),A_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1)
<=> B_2 = Ca ) ).
fof(fact_786_add__left__cancel,axiom,
! [A_1,B_2,Ca] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca)
<=> B_2 = Ca ) ).
fof(fact_787_add__left__cancel,axiom,
! [A_1,B_2,Ca] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),B_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca)
<=> B_2 = Ca ) ).
fof(fact_788_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_22,B_18,C_12] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_22),B_18)),C_12) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_22),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_18),C_12)) ).
fof(fact_789_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_22,B_18,C_12] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_22),B_18)),C_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_18),C_12)) ).
fof(fact_790_nat__add__right__cancel,axiom,
! [M,K,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K)
<=> M = N ) ).
fof(fact_791_nat__add__left__cancel,axiom,
! [K,M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N)
<=> M = N ) ).
fof(fact_792_nat__add__assoc,axiom,
! [M_1,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)) ).
fof(fact_793_nat__add__left__commute,axiom,
! [X,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)) ).
fof(fact_794_nat__add__commute,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1) ).
fof(fact_795_add__le__cancel__right,axiom,
! [A_1,Ca,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),Ca)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)) ) ).
fof(fact_796_add__le__cancel__right,axiom,
! [A_1,Ca,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),Ca)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)) ) ).
fof(fact_797_add__le__cancel__left,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),B_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)) ) ).
fof(fact_798_add__le__cancel__left,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),B_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)) ) ).
fof(fact_799_add__right__mono,axiom,
! [C_11,A_21,B_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),B_17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_21),C_11)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_17),C_11))) ) ).
fof(fact_800_add__right__mono,axiom,
! [C_11,A_21,B_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_17))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_21),C_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_17),C_11))) ) ).
fof(fact_801_add__left__mono,axiom,
! [C_10,A_20,B_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_20),B_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_10),A_20)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_10),B_16))) ) ).
fof(fact_802_add__left__mono,axiom,
! [C_10,A_20,B_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_20)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_16))) ) ).
fof(fact_803_add__mono,axiom,
! [C_9,D_6,A_19,B_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_15))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_9),D_6))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_19),C_9)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_15),D_6))) ) ) ).
fof(fact_804_add__mono,axiom,
! [C_9,D_6,A_19,B_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_9),D_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_6))) ) ) ).
fof(fact_805_add__le__imp__le__right,axiom,
! [A_18,C_8,B_14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_18),C_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_8)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_18),B_14)) ) ).
fof(fact_806_add__le__imp__le__right,axiom,
! [A_18,C_8,B_14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_8)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_18),B_14)) ) ).
fof(fact_807_add__le__imp__le__left,axiom,
! [C_7,A_17,B_13] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),A_17)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),B_13)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_17),B_13)) ) ).
fof(fact_808_add__le__imp__le__left,axiom,
! [C_7,A_17,B_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_17)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_13)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_13)) ) ).
fof(fact_809_add__less__imp__less__left,axiom,
! [C_6,A_16,B_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_16)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_12)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_16),B_12)) ) ).
fof(fact_810_add__less__imp__less__left,axiom,
! [C_6,A_16,B_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_12)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_16),B_12)) ) ).
fof(fact_811_add__less__imp__less__right,axiom,
! [A_15,C_5,B_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_15),C_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),C_5)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_15),B_11)) ) ).
fof(fact_812_add__less__imp__less__right,axiom,
! [A_15,C_5,B_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_15),C_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_5)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_15),B_11)) ) ).
fof(fact_813_add__strict__mono,axiom,
! [C_4,D_5,A_14,B_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_14),B_10))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),D_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_14),C_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_10),D_5))) ) ) ).
fof(fact_814_add__strict__mono,axiom,
! [C_4,D_5,A_14,B_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_14),B_10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_4),D_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_10),D_5))) ) ) ).
fof(fact_815_add__strict__left__mono,axiom,
! [C_3,A_13,B_9] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_13),B_9))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_3),A_13)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_3),B_9))) ) ).
fof(fact_816_add__strict__left__mono,axiom,
! [C_3,A_13,B_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_13),B_9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_3),A_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_3),B_9))) ) ).
fof(fact_817_add__strict__right__mono,axiom,
! [C_2,A_12,B_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_12),B_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),C_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_8),C_2))) ) ).
fof(fact_818_add__strict__right__mono,axiom,
! [C_2,A_12,B_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_12),B_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),C_2))) ) ).
fof(fact_819_add__less__cancel__left,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),B_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2)) ) ).
fof(fact_820_add__less__cancel__left,axiom,
! [Ca,A_1,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),B_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) ) ).
fof(fact_821_add__less__cancel__right,axiom,
! [A_1,Ca,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),Ca)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2)) ) ).
fof(fact_822_add__less__cancel__right,axiom,
! [A_1,Ca,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),Ca)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) ) ).
fof(fact_823_add__diff__cancel,axiom,
! [A_11,B_7] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_7)),B_7) = A_11 ).
fof(fact_824_diff__add__cancel,axiom,
! [A_10,B_6] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_10),B_6)),B_6) = A_10 ).
fof(fact_825_add__lessD1,axiom,
! [I_1,J,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) ) ).
fof(fact_826_less__add__eq__less,axiom,
! [M_1,N_1,K_1,L_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ) ).
fof(fact_827_add__less__mono,axiom,
! [K_1,L_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1))) ) ) ).
fof(fact_828_add__less__mono1,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) ) ).
fof(fact_829_trans__less__add2,axiom,
! [M_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))) ) ).
fof(fact_830_trans__less__add1,axiom,
! [M_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))) ) ).
fof(fact_831_nat__add__left__cancel__less,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_832_not__add__less2,axiom,
! [J,I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),I_1)) ).
fof(fact_833_not__add__less1,axiom,
! [I_1,J] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),I_1)) ).
fof(fact_834_termination__basic__simps_I2_J,axiom,
! [Y,X,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_835_termination__basic__simps_I1_J,axiom,
! [Z,X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_836_le__add2,axiom,
! [N_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) ).
fof(fact_837_le__add1,axiom,
! [N_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1))) ).
fof(fact_838_le__iff__add,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
<=> ? [K_2] : N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2) ) ).
fof(fact_839_nat__add__left__cancel__le,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_840_trans__le__add1,axiom,
! [M_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))) ) ).
fof(fact_841_trans__le__add2,axiom,
! [M_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))) ) ).
fof(fact_842_add__le__mono1,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) ) ).
fof(fact_843_add__le__mono,axiom,
! [K_1,L_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1))) ) ) ).
fof(fact_844_add__leD2,axiom,
! [M_1,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ).
fof(fact_845_add__leD1,axiom,
! [M_1,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_846_add__leE,axiom,
! [M_1,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ) ).
fof(fact_847_termination__basic__simps_I3_J,axiom,
! [Z,X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_848_termination__basic__simps_I4_J,axiom,
! [Y,X,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_849_diff__cancel2,axiom,
! [M_1,K_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) ).
fof(fact_850_diff__cancel,axiom,
! [K_1,M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) ).
fof(fact_851_diff__diff__left,axiom,
! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1)) ).
fof(fact_852_diff__add__inverse,axiom,
! [N_1,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),N_1) = M_1 ).
fof(fact_853_diff__add__inverse2,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),N_1) = M_1 ).
fof(fact_854_add__mult__distrib2,axiom,
! [K_1,M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)) ).
fof(fact_855_add__mult__distrib,axiom,
! [M_1,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1)) ).
fof(fact_856_less__add__one,axiom,
! [A_9] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_9),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),one_one_int))) ).
fof(fact_857_less__add__one,axiom,
! [A_9] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),one_one_nat))) ).
fof(fact_858_eq__add__iff2,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)
<=> Ca = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1) ) ).
fof(fact_859_eq__add__iff1,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)
<=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca) = D_1 ) ).
fof(fact_860_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_8,M_6] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_8),M_6)),M_6) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_8),one_one_int)),M_6) ).
fof(fact_861_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_8,M_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_8),M_6)),M_6) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),one_one_nat)),M_6) ).
fof(fact_862_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_5,A_7] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_7),M_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),one_one_int)),M_5) ).
fof(fact_863_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_5,A_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_7),M_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),one_one_nat)),M_5) ).
fof(fact_864_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_4] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_4),M_4) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_4) ).
fof(fact_865_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),M_4) ).
fof(fact_866_comp__fun__idem__insert,axiom,
hBOOL(finite58652534t_bool(insert_int)) ).
fof(fact_867_comp__fun__idem__insert,axiom,
hBOOL(finite1956789438t_bool(insert_nat)) ).
fof(fact_868_comp__fun__idem__insert,axiom,
hBOOL(finite2036162504e_bool(insert1744391420_state)) ).
fof(fact_869_add__less__le__mono,axiom,
! [C_1,D_4,A_6,B_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_6),B_5))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_1),D_4))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_5),D_4))) ) ) ).
fof(fact_870_add__less__le__mono,axiom,
! [C_1,D_4,A_6,B_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_1),D_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_5),D_4))) ) ) ).
fof(fact_871_add__le__less__mono,axiom,
! [C,D_3,A_5,B_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),B_4))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),D_3))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_5),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_4),D_3))) ) ) ).
fof(fact_872_add__le__less__mono,axiom,
! [C,D_3,A_5,B_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),B_4))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C),D_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),D_3))) ) ) ).
fof(fact_873_le__add__iff2,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1))) ) ).
fof(fact_874_le__add__iff1,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca)),D_1)) ) ).
fof(fact_875_less__add__iff2,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ca),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1))) ) ).
fof(fact_876_less__add__iff1,axiom,
! [A_1,E,Ca,B_2,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca)),D_1)) ) ).
fof(fact_877_less__diff__conv,axiom,
! [I_2,J_2,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_2)) ) ).
fof(fact_878_add__diff__inverse,axiom,
! [M_1,N_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1 ) ).
fof(fact_879_diff__add__assoc2,axiom,
! [I_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) ) ).
fof(fact_880_add__diff__assoc2,axiom,
! [I_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) ) ).
fof(fact_881_diff__add__assoc,axiom,
! [I_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) ) ).
fof(fact_882_le__imp__diff__is__add,axiom,
! [K,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2) = K
<=> J_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2) ) ) ).
fof(fact_883_le__add__diff__inverse2,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1) = M_1 ) ).
fof(fact_884_le__diff__conv2,axiom,
! [I_2,K,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_2)) ) ) ).
fof(fact_885_add__diff__assoc,axiom,
! [I_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) ) ).
fof(fact_886_le__add__diff__inverse,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1 ) ).
fof(fact_887_le__add__diff,axiom,
! [M_1,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),K_1))) ) ).
fof(fact_888_le__diff__conv,axiom,
! [J_2,K,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K)),I_2))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K))) ) ).
fof(fact_889_diff__diff__right,axiom,
! [I_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J) ) ).
fof(fact_890_linorder__neqE__linordered__idom,axiom,
! [X_4,Y_3] :
( X_4 != Y_3
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_4),Y_3))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_4)) ) ) ).
fof(fact_891_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_4,B_3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_4),B_3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_3),A_4) ).
fof(fact_892_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_4,B_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_4),B_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_3),A_4) ).
fof(fact_893_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx_6,Rx_6,Ry_4] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),Ry_4)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),Ry_4)) ).
fof(fact_894_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx_6,Rx_6,Ry_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),Ry_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),Ry_4)) ).
fof(fact_895_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_5,Rx_5,Ry_3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_5),Ry_3)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),Rx_5)),Ry_3) ).
fof(fact_896_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_5,Rx_5,Ry_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_5),Ry_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),Rx_5)),Ry_3) ).
fof(fact_897_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_4,Ly_4,Rx_4] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),Ly_4)),Rx_4) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_4),Rx_4)) ).
fof(fact_898_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_4,Ly_4,Rx_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),Ly_4)),Rx_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_4),Rx_4)) ).
fof(fact_899_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_3,Rx_3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Ly_3)),Rx_3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Rx_3)),Ly_3) ).
fof(fact_900_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_3,Rx_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Ly_3)),Rx_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Rx_3)),Ly_3) ).
fof(fact_901_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_2,Ly_2,Rx_2,Ry_2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),Ly_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2))) ).
fof(fact_902_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_2,Ly_2,Rx_2,Ry_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),Ly_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2))) ).
fof(fact_903_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_1,Ly_1,Rx_1,Ry_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),Ry_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),Ry_1)) ).
fof(fact_904_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_1,Ly_1,Rx_1,Ry_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),Ry_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),Ry_1)) ).
fof(fact_905_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx,Ly,Rx,Ry] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Ly)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx),Ry)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Rx)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly),Ry)) ).
fof(fact_906_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx,Ly,Rx,Ry] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Ly)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx),Ry)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Rx)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly),Ry)) ).
fof(fact_907_card_Oinsert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,A_2)) ) ) ).
fof(fact_908_card_Oinsert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,A_2)) ) ) ).
fof(fact_909_card_Oinsert,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,A_2)) ) ) ).
fof(fact_910_nat__less__add__iff1,axiom,
! [U_1,M,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M)),N)) ) ) ).
fof(fact_911_nat__less__add__iff2,axiom,
! [U_1,M,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N))) ) ) ).
fof(fact_912_nat__le__add__iff1,axiom,
! [U_1,M,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M)),N)) ) ) ).
fof(fact_913_nat__diff__add__eq1,axiom,
! [U_2,M_1,N_1,J,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U_2)),M_1)),N_1) ) ).
fof(fact_914_nat__eq__add__iff1,axiom,
! [U_1,M,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)
<=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M) = N ) ) ).
fof(fact_915_left__add__mult__distrib,axiom,
! [I_1,U_2,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),U_2)),K_1) ).
fof(fact_916_nat__eq__add__iff2,axiom,
! [U_1,M,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)
<=> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N) ) ) ).
fof(fact_917_nat__diff__add__eq2,axiom,
! [U_2,M_1,N_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U_2)),N_1)) ) ).
fof(fact_918_nat__le__add__iff2,axiom,
! [U_1,M,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N))) ) ) ).
fof(fact_919_mono__nat__linear__lb,axiom,
! [M,K,F] :
( ! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))) ) ).
fof(fact_920_convex__bound__lt,axiom,
! [V_1,U,Y_2,X_3,A_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_3),A_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),A_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_1))
=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U),V_1) = one_one_int
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U),X_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_1),Y_2))),A_3)) ) ) ) ) ) ).
fof(fact_921_card__Suc__Diff1,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2))
=> hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,A_2) ) ) ).
fof(fact_922_card__Suc__Diff1,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
=> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,A_2) ) ) ).
fof(fact_923_card__Suc__Diff1,axiom,
! [X_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2))
=> hAPP_nat_nat(suc,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) = hAPP_f1676271015ol_nat(finite1401757860_state,A_2) ) ) ).
fof(fact_924_less__zeroE,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_925_le0,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).
fof(fact_926_zero__less__Suc,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1))) ).
fof(fact_927_Suc__mono,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_928_lessI,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1))) ).
fof(fact_929_add__is__1,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N = zero_zero_nat )
| ( M = zero_zero_nat
& N = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_930_one__is__add,axiom,
! [M,N] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)
<=> ( ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N = zero_zero_nat )
| ( M = zero_zero_nat
& N = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_931_nat__mult__eq__cancel__disj,axiom,
! [K,M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)
<=> ( K = zero_zero_nat
| M = N ) ) ).
fof(fact_932_not__less__eq,axiom,
! [M,N] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) ) ).
fof(fact_933_less__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| M = N ) ) ).
fof(fact_934_Suc__less__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_935_not__less__less__Suc__eq,axiom,
! [N,M] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M)))
<=> N = M ) ) ).
fof(fact_936_less__antisym,axiom,
! [N_1,M_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1)))
=> M_1 = N_1 ) ) ).
fof(fact_937_less__SucI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_938_Suc__lessI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> ( hAPP_nat_nat(suc,M_1) != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1)) ) ) ).
fof(fact_939_less__trans__Suc,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1)) ) ) ).
fof(fact_940_less__SucE,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> M_1 = N_1 ) ) ).
fof(fact_941_Suc__lessD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_942_Suc__less__SucD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_943_add__Suc__right,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) ).
fof(fact_944_add__Suc,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) ).
fof(fact_945_add__Suc__shift,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1)) ).
fof(fact_946_Suc__leD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_947_le__SucE,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> M_1 = hAPP_nat_nat(suc,N_1) ) ) ).
fof(fact_948_le__SucI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_949_Suc__le__mono,axiom,
! [N,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),hAPP_nat_nat(suc,M)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ).
fof(fact_950_le__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
| M = hAPP_nat_nat(suc,N) ) ) ).
fof(fact_951_not__less__eq__eq,axiom,
! [M,N] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)) ) ).
fof(fact_952_Suc__n__not__le__n,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)) ).
fof(fact_953_diff__Suc__Suc,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) ).
fof(fact_954_Suc__diff__diff,axiom,
! [M_1,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_1) ).
fof(fact_955_Suc__mult__cancel1,axiom,
! [K,M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N)
<=> M = N ) ).
fof(fact_956_not__less0,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_957_neq0__conv,axiom,
! [N] :
( N != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ).
fof(fact_958_less__nat__zero__code,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_959_gr__implies__not0,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> N_1 != zero_zero_nat ) ).
fof(fact_960_gr0I,axiom,
! [N_1] :
( N_1 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ).
fof(fact_961_plus__nat_Oadd__0,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1 ).
fof(fact_962_Nat_Oadd__0__right,axiom,
! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1 ).
fof(fact_963_add__is__0,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = zero_zero_nat
<=> ( M = zero_zero_nat
& N = zero_zero_nat ) ) ).
fof(fact_964_add__eq__self__zero,axiom,
! [M_1,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = M_1
=> N_1 = zero_zero_nat ) ).
fof(fact_965_le__0__eq,axiom,
! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat))
<=> N = zero_zero_nat ) ).
fof(fact_966_less__eq__nat_Osimps_I1_J,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).
fof(fact_967_diff__0__eq__0,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_1) = zero_zero_nat ).
fof(fact_968_minus__nat_Odiff__0,axiom,
! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1 ).
fof(fact_969_diff__self__eq__0,axiom,
! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat ).
fof(fact_970_diffs0__imp__equal,axiom,
! [M_1,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1) = zero_zero_nat
=> M_1 = N_1 ) ) ).
fof(fact_971_mult__cancel2,axiom,
! [M,K,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K)
<=> ( M = N
| K = zero_zero_nat ) ) ).
fof(fact_972_mult__cancel1,axiom,
! [K,M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)
<=> ( M = N
| K = zero_zero_nat ) ) ).
fof(fact_973_mult__is__0,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = zero_zero_nat
<=> ( M = zero_zero_nat
| N = zero_zero_nat ) ) ).
fof(fact_974_mult__0__right,axiom,
! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat ).
fof(fact_975_mult__0,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N_1) = zero_zero_nat ).
fof(fact_976_mult__eq__1__iff,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N = hAPP_nat_nat(suc,zero_zero_nat) ) ) ).
fof(fact_977_Suc__inject,axiom,
! [X,Y] :
( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
=> X = Y ) ).
fof(fact_978_Suc__neq__Zero,axiom,
! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat ).
fof(fact_979_Zero__neq__Suc,axiom,
! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1) ).
fof(fact_980_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
<=> Nat_4 = Nat_3 ) ).
fof(fact_981_Suc__n__not__n,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) != N_1 ).
fof(fact_982_nat_Osimps_I3_J,axiom,
! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat ).
fof(fact_983_Suc__not__Zero,axiom,
! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat ).
fof(fact_984_n__not__Suc__n,axiom,
! [N_1] : N_1 != hAPP_nat_nat(suc,N_1) ).
fof(fact_985_nat_Osimps_I2_J,axiom,
! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1) ).
fof(fact_986_Zero__not__Suc,axiom,
! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1) ).
fof(fact_987_gr0__conv__Suc,axiom,
! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
<=> ? [M_2] : N = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_988_less__Suc0,axiom,
! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,zero_zero_nat)))
<=> N = zero_zero_nat ) ).
fof(fact_989_less__Suc__eq__0__disj,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
<=> ( M = zero_zero_nat
| ? [J_1] :
( M = hAPP_nat_nat(suc,J_1)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N)) ) ) ) ).
fof(fact_990_one__le__mult__iff,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ) ) ).
fof(fact_991_one__less__mult,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) ) ) ).
fof(fact_992_n__less__n__mult__m,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1))) ) ) ).
fof(fact_993_n__less__m__mult__n,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) ) ) ).
fof(fact_994_Suc__pred,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat))) = N_1 ) ).
fof(fact_995_diff__Suc__less,axiom,
! [I_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,I_1))),N_1)) ) ).
fof(fact_996_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).
fof(fact_997_Suc__diff__1,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)) = N_1 ) ).
fof(fact_998_less__add__Suc1,axiom,
! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),M_1)))) ).
fof(fact_999_less__add__Suc2,axiom,
! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I_1)))) ).
fof(fact_1000_less__iff__Suc__add,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
<=> ? [K_2] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)) ) ).
fof(fact_1001_Suc__le__lessD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_1002_le__less__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M)))
<=> N = M ) ) ).
fof(fact_1003_Suc__leI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) ) ).
fof(fact_1004_le__imp__less__Suc,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_1005_Suc__le__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_1006_less__Suc__eq__le,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_1007_less__eq__Suc__le,axiom,
! [N,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)) ) ).
fof(fact_1008_diff__less__Suc,axiom,
! [M_1,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),hAPP_nat_nat(suc,M_1))) ).
fof(fact_1009_Suc__mult__less__cancel1,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_1010_mult__Suc,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) ).
fof(fact_1011_mult__Suc__right,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) ).
fof(fact_1012_Suc__diff__le,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) ) ).
fof(fact_1013_Suc__mult__le__cancel1,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_1014_diff__Suc__1,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_1)),one_one_nat) = N_1 ).
fof(fact_1015_add__gr__0,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ) ).
fof(fact_1016_zero__less__diff,axiom,
! [N,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_1017_diff__less,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1)) ) ) ).
fof(fact_1018_mult__less__mono2,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))) ) ) ).
fof(fact_1019_mult__less__mono1,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))) ) ) ).
fof(fact_1020_mult__less__cancel2,axiom,
! [M,K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ).
fof(fact_1021_mult__less__cancel1,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ).
fof(fact_1022_nat__0__less__mult__iff,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ) ).
fof(fact_1023_nat__mult__less__cancel1,axiom,
! [M,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ) ).
fof(fact_1024_nat__mult__eq__cancel1,axiom,
! [M,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)
<=> M = N ) ) ).
fof(fact_1025_diff__add__0,axiom,
! [N_1,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)) = zero_zero_nat ).
fof(fact_1026_diff__is__0__eq_H,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat ) ).
fof(fact_1027_diff__is__0__eq,axiom,
! [M,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N) = zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_1028_mult__eq__self__implies__10,axiom,
! [M_1,N_1] :
( M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)
=> ( N_1 = one_one_nat
| M_1 = zero_zero_nat ) ) ).
fof(fact_1029_diff__Suc__diff__eq1,axiom,
! [M_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(suc,J)) ) ).
fof(fact_1030_diff__Suc__diff__eq2,axiom,
! [M_1,K_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)) ) ).
fof(fact_1031_nat__diff__split,axiom,
! [Pa,A_1,B_2] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),B_2)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2))
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) )
& ! [D_2] :
( A_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),D_2)
=> hBOOL(hAPP_nat_bool(Pa,D_2)) ) ) ) ).
fof(fact_1032_nat__diff__split__asm,axiom,
! [Pa,A_1,B_2] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),B_2)))
<=> ~ ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2))
& ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) )
| ? [D_2] :
( A_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),D_2)
& ~ hBOOL(hAPP_nat_bool(Pa,D_2)) ) ) ) ).
fof(fact_1033_mult__le__cancel2,axiom,
! [M,K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ) ).
fof(fact_1034_mult__le__cancel1,axiom,
! [K,M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ) ).
fof(fact_1035_nat__mult__le__cancel1,axiom,
! [M,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ) ).
fof(fact_1036_ex__least__nat__less,axiom,
! [N,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,N))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),N))
& ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2))
=> ~ hBOOL(hAPP_nat_bool(Pa,I)) )
& hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat))) ) ) ) ).
fof(fact_1037_mult__eq__if,axiom,
! [N_1,M_1] :
( ( M_1 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = zero_zero_nat )
& ( M_1 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1)) ) ) ).
fof(fact_1038_add__eq__if,axiom,
! [N_1,M_1] :
( ( M_1 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = N_1 )
& ( M_1 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1)) ) ) ).
fof(fact_1039_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat ).
fof(fact_1040_Suc__eq__plus1__left,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1) ).
fof(fact_1041_Suc__eq__plus1,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat) ).
fof(fact_1042_diff__Suc__eq__diff__pred,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1) ).
fof(fact_1043_Suc__pred_H,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)) ) ).
fof(fact_1044_inc__induct,axiom,
! [Pa,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hBOOL(hAPP_nat_bool(Pa,J_2))
=> ( ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I)))
=> hBOOL(hAPP_nat_bool(Pa,I)) ) )
=> hBOOL(hAPP_nat_bool(Pa,I_2)) ) ) ) ).
fof(fact_1045_ex__least__nat__le,axiom,
! [N,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,N))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))
& ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2))
=> ~ hBOOL(hAPP_nat_bool(Pa,I)) )
& hBOOL(hAPP_nat_bool(Pa,K_2)) ) ) ) ).
fof(fact_1046_less__imp__Suc__add,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> ? [K_2] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)) ) ).
fof(fact_1047_less__imp__add__positive,axiom,
! [I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_2) = J ) ) ).
fof(fact_1048_gr0__implies__Suc,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ? [M_2] : N_1 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_1049_zero__induct__lemma,axiom,
! [I_2,Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N_2] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2)))
=> hBOOL(hAPP_nat_bool(Pa,N_2)) )
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K),I_2))) ) ) ).
fof(fact_1050_Suc__le__D,axiom,
! [N_1,M_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_3))
=> ? [M_2] : M_3 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_1051_lessE,axiom,
! [I_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
=> ( K_1 != hAPP_nat_nat(suc,I_1)
=> ~ ! [J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> K_1 != hAPP_nat_nat(suc,J_1) ) ) ) ).
fof(fact_1052_Suc__lessE,axiom,
! [I_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1))
=> ~ ! [J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> K_1 != hAPP_nat_nat(suc,J_1) ) ) ).
fof(fact_1053_not0__implies__Suc,axiom,
! [N_1] :
( N_1 != zero_zero_nat
=> ? [M_2] : N_1 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_1054_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ) ).
fof(fact_1055_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N_2] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2)))
=> hBOOL(hAPP_nat_bool(Pa,N_2)) )
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).
fof(fact_1056_nat__induct,axiom,
! [N,Pa] :
( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( ! [N_2] :
( hBOOL(hAPP_nat_bool(Pa,N_2))
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) )
=> hBOOL(hAPP_nat_bool(Pa,N)) ) ) ).
fof(fact_1057_com_Osize_I4_J,axiom,
! [Com1_2,Com2_2] : com_size(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_2)),com_size(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1058_com_Osize_I12_J,axiom,
! [Com1_2,Com2_2] : size_size_com(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com1_2)),size_size_com(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1059_com_Osize_I9_J,axiom,
size_size_com(skip) = zero_zero_nat ).
fof(fact_1060_com_Osize_I1_J,axiom,
com_size(skip) = zero_zero_nat ).
fof(fact_1061_com_Osize_I5_J,axiom,
! [Fun_1,Com1,Com2] : com_size(cond(Fun_1,Com1,Com2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1)),com_size(Com2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1062_com_Osimps_I45_J,axiom,
! [Fun,Com1_1,Com2_1,Com1,Com2] : cond(Fun,Com1_1,Com2_1) != semi(Com1,Com2) ).
fof(fact_1063_com_Osimps_I44_J,axiom,
! [Com1,Com2,Fun,Com1_1,Com2_1] : semi(Com1,Com2) != cond(Fun,Com1_1,Com2_1) ).
fof(fact_1064_com_Osimps_I15_J,axiom,
! [Fun,Com1_1,Com2_1] : cond(Fun,Com1_1,Com2_1) != skip ).
fof(fact_1065_com_Osimps_I14_J,axiom,
! [Fun,Com1_1,Com2_1] : skip != cond(Fun,Com1_1,Com2_1) ).
fof(fact_1066_com_Osimps_I4_J,axiom,
! [Fun_1,Com1,Com2,Fun,Com1_1,Com2_1] :
( cond(Fun_1,Com1,Com2) = cond(Fun,Com1_1,Com2_1)
<=> ( Fun_1 = Fun
& Com1 = Com1_1
& Com2 = Com2_1 ) ) ).
fof(fact_1067_com_Osize_I13_J,axiom,
! [Fun_1,Com1,Com2] : size_size_com(cond(Fun_1,Com1,Com2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com1)),size_size_com(Com2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1068_com_Osize_I11_J,axiom,
! [Loc,Fun_1,Com_1] : size_size_com(local(Loc,Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1069_com_Osize_I3_J,axiom,
! [Loc,Fun_1,Com_1] : com_size(local(Loc,Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1070_com_Osimps_I36_J,axiom,
! [Loc,Fun_1,Com_1,Fun,Com1_1,Com2_1] : local(Loc,Fun_1,Com_1) != cond(Fun,Com1_1,Com2_1) ).
fof(fact_1071_com_Osimps_I37_J,axiom,
! [Fun,Com1_1,Com2_1,Loc,Fun_1,Com_1] : cond(Fun,Com1_1,Com2_1) != local(Loc,Fun_1,Com_1) ).
fof(fact_1072_com_Osimps_I2_J,axiom,
! [Loc,Fun_1,Com_1,Loc_1,Fun,Com] :
( ( is_loc(Loc)
& is_loc(Loc_1) )
=> ( local(Loc,Fun_1,Com_1) = local(Loc_1,Fun,Com)
<=> ( Loc = Loc_1
& Fun_1 = Fun
& Com_1 = Com ) ) ) ).
fof(fact_1073_com_Osimps_I10_J,axiom,
! [Loc_1,Fun,Com] : skip != local(Loc_1,Fun,Com) ).
fof(fact_1074_com_Osimps_I11_J,axiom,
! [Loc_1,Fun,Com] : local(Loc_1,Fun,Com) != skip ).
fof(fact_1075_com_Osimps_I35_J,axiom,
! [Com1_1,Com2_1,Loc,Fun_1,Com_1] : semi(Com1_1,Com2_1) != local(Loc,Fun_1,Com_1) ).
fof(fact_1076_com_Osimps_I34_J,axiom,
! [Loc,Fun_1,Com_1,Com1_1,Com2_1] : local(Loc,Fun_1,Com_1) != semi(Com1_1,Com2_1) ).
fof(fact_1077_com_Osize_I6_J,axiom,
! [Fun_1,Com_1] : com_size(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1078_com_Osize_I14_J,axiom,
! [Fun_1,Com_1] : size_size_com(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1079_com_Osimps_I39_J,axiom,
! [Fun,Com,Loc,Fun_1,Com_1] : while(Fun,Com) != local(Loc,Fun_1,Com_1) ).
fof(fact_1080_com_Osimps_I38_J,axiom,
! [Loc,Fun_1,Com_1,Fun,Com] : local(Loc,Fun_1,Com_1) != while(Fun,Com) ).
fof(fact_1081_com_Osimps_I47_J,axiom,
! [Fun,Com,Com1,Com2] : while(Fun,Com) != semi(Com1,Com2) ).
fof(fact_1082_com_Osimps_I46_J,axiom,
! [Com1,Com2,Fun,Com] : semi(Com1,Com2) != while(Fun,Com) ).
fof(fact_1083_com_Osimps_I17_J,axiom,
! [Fun,Com] : while(Fun,Com) != skip ).
fof(fact_1084_com_Osimps_I16_J,axiom,
! [Fun,Com] : skip != while(Fun,Com) ).
fof(fact_1085_com_Osimps_I5_J,axiom,
! [Fun_1,Com_1,Fun,Com] :
( while(Fun_1,Com_1) = while(Fun,Com)
<=> ( Fun_1 = Fun
& Com_1 = Com ) ) ).
fof(fact_1086_com_Osimps_I53_J,axiom,
! [Fun,Com,Fun_1,Com1,Com2] : while(Fun,Com) != cond(Fun_1,Com1,Com2) ).
fof(fact_1087_com_Osimps_I52_J,axiom,
! [Fun_1,Com1,Com2,Fun,Com] : cond(Fun_1,Com1,Com2) != while(Fun,Com) ).
fof(fact_1088_expand__Suc,axiom,
! [V] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,V)))
=> hAPP_int_nat(number_number_of_nat,V) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V)),one_one_nat)) ) ).
fof(fact_1089_min__Suc__Suc,axiom,
! [M_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1)) ).
fof(fact_1090_min__diff,axiom,
! [M_1,I_1,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1)),I_1) ).
fof(fact_1091_min__0L,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N_1) = zero_zero_nat ).
fof(fact_1092_min__0R,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N_1),zero_zero_nat) = zero_zero_nat ).
fof(fact_1093_plus__numeral__code_I9_J,axiom,
! [V,W_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V)),hAPP_int_int(number_number_of_int,W_1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W_1)) ).
fof(fact_1094_times__numeral__code_I5_J,axiom,
! [V,W_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V)),hAPP_int_int(number_number_of_int,W_1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V),W_1)) ).
fof(fact_1095_less__number__of__int__code,axiom,
! [K,L] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,K)),hAPP_int_int(number_number_of_int,L)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) ) ).
fof(fact_1096_less__eq__number__of__int__code,axiom,
! [K,L] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,K)),hAPP_int_int(number_number_of_int,L)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)) ) ).
fof(fact_1097_zmult__1,axiom,
! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z ).
fof(fact_1098_zmult__1__right,axiom,
! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),one_one_int) = Z ).
fof(fact_1099_zle__diff1__eq,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)) ) ).
fof(fact_1100_zle__antisym,axiom,
! [Z,W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z))
=> Z = W_1 ) ) ).
fof(fact_1101_zle__trans,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1)) ) ) ).
fof(fact_1102_zle__linear,axiom,
! [Z,W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z)) ) ).
fof(fact_1103_zle__refl,axiom,
! [W_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),W_1)) ).
fof(fact_1104_zless__linear,axiom,
! [X,Y] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),Y))
| X = Y
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),X)) ) ).
fof(fact_1105_zless__le,axiom,
! [Z_1,W] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W))
& Z_1 != W ) ) ).
fof(fact_1106_zmult__assoc,axiom,
! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3)) ).
fof(fact_1107_zmult__commute,axiom,
! [Z,W_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W_1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z) ).
fof(fact_1108_zdiff__zmult__distrib2,axiom,
! [W_1,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z2)) ).
fof(fact_1109_zdiff__zmult__distrib,axiom,
! [Z1,Z2,W_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W_1)) ).
fof(fact_1110_zadd__assoc,axiom,
! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3)) ).
fof(fact_1111_zadd__left__commute,axiom,
! [X,Y,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z)) ).
fof(fact_1112_zadd__commute,axiom,
! [Z,W_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),W_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),Z) ).
fof(fact_1113_zadd__left__mono,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),J))) ) ).
fof(fact_1114_zadd__strict__right__mono,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),K_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K_1))) ) ).
fof(fact_1115_zadd__zless__mono,axiom,
! [Z_3,Z,W_2,W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_3),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_2),Z_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),Z))) ) ) ).
fof(fact_1116_zle__add1__eq__le,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1)) ) ).
fof(fact_1117_add1__zle__eq,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)) ) ).
fof(fact_1118_zless__imp__add1__zle,axiom,
! [W_1,Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z)) ) ).
fof(fact_1119_zless__add1__eq,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),one_one_int)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1))
| W = Z_1 ) ) ).
fof(fact_1120_zadd__zmult__distrib,axiom,
! [Z1,Z2,W_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W_1)) ).
fof(fact_1121_zadd__zmult__distrib2,axiom,
! [W_1,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z2)) ).
fof(fact_1122_int__0__less__1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)) ).
fof(fact_1123_pos__zmult__eq__1__iff,axiom,
! [N,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
=> ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N) = one_one_int
<=> ( M = one_one_int
& N = one_one_int ) ) ) ).
fof(fact_1124_int__one__le__iff__zero__less,axiom,
! [Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)) ) ).
fof(fact_1125_less__bin__lemma,axiom,
! [K,L] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int)) ) ).
fof(fact_1126_zmult__zless__mono2,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),J))) ) ) ).
fof(fact_1127_zadd__0__right,axiom,
! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),zero_zero_int) = Z ).
fof(fact_1128_zadd__0,axiom,
! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z) = Z ).
fof(fact_1129_le__imp__0__less,axiom,
! [Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z))) ) ).
fof(fact_1130_odd__less__0,axiom,
! [Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_1)),Z_1)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)) ) ).
fof(fact_1131_odd__nonzero,axiom,
! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int ).
fof(fact_1132_zdiv__mono2__neg__lemma,axiom,
! [B_1,Q_2,R_2,B,Q_1,R_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),B_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2)) ) ) ) ) ) ) ).
fof(fact_1133_unique__quotient__lemma__neg,axiom,
! [B_1,Q_1,R_1,Q_2,R_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_2),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1)) ) ) ) ) ).
fof(fact_1134_number__of__is__id,axiom,
! [K_1] : hAPP_int_int(number_number_of_int,K_1) = K_1 ).
fof(fact_1135_int__0__neq__1,axiom,
zero_zero_int != one_one_int ).
fof(fact_1136_self__quotient__aux2,axiom,
! [R_2,Q_2,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( A = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A),Q_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),one_one_int)) ) ) ) ).
fof(fact_1137_self__quotient__aux1,axiom,
! [R_2,Q_2,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( A = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A),Q_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),A))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_2)) ) ) ) ).
fof(fact_1138_q__pos__lemma,axiom,
! [B,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)) ) ) ) ).
fof(fact_1139_q__neg__lemma,axiom,
! [B,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)) ) ) ) ).
fof(fact_1140_unique__quotient__lemma,axiom,
! [B_1,Q_1,R_1,Q_2,R_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2)) ) ) ) ) ).
fof(fact_1141_zdiv__mono2__lemma,axiom,
! [B_1,Q_2,R_2,B,Q_1,R_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),B_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1)) ) ) ) ) ) ) ).
fof(fact_1142_int__less__induct,axiom,
! [Pa,I_2,K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K))
=> ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),one_one_int)))
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ) ).
fof(fact_1143_int__le__induct,axiom,
! [Pa,I_2,K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K))
=> ( hBOOL(hAPP_int_bool(Pa,K))
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ) ).
fof(fact_1144_int__gr__induct,axiom,
! [Pa,K,I_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2))
=> ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),one_one_int)))
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ) ).
fof(fact_1145_int__ge__induct,axiom,
! [Pa,K,I_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2))
=> ( hBOOL(hAPP_int_bool(Pa,K))
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ) ).
fof(fact_1146_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [Y,X] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y))) ) ) ).
fof(fact_1147_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) ).
fof(fact_1148_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ).
fof(fact_1149_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [Y,X] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y))) ) ) ).
fof(fact_1150_decr__mult__lemma,axiom,
! [K,Pa,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
=> ( ! [X_2] :
( hBOOL(hAPP_int_bool(Pa,X_2))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
=> ! [X_2] :
( hBOOL(hAPP_int_bool(Pa,X_2))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))) ) ) ) ) ).
fof(fact_1151_incr__mult__lemma,axiom,
! [K,Pa,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
=> ( ! [X_2] :
( hBOOL(hAPP_int_bool(Pa,X_2))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
=> ! [X_2] :
( hBOOL(hAPP_int_bool(Pa,X_2))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))) ) ) ) ) ).
fof(fact_1152_imp__le__cong,axiom,
! [P_1,Pa,X_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(Pa)
<=> hBOOL(P_1) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> hBOOL(Pa) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> hBOOL(P_1) ) ) ) ).
fof(fact_1153_conj__le__cong,axiom,
! [P_1,Pa,X_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(Pa)
<=> hBOOL(P_1) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
& hBOOL(Pa) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
& hBOOL(P_1) ) ) ) ).
fof(fact_1154_int__induct,axiom,
! [I_2,Pa,K] :
( hBOOL(hAPP_int_bool(Pa,K))
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
=> ( ! [I] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
=> ( hBOOL(hAPP_int_bool(Pa,I))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ) ).
fof(fact_1155_plusinfinity,axiom,
! [Pa,P_1,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
=> ( ! [X_2,K_2] :
( hBOOL(hAPP_int_bool(P_1,X_2))
<=> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
=> ( ? [Z_2] :
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),X_2))
=> ( hBOOL(hAPP_int_bool(Pa,X_2))
<=> hBOOL(hAPP_int_bool(P_1,X_2)) ) )
=> ( ? [X1] : hBOOL(hAPP_int_bool(P_1,X1))
=> ? [X1] : hBOOL(hAPP_int_bool(Pa,X1)) ) ) ) ) ).
fof(fact_1156_minusinfinity,axiom,
! [Pa,P1,D_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
=> ( ! [X_2,K_2] :
( hBOOL(hAPP_int_bool(P1,X_2))
<=> hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
=> ( ? [Z_2] :
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_2))
=> ( hBOOL(hAPP_int_bool(Pa,X_2))
<=> hBOOL(hAPP_int_bool(P1,X_2)) ) )
=> ( ? [X1] : hBOOL(hAPP_int_bool(P1,X1))
=> ? [X1] : hBOOL(hAPP_int_bool(Pa,X1)) ) ) ) ) ).
fof(fact_1157_tsub__def,axiom,
! [Y,X] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = zero_zero_int ) ) ).
fof(fact_1158_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [Y,X] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y))) ) ) ).
fof(fact_1159_tsub__eq,axiom,
! [Y,X] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y) ) ).
fof(fact_1160_incr__lemma,axiom,
! [Z,X,D] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D)))) ) ).
fof(fact_1161_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y)) ).
fof(fact_1162_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [Z] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z))) ).
fof(fact_1163_transfer__int__nat__quantifiers_I2_J,axiom,
! [Pa] :
( ? [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
& hBOOL(hAPP_int_bool(Pa,X_2)) )
<=> ? [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) ) ).
fof(fact_1164_transfer__int__nat__quantifiers_I1_J,axiom,
! [Pa] :
( ! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
=> hBOOL(hAPP_int_bool(Pa,X_2)) )
<=> ! [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) ) ).
fof(fact_1165_transfer__int__nat__numerals_I2_J,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ).
fof(fact_1166_transfer__int__nat__numerals_I1_J,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ).
fof(fact_1167_transfer__int__nat__relations_I3_J,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) ) ).
fof(fact_1168_transfer__int__nat__relations_I2_J,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) ) ).
fof(fact_1169_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)) ).
fof(fact_1170_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y)) ).
fof(fact_1171_int__Suc,axiom,
! [M_1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1)) ).
fof(fact_1172_int__Suc0__eq__1,axiom,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int ).
fof(fact_1173_zless__iff__Suc__zadd,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1))
<=> ? [N_2] : Z_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2))) ) ).
fof(fact_1174_zle__int,axiom,
! [M,N] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_1175_zless__int,axiom,
! [M,N] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_1176_zmult__int,axiom,
! [M_1,N_1] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) ).
fof(fact_1177_int__mult,axiom,
! [M_1,N_1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) ).
fof(fact_1178_zadd__int__left,axiom,
! [M_1,N_1,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N_1)),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))),Z) ).
fof(fact_1179_zadd__int,axiom,
! [M_1,N_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) ).
fof(fact_1180_zle__iff__zadd,axiom,
! [W,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1))
<=> ? [N_2] : Z_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),hAPP_nat_int(semiri1621563631at_int,N_2)) ) ).
fof(fact_1181_abs__int__eq,axiom,
! [M_1] : hAPP_int_int(abs_abs_int,hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1) ).
fof(fact_1182_int__1,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int ).
fof(fact_1183_int__eq__0__conv,axiom,
! [N] :
( hAPP_nat_int(semiri1621563631at_int,N) = zero_zero_int
<=> N = zero_zero_nat ) ).
fof(fact_1184_int__0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int ).
fof(fact_1185_int__less__0__conv,axiom,
! [K_1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_1)),zero_zero_int)) ).
fof(fact_1186_zero__zle__int,axiom,
! [N_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_1))) ).
fof(fact_1187_int__le__0__conv,axiom,
! [N] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,N)),zero_zero_int))
<=> N = zero_zero_nat ) ).
fof(fact_1188_zabs__less__one__iff,axiom,
! [Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,Z_1)),one_one_int))
<=> Z_1 = zero_zero_int ) ).
fof(fact_1189_abs__zmult__eq__1,axiom,
! [M_1,N_1] :
( hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1)) = one_one_int
=> hAPP_int_int(abs_abs_int,M_1) = one_one_int ) ).
fof(fact_1190_zdiff__int,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) ) ).
fof(fact_1191_zero__less__int__conv,axiom,
! [N] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ).
fof(fact_1192_zmult__zless__mono2__lemma,axiom,
! [K_1,I_1,J] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),J))) ) ) ).
fof(fact_1193_zdiff__int__split,axiom,
! [Pa,X_1,Y_1] :
( hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_int_bool(Pa,zero_zero_int)) ) ) ) ).
fof(fact_1194_decr__lemma,axiom,
! [X,Z,D] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))),Z)) ) ).
fof(fact_1195_int__val__lemma,axiom,
! [K,F,N] :
( ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),N))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,N)))
=> ? [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N))
& hAPP_nat_int(F,I) = K ) ) ) ) ).
fof(fact_1196_nat0__intermed__int__val,axiom,
! [K,F,N] :
( ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),N))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,N)))
=> ? [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N))
& hAPP_nat_int(F,I) = K ) ) ) ) ).
fof(fact_1197_transfer__int__nat__relations_I1_J,axiom,
! [X_1,Y_1] :
( hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_1)
<=> X_1 = Y_1 ) ).
fof(fact_1198_int__if__cong,axiom,
! [X_1,Y_1,Pa] :
( ( hBOOL(Pa)
=> hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1)) )
& ( ~ hBOOL(Pa)
=> hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1)) ) ) ).
fof(fact_1199_int__int__eq,axiom,
! [M,N] :
( hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,N)
<=> M = N ) ).
%----Helper facts (40)
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP_bool_bool(fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(fNot,P)) ) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_fdisj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
| hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fimplies_1_1_U,axiom,
! [Q,P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
| ~ hBOOL(P)
| hBOOL(Q) ) ).
fof(help_If_1_1_If_000tc__Nat__Onat_T,axiom,
! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X),Y) = X ).
fof(help_If_2_1_If_000tc__Nat__Onat_T,axiom,
! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X),Y) = Y ).
fof(help_If_3_1_If_000tc__Nat__Onat_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__Int__Oint_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Int__Oint_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_int_bool(cOMBK_bool_int(P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U,axiom,
! [P,Q,R] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBB_bool_bool_int(P),Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBB_bool_bool_nat(P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBS_int_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_i68813070l_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_001,axiom,
! [P,Q,R] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H242767318e_bool(cOMBK_988866959_state(P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBB_325909978_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBS_865875691l_bool(P),Q),R) = hAPP_bool_bool(hAPP_H1270401638l_bool(P,R),hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_002,axiom,
! [P,Q,R] : hAPP_H1270401638l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_H216526335e_bool(cOMBC_1967329268e_bool(P),Q),R) = hAPP_H242767318e_bool(hAPP_H216526335e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___003,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBC_538205282l_bool(P),Q),R) = hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(P,R),Q) ).
%----Conjectures (3)
fof(conj_0,hypothesis,
hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_Mirabelle_MGT(c)),bot_bo784226126e_bool))) ).
fof(conj_1,hypothesis,
hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(p,c,q)),bot_bo784226126e_bool))) ).
fof(conj_2,conjecture,
hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(p,c,q)),bot_bo784226126e_bool))) ).
%------------------------------------------------------------------------------